text
stringlengths 6
976k
| token_count
float64 677
677
| cluster_id
int64 1
1
|
|---|---|---|
I dont get linear algebra
I dont get linear algebra
I had a linear algebra course for my 1st year civil engineering curriculum, and I passed with a 3.2 GPA but I only conceptually understood about 10% of what was taught to me.
I don't know what an eigenvalue/eigenvector is, what the hell is a subspace, nullspace, imagespace. What the hell is a linear transformation, what the hell is a determinant of an nxn matrix, what the hell is a matrix.
How the hell was I able to get a decent mark in a subject I know nothing about?
Facepalm.
I found calculus 1 (single variable) way easier to understand than this stuff.
I can't explain the whole linear algebra curriculum in a short post, but it is a fundamental part of mathematics. It sounds like you basically know nothing about the subject but you managed to pass with a decent grade. Good job?
1. Solving systems of linear equations is part of linear algebra, and this is probably the part that is used the most by the most people.
2. Finish calculus and differential equations and then revisit linear algebra. Conceptually it might make more sense then.I dont get linear algebra
Quote by tahayassenIf you want to understand linear algebra intuitively, you'll get better advice by asking for an explanation of one concept at a time rather than by asking for an explanation of the entire subject. When it comes to intuition, people have a wide variety of ways of looking at mathematical concepts. You can get 5 different ways of looking at one simple idea.
The key with linear algebra is mathematical maturity. You need to understand that definitions are just definitions. There's nothing deeper.
An eigenvalue, λ, and eigenvector, x of a matrix A are such that Ax=λx. That's IT. There's absolutely nothing more to it than that. That's all that it means. Why you care, how it's used is a completely different question. But that's all it is.
A matrix is just an array of numbers. That's ALL. Nothing more. That's all there is to it. Nothing deeper, nothing more. An array of numbers. Don't try to pull things out of it that simply aren't there. Yes, you can do cool things with it. Yes, you apply it in weird places. But that's ALL IT IS. An array of numbers.
The one thing I think that's taught poorly is vector spaces. Why they give you an example of an algebraic structure before you understand what an algebraic structure IS, is completely past me.
An algebraic structure is a SET with ONE OR MORE operations defined on it. In a VECTOR SPACE, the set is the set of vectors. The operations are scalar multiplication and vector addition.
An algebraic structure IS math. It's such a confusing, deep subject if you don't really understand what's going on. But when you get it, it's pretty cool. Anything you do in math is in an algebraic structure (most the time, you're dealing with Euclidean space. Euclidean space is the "normal" space with "normal" rules).
A much better example of a structure is what's called a FIELD. (NOT a vector field, when you get to multivariate calculus. This is extremely important) A FIELD is a structure with elements that has two operations, + and * defined over it. It has a list of axioms; closure, 4 additive ones, 4 multiplicative ones, one associative one. An axiom is a DEFINITION.
See, in the real world we don't have wild 2s running around. "2" does NOT exist in nature. You always have 2 something. 2 rocks, 2 buildings, 2 blades of grass, 2 whatever. But "2" does NOT exist. We CREATE "2" to describe the real world. To describe the world, we create these ALGEBRAIC STRUCTURES.
A field IS numbers. When you ask your friend what 2+2 equals, you're working in a FIELD, namely R (the real numbers). Make sense? An algebraic structure IS math. Whatever you do in math is a structure. A vector space is ANOTHER example of a structure. Just one that's studied extensively in linear algebra. Anything you want to know about the operations (EXCEPT WHAT THE OPERATIONS ARE ACTUALLY DOING!), you can derive from the axioms. In a vector space, you can derive ALL you want to know about scalar multiplication or vector addition from the axioms. BUT the one thing you CAN'T derive is WHAT YOU'RE ACTUALLY DOING when you add vectors. YOU must define that.
So long story short, you probably DO understand it. You're just looking for something that's not there. Definitions are just definitionsLinear algebra isn't meaningless at all, when did I ever say anything like that? You're just learning things rigorously, without much if any physical intuition.
Like with eigenvalues/eigenvectors. There really isn't a physical intuition behind it (maybe there is? I just never heard of any). It just is. That doesn't mean that it's "meaningless". It's used to solve differential equations later, which renders them super useful.
I amend my comment to say that without context, an abstract system of rules and definitions such as linear algebra can be hard to hold onto.
Quote by johnqwertyful
Not everything in math has some physical significance.
I know at least one other poster here who would agree with this. I tend to disagree though.
In the case of an eigenvector, its physical significance is that it represents a subspace that is invariant under a linear transformation. The eigenvalue is the scaling factor applied to that invariant subspace. (geometry is physical enough for me )Since you, according to one of your recent posts, are currently studying Algebra 1, you are not yet ready to understand much of Linear Algebra. Give yourself about 2 more years.
Attitude? I was simply expressing my confusion over this newly (I can't stress the word newly enough) learned subject. It is my sole intention to strengthen my intuition with the subject in the same way I am intuitive with calculus and geometry.
I don't hate linear algebra, it not as though I want to attack it with a light saber, I just find it more abstract than any other branch of math I have been exposed to.
Perhaps soil mechanics is your bag
As I am a 1st year undergrad student with no exposure whatsoever to the specialties of civil engineering, drawing such conclusions based on the limited info and limited time of exposure I have had with linear algebra (3 months) is a little too extreme.
Funny,
I thought Linear Algebra was easier to grasp than Calculus. I guess it's because it's hard for me to visualize a mathematical concept (it took me a while to understand what a derivative is from a geometric point of view). With linear algebra you just take a system of linear equations, strip the constants and coefficients from it and viola, you have a matrice! And from there you can apply elementary row operations on it to get a solution, find it's inverse, it's determinant, etc...
To be fair though I learned Linear Algebra independently (which probably made it easier), and I've only gotten the basics (I haven't learned about eigenvalues or linear transformations yet). | 677.169 | 1 |
This book can be strongly recommended not only to students interested in the field, but also to mathematicians collaborating with non-mathematicians in research or hard practice, moreover to engineers, physicists and other natural scientists needing effective methods in scientific computing and wanting to know their underlying theory. The authors present the treated topics in a convincing synthesis of theory and practice, with well-chosen motivating examples, and when appropriate for understanding the principles not shying away from giving occasional proofs, use of basic functional-analytic concepts (like norms) and other analytical tools. They lay emphasis on complexity considerations (as important for efficient applicability) of methods, furthermore on questions of accuracy (via condition numbers) and stability. Many exercises offer the student the opportunity to gain more insight and to aquire a solid working knowledge. For useful algorithms written in MATLAB a web page is offered. To give a rough overview on the scope of the book let us look into the list of contents. Ch. 1: Mathematical review and computer arithmetic. Ch. 2: Numerical solution of nonlinear equations of one variable. Ch. 3: Numerical linear algebra. Ch. 4: Approximation theory. Ch. 5: Eigenvalue-eigenvector computation. Ch. 6: Numerical differentiation and integration. Ch. 7: Initial value problems for ordinary differential equations. Ch. 8: Numerical solution of systems of nonlinear equations. Ch. 9: Optimization. Ch. 10: Boundary-value problems and integral equations.
Reviewer:
Rudolf Gorenflo (Berlin) | 677.169 | 1 |
What Is Mathematics?: An Elementary Approach to Ideas and Methods...more--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.(less)
Paperback, 592 pages
Published
July 18th 1996
by Oxford University Press, USA
(first published January 1st 1967)
Community Reviews
abo...more about mathematics think that it is about arithmetic or calculation - it is easy to get that impression when school mathematics centers mostly around solving uninteresting problems, which often involve a lot of calculation.
This book shows that mathematics is about understanding the properties and behaviour of mathematical objects. What are numbers? Why do they behave the way they do when we carry out operations on them? Why can some shapes be constructed with ruler and compass, but some not?
The book requires patience and time to read. Don't read it if you are in a hurry.(less)
l...more lectures in that course. This book ties it all up with a nice bow. The long chapter on maxima and minima -- went on long, I was ready to put the book down and then it made this brilliant transition to the calculus.
I'm sure the more math you've had, the more you will get out of this book -- some sections may be rough if you haven't had some trig and the calculus and I was a little lost more than once anyway.(less)
font...more fonts are difficult to read, and some of the shorthand is less than modern.
This may have been a good introduction/refresher at some point in time, but there have to be better books out there now. For one, your time would be better spent reading Heath's translation of Euclid. Some day I hope to make time for The Princeton Companion to Mathematics. I'll see how it compares. (less)
would have been nice for upper-level physics! oh well!). I think this will be my default high school graduation present to anyone with an inkling...more would have been nice for upper-level physics! oh well!). I think this will be my default high school graduation present to anyone with an inkling of mathematical talent from now on (rather than the more intimidating Road to Reality, which likely just frightens people).
As they said in Mathematical Review, "A work of extraordinary perfection."(less)
Skimmed through and it is quite useful, very similar to one of Felix Klein's books in terms of style. A little too mathematics for my purposes which is more towards physics, some insights are good nonetheless. | 677.169 | 1 |
If a book or article cannot be found in PVAMU's resources, it can usually be borrowed from another library.
Fill out the Interlibrary Loan form, and please note that it may take several weeks to receive the item.
How to prepare for the TAKS : Texas assessment of knowledge and skills high school math exit exam - QA43 .E64 2004
100 math tips for the SAT and how to master them now - LB2353.57 .G85 2002
Encyclopedia of mathematics education - QA 11 E665 2001
Selected Print Mathematics Journals
Advances in mathematics
American journal of mathematics
Annals of mathematics
Journal for research in mathematics education
Journal of applied mathematics and mechanics
Mathematics teacher
Arithmetic teacher
American Mathematical Society ( - The American Mathematical Society promotes mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.
Centre For Innovation in Mathematics Teaching ( - The centre is a focus for research and curriculum development in Mathematics teaching and learning, with the aim of unifying and enhancing mathematical progress in schools and colleges.
K-6 Math Playground ( - Math Playground is an action packed site for students in grades K to 6. Practice your math skills, play a logic game
Math Forum ( - Online resource for improving math learning, teaching, and communication. This is a great Mathematics Website but the access is not free.
Mathematics Virtual Library ( This collection of Mathematics-related resources is maintained by the Florida State University Department of Mathematics.
Mathematical Association of America ( - The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level.
Metamath proof explorer ( This Website contains more than 5,000 computer-verified formal proofs, definitions, and axioms in logic and set theory. | 677.169 | 1 |
Maple V Release 5.1 - Maple
V is a comprehensive computer system for advanced mathematics. It includes facilities
for interactive algebra, calculus, discrete mathematics, graphics, numerical
computation and many other areas of mathematics. | 677.169 | 1 |
Systematic Mathematics
Systematic Mathematics is a video-based home school math curriculum that explains the system of mathematics. The core of the curriculum is the lesson DVDs, alongside which there are materials that you need to print yourself from the accompanying CD.
Price: about $128-$138 per year
Reviews of Systematic Mathematics
Your situation:
Our son just returned to homeschooling, after one year back in the public school system. The large class size and fast paced introduction of math concepts were overwhelming and he was falling behind. More importantly, he felt frustrated and inadequate as a math student.
Why you liked/didn't like the book:
We chose Systematic Mathematics because it taught the why of doing math, not just rushing through concepts and hoping they would stick. The DVD is good because my son is able to watch Mr. Ziegler do the math problem(s) and is able to stop, or backup if needed. The worksheets are on CD, so you can print as many as needed. I recommend this curriculum to anyone who has a child who is discouraged with math, at any level. Our son has actually begun to say things like, "Math is fun" or "I like doing math". When he says that I know he will remember what he's been taught
Michele Tubbs
Review left February 9, 2012
Time: 1 semester
Your situation: I've been home educating for over 20 years, and currently educating my 6th grader. I've tried various other math curricula, but this is the only one that he seems to be really understanding.
Why you liked/didn't like the book:
Like:
*Covers things systematically--'old school' before all the 'modern' math. I would equate it with the way phonics used to be taught and built upon.
*Taught by a former Public School teacher in the days before modern math, and he wrote this curriculum in frustration over what he saw and didn't like in modern math textbooks.
*Short lessons
*Can be used over and over by more than one student in the family, so is cost effective
*Teacher isn't drab and boring
Dislike:
*Would like to see some of the answers completely worked out in the answer key--just for speed on my part as the teacher checking the work.
*DVD's are pretty basic (not professional), but this doesn't really bother us too much
*Would like to see the worksheets offered already printed out in workbook form--right now you print off the worksheets on the computer as a pdf file.
Any other helpful hints:
This has been great for us so far, and we have used a lot of different math programs through the years. This one fits my students needs great so far!
Sandy
Review left January 11, 2012
Time: 2 years
Your situation:
I had trouble doing math and I was falling behind! I was using AOP SOS Math, Teaching Textbooks, tried using Math Mammoth but I can't say that they worked for me.
Why you liked/didn't like the book:
There is NO textbook required and you can print as many worksheets as you want. Just watch the DVD and print out the worksheet or test. Mr. Ziegler (the teacher) is better at explaining things than many teachers. The price is very good for people with not much money. I now understand math much more than before, not just remembering what to do.
Any other helpful hints:
:)
Matthew Kwan
Review left June 19, 2011
Time: 2 years
My son was dropping further and further behind in math. He was close to 3 years behind. We used Abeka math and Saxon math and although I don't see any problems with those curricula, he was not able to grasp the mathematic principles and complete the work. His math skills (math facts) were fine, he just couldn't understand the processes especially for word problems.
Why you liked/didn't like the book:
After 1 year of intense "catch up" in math we have come to within 1 year of where he should be and with all A's and B's on exams. He really appreciates being able to see someone work the problems and being able to review the processes has really helped him. Mr. Ziegler (the teacher) makes everything easy to understand and teaches the why's and not just the how's to understanding and mastering math.
Any other helpful hints:
Another great thing about this curriculum is that I can use it with all of my children. The worksheets are all on a cd rom and can be printed as many times as you need it to be.
Scot Dyess Review left September 21, 2010
Grade: Algebra Time: 2 years
Your situation:
Algebra (beyond the very basics) was a painful process for my son and I. To this point, he had been a great math student. By the end of Algebra 2 he had given up. We were using Video Text at the time, after having used Key To. I knew I couldn't take the same approach with my younger daughter, and when I read a review for Systematic Mathematics, decided to give it a try.
Why you liked/didn't like the book:
This is a DVD curriculum with cds for printing off worksheets and tests, as needed. In comparison, it's fairly inexpensive. It is truly systematic in approach, never giving the student too much information at once. We were able to go through lessons, start to finish, in about 30 minutes. No tears, no frustration.
The writer is a former public school math teacher who realized new methods weren't getting the job done. This was the answer for our family.
You can purchase individual modules, instead of buying the whole curriculum at once. On a couple of occasions I had questions. Very promptly, I received either an email reply or a personal phone call. | 677.169 | 1 |
KS5 Alevel Maths Standards units: mostly calculus
Maths worksheet activities and lesson plans. core 1 equations and quadratics. Unit C1 Linking the Properties and Forms of Quadratics. Students classify quadratic functions according to the properties of their graphs and their algebraic forms. This is part of the "Mostly Calculus" set of materials fr More…om Standards unit: Improving learning in mathematics. To enable learners to: identify different forms and properties of quadratic functions; connect quadratic functions with their graphs and properties, including intersections with axes, maxima and minima.
This is fantastic. I'm using it an in introduction to quadratic graphs, every ability is catered for with the use of TI-nSpire for the weaker students and pen&paper for the top group. They are all so engaged at making connections. Thank you so much, I was about to create something like this, but nowhere near as good! | 677.169 | 1 |
Designed to be used in a variety of modes of teaching; direct instruction, whole group, small group, cooperative group, independent or discovery learningThese tricks cover a broad range of concepts, from simple variable equations to factored polynomials, all with an engaging twist of magic
Product Information
Subject :
Algebra
Grade Level(s) :
6-12
Usage Ideas :
Designed to be used in a variety of modes of teaching; direct instruction, whole group, small group, cooperative group, independent, or discovery learning. | 677.169 | 1 |
The guiding principles of the Mathematics syllabus direct that Mathematics as taught in Caribbean schools should be:
relevant to the existing and anticipated needs of Caribbean society;
related to the ability and interest of Caribbean students;
aligned to the philosophy of the educational system.
These principles focus attention on the use of Mathematics as a problem solving tool, as well as on some of the functional concepts which help to unify Mathematics as a body of knowledge. The syllabus explains general and unifying concepts that facilitate the study of Mathematics as a coherent rather than as a set of unrelated topics. | 677.169 | 1 |
Return here for REGISTRATION
Algebra 1 online Review is for the student that has already completed an Algebra 1 course in the recent past and needs to review the course before taking Algebra 2 or Geometry.
In this algebra class you will receive prompt replies (daily emails) to any algebra question you have, as well as,
receive a review of solving equations, multiplying and factoring polynomials, graphing lines, finding slopes of lines and creative ideas of solving word problems.
Each Lesson gives several examples and explanation of the math topic. Most have videos or games to use to help you learn the topic better. Each lesson has 1 or 2 assignments for you to complete and submit to me. I grade all assignments and tests the day that they are submitted to the classroom.
I answer email within 24 hours, but often it is in just a few hours.
The topics to be reviewed include solving linear equations, multiplying polynomials, factoring polynomials, money word problems, graphing lines, finding the slope of a line and finding the midpoint and length of a line segment.
You must already know how to add, subtract, multiply and divide integers and know how to use well the Order of Operations. -2+12(8-13) /20 =?
I answer email at least 350 days of the year.
The student must have a valid email address and must be able to easily check his emails and SAVE them in a folder on his computer.
Numbers 6: 24-26 | 677.169 | 1 |
Supporting Mathematics These range from entry level to level three.
The workshop also provides a place where students can go at any time of the college day to seek help and support with their learning in mathematics. They encourage self-learning and provides a supportive environment for students to work, full in the knowledge that help is nearby.
The project's aim is to provide appropriate part-time courses for students and offer easy access to support in order to keep them engaged in learning | 677.169 | 1 |
Hi math lovers, I heard that there are various programs that can help with us studying,like a teacher substitute. Is this really true? Is there a software that can assist me with math? I have never tried one before, but they are probably not hard to use I think. If anyone has such a program, I would really appreciate some more information about it. I'm in Remedial Algebra now, so I've been studying things like finding the sum and product of the quadratic equation and it's not easy at all.
You don't need to ask anyone to solve any sample questions for you; as a matter of fact all you need is Algebra Buster. I've tried many such algebra simulation software but Algebra Buster is way better than most of them. It'll solve any question that you have and it'll even explain each and every step involved in reaching that answer. You can try out as many examples as you would like to, and unlike us human beings, it won't ever say, Oh! I've had enough for the day! ;) I used to have some problems in solving questions on hyperbolas and rational expressions, but this software really helped me get over those.
Even I've been through that phase when I was trying to figure out a solution to certain type of questions pertaining to side-side-side similarity and point-slope. But then I found this piece of software and I felt as if I found a magic wand. In a flash it would solve even the most difficult problems for you. And the fact that it gives a detailed step-by-step explanation makes it even more handy. It's a must buy for every algebra student. | 677.169 | 1 |
Many schools now require calculators. This site is
not the place for a discussion of the problems (financial and otherwise) that this can cause, or
of the "philosophy" on which these policies are often based. If you are interested in
the politically-incorrect side of this issue, visit Mathematically Correct.
(And for an interesting discussion of the value of a broken calculator, try here.)
But if you are wondering which calculator to buy,
the following is my advice.
Scientific, business, etc, calculators
If you are looking for a "scientific"
or "business" or "statistics" calculator, then there are many affordable options
available to you. You can find cheap calculators at office-supply stores, discount department stores,
and electronics stores, among other places. I have only one specific recommendation: make sure
that the calculator has a fraction key; it usually looks something like this:
This is a very
helpful key, and will speed up fraction addition, simplification, and conversion.
Graphing calculators: Texas Instruments
If you are supposed to get a "Texas Instruments
graphing utility", then you would probably want one of the calculators from their line of
TI-84 models. The TI-84 is an update of their TI-83 which incorporates additional capabilities
(increased memory, computer connectivity, default apps, etc) but which is backwards compatible
with the TI-83. That is to say, the TI-84 will allow you to do more, while still remaining largely
keystroke compatible with the TI-83 that your teacher is using.If you are supposed to get a TI-83,
you might want to look at spending a little more to get the TI-84.
ADVERTISEMENT
(Note: There are some slight differences in the
models. For information, try here.)
However, the TI-84 seems to assume that you have
reliable access to a newer computer. Much of the manual is accessible only through the CD that
comes with the calculator, calculator-to-computer connectivity relies on USB ports, and you may
need to download and install at 23-meg Micro$oft program (.NET Framework) to get the computer side
of the calculator to work. You may also need to upgrade your browser, since the TI-84 appears to
require Internet Explorer 6 or newer. So I would recommend the TI-84 (over the TI-83) for the updated
capabilities, but only if you have ready access to an updated computer and a good Internet connection.
(Note: I have heard, from experienced users, that installation and use is not always problematic.
The above warnings reflect my personal experience. As they say, "your mileage may vary.")
Do NOT get a TI-92, nor its update, the Voyage 200,
unless you have verified that your school allows them; many schools are banning them. For some
reason, though the TI-89 has many of the same capabilities that are getting the TI-92 / Voyage
200 banned, the TI-89 is generally allowed. However, it would still be a good idea to check first.
Note that many (most?) instructors, especially at the high-school level, don't know how to use
the TI-86, -89, or -92, or the Voyage 200, so you'll be on your own when it comes to learning how
to use them. And their owners manuals tend to be the size of small textbooks.
If the only specification is that you are to get
"a graphing utility", then the choice is up to you. Many companies produce perfectly
nice calculators, but textbooks and teachers usually push the Texas Instruments TI-83 or -84. If
you're willing and able to read the manual for yourself, then get whatever calculator you like.
Otherwise, stick with Texas Instruments.
If you do get a TI-8X calculator, learn where the
"convert to fraction" menu item is (this varies from model to model; check your manual).
The command looks like this:
This command will convert the last value to its
fractional form, if possible. It's a very handy command. If you have the "Custom" menu
option, you might want to install the "convert to fraction" command on your custom menu,
for convenience sake.
(By the way, if you already have a TI-85, and would
like to have the "TABLE" feature that the TI-82, TI-83, and TI-86 have, use my "Table"
program. The page in the preceding link contains the program as a text file; you'll have to type
the program into your calculator yourself.)
Graphing calculators: Final thoughts....
If you are thinking of getting a Hewlett-Packard
(HP) calculator (graphing or otherwise), see if you can find a friend or a fellow student who will
let you borrow one. In my experience, people either love HPs or they really, really,hate them,
and it would be a shame to spend a couple hundred dollars just to learn that you're one of the
folks who hates 'em. They slice, they dice, they whistle "Dixie", but they might not
be your cup of tea. Take a good look first.
In "real life", any of the scientific
(or business or statistical, etc) calculators will serve most needs. Unless you're going into courses
where graphing calculators are expected, a cheap calculator that has trigonometric keys (the "sin",
"cos", and "tan" keys) should have just about anything you'll need. But graphing
calculators can be nice, even in "real life", for much the same reason that some of us
old-timers liked adding machines with a printout: the screen on a graphing calculator can display
more information and, in particular, can make it easier to find one's mistakes. So, for instance,
I tend to use a graphing calculator to balance my checkbook.
There is one other consideration: If there is no
specification regarding which calculator you should get (or if you are given a list of models from
which to choose), and you are planning on entering a scientific field of study at your college
or university (math, engineering, or physics, for instance, as opposed to Poly-Sci or French Lit),
then you might want to contact the appropriate departments to see if those departments have their
own preferences. Be forewarned: It is entirely possible that you will be required to buy multiple
calculators: one for the math department, another for the physics department, and yet-another for
the engineering department. Calculators are very trendy, but the trend-oids don't often think about
the real-world implications of their policies.
There; now ya know: I'm politically incorrect.
If you have lost the manual to your Texas Instruments
graphing calculator, look into downloading a new copy from the Texas Instruments' site.
The guidebooks are Adobe Acrobat documents, and fairly large ones at that, so you might want to
download the manual one chapter at a time if you have a slow or twitchy connection. | 677.169 | 1 |
In answer to your other questions
>>Anyways, must I learn the analytic geometry if I just want to make simple programs that resemble something of 3d, but maybe not 100% accurate?
No, you can write very simple programs without understanding the maths. But that's all you'll be able to do. If you learn a little more, you'll be able to go much further. And you'll be able to make more sense of the maths on Wikipedia.
>>They don't teach any useful math at school and they aren't any time soon so I don't know where to start learning
Don't forget that it's more important to a teacher that the dull students aren't left behind, than the bright students get ahead. Maybe you can find a teacher who is willing to explain something to you outside of class. Or maybe a parent or relative of yours could help.
At my school there was a maths society where we explored topics outside of the curriculum...
Having a good teacher is probably the best way to learn this sort of stuff, but failing that a good book might be helpful. Check your library for something that's at the right level for you.
>>And I don't what this type of stuff means:
>>sin^2 (x) <<????
Basically, computer programmers need to make sure the computer understands them. Mathematicians need to make sure that other mathematicians understand them. So while programming languages tend to be fairly simple and consistent, mathematical notation is much less so.
Also remember that mathematics until recently was nearly always written by hand, and even today much is written by hand. A notation that's easier to read in slightly messy writing is a winner.
There are many areas of mathematics where there are a few different notations in popular usage. Often say Europe will use one notation and the US will use another.
Anyway, this is one case where "everybody knows" that sin^2(x) means sin(x)*sin(x). Just learn it.
>>$variable = new variabletype();
This is to do with object oriented programming, a big topic that I don't think you should worry about just yet. PHP does not require you to use it. | 677.169 | 1 |
Contents
The Jeff Tech Mathematics Team
The Jeff Tech Mathematics Team is a non-remedial excellence program that operates under an amalgamation of methodologies and learning strategies. One facet of the Jeff Tech Mathematics Team is collaborative seminars in which students work together to mathematically develop, compare, problem-solving strategies, and prepare for the various competitions that we participate in.
New Techniques
The Jeff Tech Mathematics Team teaches you not only "what to learn", but "how to learn". Participants discover how to apply study strategies to course topics and problems as they review content material, questioning techniques, and precise mathematical communication. The key to the program is developing student leaders who are presented as "model students of the subject". Above all else, students will develop critical thinking and problem solving skills.
Mission
The purpose of the Jeff Tech Mathematics Team is to promote the interest of mathematics at Jeff Tech, and to aid math students or anyone with an interest in mathematics, and also to promote interaction among students and faculty. | 677.169 | 1 |
Abstract algebra
Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields.
The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers.
Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra. Because of this, abstract algebra has numerous fruitful connections to all other branches of mathematics.
In universal algebra, all those definitions and facts are collected that apply to all algebraic structures alike. All the above classes of objects, together with the proper notion of homomorphism, form categories, and category theory frequently provides the formalism for translating between and comparing different algebraic structures | 677.169 | 1 |
Lula, GA ACT believe that this allows the student to understand how science works, and understanding the process allows them to more easily see where the answers that they might have formerly memorized are coming from. As a research scientist, I use Microsoft Excel extensively to analyze data. I routinely use statistical and logical functions and data plots in my data analysis.
...Therefore, the integers are a natural tool of study in the field of discrete math.)
EXPERIENCE:
I have extensive experience in subjects which may fall under the umbrella of discrete math, as approximately half of my mathematical training has revolved around subjects such as topology, algebra, an... | 677.169 | 1 |
Fundamental Concepts of Abstract Algebra
MAA Review
[Reviewed by Allen Stenger, on 09/13/2012]
This is a competent but uninspiring first course in abstract algebra, concentrating on groups, rings, and fields; but with an extensive coverage of vector spaces, much more than is needed to explain extension fields. It is an unaltered reprint of a 1991 work published by PWS-Kent.
The book includes a large number of exercises, most of moderate difficulty. A novel feature is that each problem section starts with a set of easy true-false questions to test the student's understanding; for example, an exercise on p. 188 is "the polynomial x4 + 3x3 + 9x2 + 9x + 18 is irreducible over the rational field", and an exercise on p. 332 is "a regular 680-gon is constructible". | 677.169 | 1 |
600 MANUALLY SELECTED MATH SOFTWARE RESOURCES600 MANUALLY SELECTED MATH SOFTWARE RESOURCES:600 MANUALLY SELECTED MATH SOFTWARE RESOURCES: 1/12/2009 10:23600 MANUALLY SELECTED MATH SOFTWARE RESOURCES: 11/2/2006 2:58600 MANUALLY SELECTED MATH SOFTWARE RESOURCES: 4/30/2007 1:42 | 677.169 | 1 |
Introductory Algebra through Applications 2nd Edition
0321518020
9780321518026 KEY TOPICS: Whole Numbers; Fractions; Decimals; Basic Algebra: Solving Simple Equations; Ratio and Proportion; Percents; Signed Numbers; Basic Statistics; More on Algebra; Measurement and Units; Basic Geometry MARKET: for all readers interested in introductory algebra. «Show less... Show more»
Rent Introductory Algebra through Applications 2nd Edition | 677.169 | 1 |
Understandable and convenient interface:
A flexible work area lets you type in your equations directly. It is as simple as a regular text editor. Annotate, edit and repeat your calculations in the work area. You can also paste your equations into the editor panel.
Example of mathematical expression:
5.44E-4 * (x - 187) + (2 * x) + square(x) + sin(x/deg) + logbaseN(6;2.77)
History of all calculations done during a session can be viewed. Print your work for later use. Comprehensive online help is easily accessed within the program.
2)
Factor Calculator 5.6.2
Calculate the factors of any number with a single click. Small application window allows simultaneous use with Word, Outlook, Excel, etc.. Recommended on The Math Forum @ Drexel (University) for Middle School, High School and College, ages 6+. 99ΒΆ License:Shareware,
$0.99 to buy Size:
2592KB
7)
Kids Abacus 2.0 License:Shareware,
$ to buy Size:
2901KB
8)
Machinist MathGuru 1.0.90
Solve common trade maths problems in a whiz with Machinist's Math Guru software.
This inexpensive, easy to use utility is designed primarily for students, machinists, toolmakers and CNC programmers. License:Shareware,
$37.00 to buy Size:
3462KB
9)
ASCII Art Generator 3.2.4.6
ASCII Art Generator is an amazing graphics art to text art solution, which converts digital pictures into full color text-based images, and makes them eye-catching with a very cool and readable texture, composed of letters and digits. License:Shareware,
$29.95 to buy Size:
668KB
1) Math Game 1.1
Time that children spend on computer games has not been decreasing. In this new age, parents and teachers can find ways to use the entertainment industry to educate and enlighten our youth. License:Shareware,
$9.95 to buy Size:
8292KB
2)
FindGraph 2.22
FindGraph is a graphing, curve-fitting, and digitizing tool for engineers, scientists and business. Discover the model that best describes your data. License:Shareware,
$79.95 to buy Size:
3370KB
5) Multivariable Calculator - SimplexCalc 4.1.4
SimplexCalc is a multivariable desktop calculator for Windows. It is small and simple to use but with much power and versatility underneath. It can be used as an enhanced elementary, scientific, financial or expression calculator. License:Shareware,
$15.00 to buy Size:
1060KB
6) Multipurpose Calculator - MultiplexCalc 5.4.4
MultiplexCalc is a multipurpose and comprehensive desktop calculator for Windows. It can be used as an enhanced elementary, scientific, financial or expression calculator. License:Shareware,
$15.00 to buy Size:
1184KB | 677.169 | 1 |
Book DescriptionThe one published in 1959 deserves to be one of the finest books written about vectors .The way it deals with the subject prepare the reader smoothly in mastering the basics of vector analysis, its for the engineer, physicist and mathematician.
By the way the full name of the book is "Vector Analysis and an Introduction to Tensor Analysis"
This is great as a preparatory or supporting text. I worked through virtually all of the 'supplementary' problems and found the chapters on curvilinear coordinates and tensor analysis very useful preparation for the study of General Relativity texts. Major parts of Landau and Lipschitz 'Classical Theory of Fields' and many other texts were readily accessible after doing the sums from Spiegel. Eminently suitable for independent study.
I love this book. I've owned three copies of it over the years and I can honestly say that I would not have achieved the final class of degree in Physics that I did without it.
The learning curve is very gentle - really nothing is assumed about the reader's background beyond basic integral and differential calculus. The concepts of vectors are introduced one by one, and the book builds logically towards its final stages (introductory tensor analysis) via, inter alia, dot and cross products, partial differential operators on vector spaces (grad, div, curl, Laplacian etc.), line and surface integrals (along with vital allied therorems such as Stokes' and Green's theorems), and general theory of curvilinear coordinate systems (in which the differential operators are refined and generalised).
This book is absolutely ideal for an undergraduate course in Physics, Electronic Engineering or Vector Analysis. | 677.169 | 1 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
SELECT exp_id AS exp_id, exp_short_desc AS exp_short_desc, exp_long_desc AS exp_long_desc, author_id AS author_id, sense_id AS sense_id, loc_id AS loc_id, rank_id AS rank_id, date AS date, time AS time, 'ilee4320' FROM ilee4320.experience WHERE 1SE
Review for Final Exam Math 230, Fall 2006 The final exam is scheduled on 12/18/2006 12:20 PM - 2:10PM, 121 Sparks (Section 7 and 8) This is a comprehensive exam, you should consult your previous midterm review sheets for highlights of Sections 13.1-1
Math 230, Fall 2006Review sheet for Exam 1Our rst midterm exam will be given on October 5, 2006. It will cover the material from Chapters 13-14.Some important skillsSection 13.1: Three-dimensional Coordinate Systems Find the distance from a po
Math230 Take home quiz No. 6, Oct.20, Name:, StudentID:(1) ( 2 points) Find the first partial derivative$ of the function:(2) ( 3 p oints) Find the equation of the tangent plane to the given surface a t the specified point.
Outline Object-oriented programming Objects and classes, examplesObject-Oriented Programming (OOP) A programming technique based on objects. Advantages:Good at modeling real-world objects you find in everyday life. Speedy development, high
To-do ReviewMembers in class definition Object creation ArrayClasses Name the class members you know about variables (i.e. fields)instance variables, class variables (with keyword static) A special kind of method A constructor is calle | 677.169 | 1 |
Calculus: Understanding Its Concept and Methods is a complete electronic textbook featuring live calculations and animated, interactive graphics. It uses the included Scientific Notebook® program to display text, mathematics, and graphics on your screen and to provide an interactive environment including examples with user-defined functions, animations, and algorithmically generated self-tests. This environment encourages a focus on mathematical problem solving, experimentation, verification, and communication of results.
This electronic book covers the content normally taught in a three-semester calculus sequence. The material is presented in a way that encourages mathematical problem solving, experimentation, exploration, and communication. It includes explanations, examples, explorations, problem sets, self tests, and resource information. Many of the files contain animations that you can manipulate and control. Other files are interactive: you can define your own function, or change some parameters, and observe the results. This allows you to achieve important insights from specific examples.
Calculus: Understanding Its Concept and Methods is thoroughly indexed and hyperlinked to provide easy access to relevant information. It is appropriate for independent study, as a supplement to any standard calculus text, or for distance learning.
Calculus is the mathematics of change and approximation. With the computer algebra system in Scientific Notebook®, you can interactively explore examples and carry out experiments. The skills you develop will help you to solve problems you encounter in the future because you are always dealing with natural mathematical notation and general problem-solving methods. | 677.169 | 1 |
umerical Mathematics and Computing
Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give ...Show synopsisAuthors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITIONEx-Library book-will contain library markings. Very good...Ex-Library book-will contain library markings. Very good condition book with only light signs of previous use. Sail the Seas of Value | 677.169 | 1 |
Visual and interactive way to thorough understanding and mastering Trigonometry without getting wearied on the very first chapter! Java- and web-based math course includes theoretical concepts, hands-on examples featuring animated graphics and live formulas, problem-solving lessons, and customizable real time tests with solutions and evaluations. | 677.169 | 1 |
Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. | 677.169 | 1 |
Age-Specific Population Models
Allen E. Martin
Abstract
An age-specific population model is built, based on Fibonacci's rabbit problem. The model is examined using spreadsheets, matrices, iteration and exponential regression. The investigations are based on the assumption that students will have a graphing calculator and/or spreadsheet available to them. The suggested investigations encourage students to use a variety of representations and seek links between them. This module might be used as a lead-in to a discussion of Leslie models for population growth, or as an enrichment project after a discussion of exponential regression.
In Liber Abaci, Leonardo of Pisa (Fibonacci, ca. 1202) proposed one of the earliest mathematical models for population growth. The problem situation stated below is a reworking of Fibonacci's original problem which generates an introductory age-specific population model.
Imagine that we start with one pair of rabbits (one female and one male). After N days, this pair matures to reproductive age and immediately produces a new pair. After N more days, the first pair again produce offspring. Thus, each pair of rabbits will reproduce two times during their lifetime (exactly one pair immediately at the start of each new stage, where "pair" always means one female and one male), at intervals separated by N days, and each new pair of rabbits will go on in a similar fashion.
The problem statement suggests that the rabbit population can be broken down into three groups: "newly born", "young adults" and "mature adults". Each pair of newly born rabbits survives to become young adults and to produce one new pair of offspring at this stage. Each pair of young adults survives to become mature adults and to produce another pair of offspring. Finally, each pair of mature adults moves on to "rabbit heaven"; no survival is allowed after stage 3.
This process of moving through the age-structure and the patterns that emerge can be represented several ways:
with diagrams, to break down and understand the dynamics of the problem
with spreadsheets, to capture patterns and create graphs
with matrices, to emphasize the age-structure and make it more explicit
with recursive formulas (iteration), to capture the dynamics algebraically for further analysis
Analysis by Diagram
The first step in understanding the model is to find a way to "make sense" of the problem situation. A chart or diagram like the one shown below is helpful. The columns display the age structure for each of the first 6 time steps. The rows show the first 6 generations.
Diagram Breakdown of the Rabbit Population
Generation
1
NB
YA
MA
2
NB
YA
MA
NB
YA
MA
3
NB
YA
MA
NB
YA
MA
NB
YA
MA
4
NB
YA
MA
NB
YA
NB
YA
NB
YA
NB
YA
5
NB
YA
NB
NB
NB
NB
NB
NB
NB
6
NB
Time Step
1
2
3
4
5
6
Newly Born
1
1
2
3
5
8
Young Adult
0
1
1
2
3
5
Mature Adult
0
0
1
1
2
3
Total
1
2
4
6
10
16
This diagram captures many of the key aspects of the growth process of this rabbit population. Viewing the chart by columns, we can see the age-specific breakdown for each time-step. For example, in the 4th column we see that there are 3 newly born, 2 young adults and 1 mature adult. Viewing the chart by rows, we see the progression of the pairs born in a given generation as they move through the age-specific categories for the rabbit population. For example, the two pairs born in the 3rd generation become young adults in the next column, contributing 2 pairs of newly born to the 4th generation below them; they then survive to produce one last time, contributing to the 5th generation.
Analysis by Spreadsheet
The information contained in the diagram can then be summarized in a spreadsheet like the one shown below.
Time
Newly
Young
Mature
Total of
Step
Born
Adults
Adults
Rabbits
1
1
0
0
1
2
1
1
0
2
3
2
1
1
4
4
3
2
1
6
5
5
3
2
10
6
8
5
3
16
7
13
8
5
26
8
21
13
8
42
9
34
21
13
68
10
55
34
21
110
Once the spreadsheet has been created, we can view large amounts of data conveniently, include the data in reports, and easily create graphs. Also, we can vary the assumptions of the model and explore variations of the problem situation quickly.
Investigation #1
Starting with 1 pair of "newly born" rabbits, suppose that each pair of rabbits survives through 4 time steps, instead of three.
(a) Create a "diagram analysis" to break this problem situation down
(b) Create a spreadsheet that shows the data for each of the 4 age categories
(c) Create a graph showing Newly Born vs. Time Step
Investigation #2
Suppose that each pair of rabbits survives through 3 time steps (as in the original setup), but that each pair of young adults has 2 pairs of newborns. Also suppose that mature adults have only 1 pair each.
(a) Create a table showing each age category and the total number of rabbits for time steps = 1, 2, 3, ... , 10
(b) Create a graph showing Newly Born vs. Time Step
Analysis with Matrices
Let's return to the original problem situation. For any given time step, the population can be conveniently broken down into its age-specific groups with matrix notation.
So the information in the diagram and spreadsheet can be expressed as follows:
Step123456 n
Structure
Now, as the population moves from one time step to the next, we see that
Bold ---> Ynew , Yold ---> Mnew, and then Ynew + Mnew ---> Bnew
This transformation can be accomplished by matrix multiplication!
This can be expressed in a more compact form:
where T is the transition matrix
and Pold & Pnew are the population matrices.
This multiplication can be accomplished on a calculator with "Answer-Key" iteration. First enter the transition matrix into matrix [A], then the initial population matrix into matrix [B]. Next call matrix [B] and press <enter>. Then call matrix [A] and multiply by ANS. Finally, press <enter>, <enter>, <enter>, ... to get the 2nd, 3rd, 4th, ... generations.
Analysis by Iteration
As can be seen in both the diagram and the spreadsheet, the values of each age group can be determined from previous values. These patterns can be expressed iteratively.
Let = # of newly born in the nth time step
= # of young adults in the nth time step
= # of mature adults in the nth time step
then, moving from one time-step to the next, we can see that
,
and then
Note: It follows that
Since all three age groups have the characteristic Fibonacci-like pattern
(b) Extend this table further out to the right (by letting n = 10, 20, 30, ...); then describe what happens to the values of .
(c) Sketch a graph of vs. n.
In the third investigation, we find that grows exponentially:
for n = 1, 2, 3, ..., 10
and, for n = 1, 2, 3, ..., 20
.
The fourth investigation reinforces this, since the ratio gets very close to 1.618 as n gets large; hence .
In fact, if we assume that and apply this to the iteration , we get
The roots of this equation are
Key Observation:Notice the striking similarity between the base of the exponential, the limiting value of the ratio and one of the roots of this "characteristic polynomial". What is going on here? The next two investigations will explore this similarity further.
Investigation #5 --
In investigation #1, we found that the "newly born" followed the pattern shown above. Using this ...
(a) Determine the characteristic polynomial for this iteration, then graph this polynomial on your calculator. How many real roots does it have? Approximate any real roots you find. | 677.169 | 1 |
Seventh-grade extended math completes the remaining seventh grade and all of the eight grade Standards of Learning set by the State of Virginia, and in some cases goes beyond state standards. Students in this course will take the Grade 8 Mathematics SOL exam in the spring.
The seventh-grade standards place emphasis on solving problems involving consumer applications, using proportional reasoning, and gaining proficiency in computations with integers. The students will gain an understanding of the properties of real numbers, solve one-step linear equations and inequalities, and use data analysis techniques to make inferences, conjectures, and predictions. Two- and three-dimensional representations, graphing transformations in the coordinate plane, and probability will be extended.
The eighth-grade standards contain both content that reviews or extends concepts and skills learned in previous grades and new content that prepares students for more abstract concepts in algebra and geometry. Students will gain proficiency in computation with rational numbers (positive and negative fractions, positive and negative decimals, whole numbers, and integers) and use proprotions to solve a variety of problems. New concepts include solving two-step equations and inequalities, graphing linear equations, visualizing three diminsional shapes represented in two-dimensional drawings, applying transformations to geometric shapes in the coordinate plane, and using matrices to organize and interpret data. Students will verify and apply the Pythagorean Theorem and represent relations and functions using tables, graphs, and rules.
For a summary of the Standards of Learnings taught in the seventh-grade extended math see the parent-brochure below.
Documents
PWCS Extended Grade 7 Curriculum Guide (Word) - This document contains the pacing guide and curriculum guide to be used beginning with school year 2012-2013 for Grade 7 Extended Mathematics. The pacing guide has been updated. Updated August 2012.
Extended Grade 7 Curriculum Map (Word) - This document is an abbreviated form of the curriculum guide. It only contains the objectives and essential knowledge and skills. It is in a table format with an extra column. It may be used to create blueprints for unit assessments, making notes for units and lesson plans etc.
SOL Electronic Practice Items and Tools Practice - contains a sample of practice items for each standards of learning test and a companion guide to assist in stepping through the sample problems and learning the online tools for the technically enhanced questions. There is also a separate application for just practicing with the online tools | 677.169 | 1 |
Careers in math: The
Funworks site describes many career
fields, and includes a category of careers that use math, useful for when you have to write a "how
people use math in real life" sort of paper.
Common Errors in College Math: Professor Eric Schechter has compiled an extensive list of
the errors most commonly seen in college math courses. While some of his illustrations are specific
to calculus, any high-school or college algebra student would benefit from reviewing his warnings
and recommendations.
Culturally Situated Design Tools:
If you need to do a "math in other cultures" report, this
site might be helpful. Their connections between "culture" and math seem fairly strained
(do you really think ancient Africans were "engaging" in transformational geometry
when they were braiding their kids hair?), but their articles should give you what your teacher
is wanting to hear.
Curious and Useful Math:
Clay Ford has developed a "curious" site
which covers taking square roots by hand, doing mental math, and playing math tricks, among other
things.
Cut-the-Knot: A fascinating site,
you will find topics that go right over your head (mine, too) right next to topics that usefully
answer annoying take-home-project homework questions. Many topics have Javascript illustrations.
Earliest Uses of Math Terms and Symbols: These pages are great for finding the first known use of the division
symbol, the fraction bar, the term "x-intercept", or other mathematical terms or symbols.
Finding your Way Around:
MathBits.com has an extensive listing of instructions
for using your Texas Instruments TI-83 or TI-84 calculator for various tasks.
Graphing Calculator
Help: The Prentice-Hall publishing company has extensive examples
for some Texas Instruments graphing calculator models, along with the Casio FX2, the Sharp
EL9600C, the CFX-9850, and HP48G.
MailWasher Pro:
Okay, this isn't math-related, but I love this e-mail utility. The MailWasher (MW) program
isn't really for catching or preventing spam, though it does have tools that can help in that regard.
The great thing about MW is that it allows you to delete the garbage e-mails straight off
your ISP's mail server; the junk never touches your computer. You can try the program before
buying; it took me about twenty minutes of using MW to decide that it was worth the price.
Math and Music:
If you need to write a paper on "applications of math", the research posted by
Professor Hall might be a good place to start. Note: Her resources are largely PDF files, so make
sure you've got Acrobat Reader installed.
Math in Daily Life: If you need to write a paper on "How Math is Useful
in Everyday Life", this
is a good place to start.
Mathematical Fiction:
This categorized and searchable index of fictional
works relating to mathematics is categorized according to medium (comic books, movies, etc), genre
(horror, sci-fi, etc), motif (aliens, music, insanity, etc), and topic (logic, chaos, etc). You
can also search by title or author, or in chronological order. If you're having to do a report
or presentation on "something mathematical", this could be a great place to start.
Mathematical Moments:
This American Mathematical
Society page lists various disciplines in
which math is used "in real life". The first two links for each topic take you to a descriptive
flyer; the third link takes you to the actual information.
Mathwords:
If you're looking for a definition, try this site. There is an alphabetic
index available along the left-hand side of the page, or you can enter your term into the search
box in the top right corner.
Meracl FontMap: Did you know that the degree symbol " ° ", the
empty-set symbol "Ø", the division symbol "÷", and the plus-minus symbol "±"
are all standard characters, and that you can type them into e-mails and such without having to
resort to special fonts that your recipient might not be able to read? This free
program lets you "see" all these characters in your preferred font, and lets you
paste them into your document. A "must" for those of us who can't read the tiny little
"Character Map" that comes with Windows.
The Nine Digits
Page: If you have one of those "impossible"
puzzle problems that you have to solve using the digits "1" through "9", this site might contain the archived solution.
No Boundaries:
USAToday has created a service allowing the interested student to "explore careers in science, technology, engineering and math" within NASA. The site is designed for
group projects within the classroom, but the information can be adjusted to, say, help in writing
a report on "careers in math".
Practical Uses of Math and Science:
Need to write one of those "how math is used in real life" papers? Check out the PUMAS listing created by NASA. Topics include how to calculate square roots
with a carpenter's square, the mathematical implications of lying, and why clouds don't fall out
of the sky. Click on the title, and then click on "View this Example".
Print Free Graph Paper:
The PDFPad site provides free
graph paper that you can view and print
with the Acrobat Reader browser plug-in.
Stan Brown's Math and Calculator articles: Professor Brown has created a nice collection of tutorials
covering many common tasks, and some not-so-common ones, for classes from algebra through calculus
and statistics. Includes programs you can download and install, step-by-step instructions, illustrations,
and a conversational tone.
TI-83 tutorial: This
highly graphical tutorial covers some basic topics such as setting the window, creating
a table, and doing a regression. A floating red arrow takes you step-by-step through the processes.
Women in Mathematics:
Need to write a paper on minorities, or specifically on women, in mathematics? This might be a
good place to start.
If you have found a particular web
site to be useful for geometry, proofs, trigonometry, linear algebra, or calculus, please let me know. Thank you!
If you think your site should be listed here, please submit
the URL, explaining how you think your free (or free-to-try) products and/or services
would aid algebra students. Listings are added at the webmistress' discretion; listings for "calculators"
and "graphers" are no longer accepted. Sorry. | 677.169 | 1 |
Develop a rich understanding of the rudiments of algebra in a relaxed and supportive learning environment. This course will help you understand some of the most important algebraic concepts, including orders of operation, units of measurement, scientific notation, algebraic equations, inequalities with one variable, and applications of rational numbers.
Learning Objectives:
Identify types of numbers, practical applications, and history of algebra.
You will need to create a login for your online classroom. Go to Find your course by browsing the catalog or using the search bar. Click the "Enroll Now" button. Select your start date and then create a Username and Password. At the end, you will be asked to click on the "Already Paid" button if you have already paid. You must make an 80 or higher on the final exam (online) to successfully complete the course. You may only take the exam once.
If you are a certified teacher in Georgia and are interested in taking this course for PLUs, please complete the PLU notification form once you have registered. This course grants 2 PLUs upon successful completion.
If you have questions about this course, please contact the online coordinator at 770-499-3355 or [email protected]. | 677.169 | 1 |
linear algebra.
...continue to expand their problem-solving skills, in particular, visualization and abstraction.
...gain knowledge and skills to formalize their ideas and express them with a full mathematical rigour.
Content:
Systems of Linear Equations.
Matrices.
Determinants
Vector Spaces
Inner Product Spaces.
Linear Transformations.
Eigenvalues and Eigenvectors.
Course Philosophy and Procedure
Just keep this simple principle in mind: If you are not enjoying this course, if the work is not fun, then something most be wrong. Talk to me right away! This course involves a lot of concepts that easily translate into fairly straightforward (but sometimes lengthy) calculations. Geometry, i.e., visualization is essential. There are also some topics that involve a greater level of abstraction yet there will be plenty of exercises available to check and enhance your understanding of those concepts. You will find that the concepts learned in this course can be applied to many problems in Mathematics and Science.
You should plan to reserve a significant amount of time to study for this course. The material is easy, but the nature of the exercises is such that they are going to be time consuming. Being focused is of utmost importance. Don't rush in doing the problems!
Grading will consist of two semester (100 points each) and the final exam) worth 200 points each. The homework and chapter projects will total to 200 points.
My grading scale is
A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.
Final Exam: 12/12 from 12:50-2:50 | 677.169 | 1 |
So you want to include some history of mathematics in your upper-level courses, but you just can't imagine how you can possibly fit anything else in this semester. How will you get to all the topics you want to cover, and still have time for some history?
Instead of giving a lecture on a history topic, or on the name behind a famous theorem, why not let students find the information themselves? Using a discovery worksheet is fun, saves class time, and encourages students to learn things on their own. Some of the answers may be in their own textbooks, or in library books on the history of mathematics, but the activities in this article are designed so that students are encouraged to search the Internet for information. In the process, students will probably be surprised to learn how much material is 'out there' about mathematics and its history and will begin to learn how to separate the online wheat from the chaff. The examples that follow are intended for students in linear algebra and differential equations courses, as indicated, but you can obviously use this idea in any class. This assignment is very flexible: you may assign the worksheets for homework or use them as a class activity; you may have students work independently or in groups.
Students enrolled in a linear algebra class may never have stopped to think that Gaussian elimination was named for someone named Gauss, or that there was a Cramer behind Cramer's Rule. They may be surprised to learn that people have been solving systems of linear equations for thousands of years | 677.169 | 1 |
Haymarket Algebra getting to know your specific need and to help you achieve your objectives. Respectfully Yours,
John B., BSME, FE(EIT), MBA, PMP, ITILv3, CSSGBEngineers & Scientists use Mathematics to communicate as much as divers use air to breath. As an Engineer myself, I've come to realiz...Most of my family is deaf, including both parents and both step parents. I also have a sister who is deaf along with her husband and her two kids. My other sister who is hearing, is a sign language interpreter.
...Hence, much will depend on student?s standing. The following is a snapshot of what will be covered in the course: algebraic expressions, setting up equations by translating word problems; evaluating expressions by adding and subtracting polynomials; factoring polynomials (trinomials) using FOIL ... | 677.169 | 1 |
Find a Lucerne, CO took a course in Differential Equations at St. Petersburg University and passed this course with "B". I defended my PhD on mathematical modeling based on the use of Partial and Ordinary differential equations in Earth scienceIt's a necessary prerequisite for all future math and science classes, and nearly every high school and college requires it as a core course. Fortunately, because it is a class that's mandatory, it's also class that everyone should be able to pass. Sometimes it just takes a little bit of help. | 677.169 | 1 |
This book is the ultimate math resource or home which has everything you need for math success. Also includes a handy Almanac with math prefixes and suffixes, problem-solving strategies, study tips, guidelines for using spreadsheets and databases, test-taking strategies, helpful lists and tables, and more. | 677.169 | 1 |
Combinatorial Problems and Exercises
9780821842621
ISBN:
0821842625
Pub Date: 2007 Publisher: American Mathematical Society
Summary: The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems.
Ships From:Boonsboro, MDShipping:Standard, Expedited, Second Day, Next DayComments:Brand new. We distribute directly for the publisher. The main purpose of this book is to provide... [more]Brand new. We distribute directly for the publisher. The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allo [less] | 677.169 | 1 |
This part of the tool allows the user to graph any surface in 3D and then plot the Taylor Polynomial of degrees 0 through 5. Both the algebraic equation and the graph are given of the Taylor Polynomial. The user can set the center point of the polynomial and can use a slider to change from degree to degree. CalcPlot3D also contains a parametric surface graphing capability, including the ability to display a "trace" point on the surface.
Discuss this resource
Ways you have used CalcPlot3D
by Paul Seeburger (posted: 11/14/2011 )
I would love to see some comments added to this resource to reflect the ways many instructors have used this applet in their teaching. I created this resource to help my students to see the connections between the concepts we study in multivariable calculus more clearly.
I use it to demonstrate certain properties in my lectures like the fact that the gradient vector points in the compass direction we should move along a surface in order to go most steeply uphill.
I also use it in lectures to visually verify solutions to various boardwork exercises like finding the equation of the plane determined by three non-collinear points and the intersection of two planes (or other surfaces).
I then get my students to use the applet by requiring them to visually verify solutions to various homework problems on graded worksheets. They print out their resulting graphs from the applet and hand them in with their homework. I have them do this with various topics including those mentioned above, as well as contour plots, level surfaces, tangent planes, flowlines through vector fields.
I also ask my students to complete several concept explorations that use the applet to consider the geometric properties of dot products, cross products, velocity and acceleration vectors, and Lagrange multiplier optimization.
I use it for some "what-if" types of explorations in class when we study space curves as well.
I would love to hear what others are doing, and in particular, I think it would be helpful to share particular functions, space curves, etc. and activities that could be done by students using this applet (or similar resources). | 677.169 | 1 |
The
purpose is to promote and cultivate a higher curiosity, appreciation and
understanding of Mathematics for all the students at NIU. Also, Math Club
will provide support to its members in all of their math related
endeavors. | 677.169 | 1 |
Precalculus -- Preparing Students for
Calculus
Precalculus,
by Warren Esty
Sixth edition (This page updated Sept. 25, 2012)
A text
designed to produce a deep understanding of algebra and
trigonometry so that students will be comfortable with their
next math. Students will be well-prepared for calculus.
This text is designed to be appropriate for self-study, as
well as classroom use.
The content includes the usual precalculus
material (functions, powers, polynomials, logs, exponentials,
trig, etc.). Graphing calculators play an important role.
However, this text is unlike others because it does not just
use calculators to do old-style problems, but actually
incorporates calculators as a learning tool
and not just a "doing" tool.
This text has been used at Montana State University and
elsewhere by about a hundred different instructors and many
thousands of students. A great deal of experience has gone into
making this text an effective learning tool.
"As a home-schooled junior in high school
this year, I used your Precalculus book. [clip] I would just
like to thank you so much for writing that book. It changed my
entire perspective on math. Up to this year, I considered math
to be a distasteful medicine [clip]. No text book on a language
was ever written better. I quickly became enthralled with your
ideas, and now I love Math. Precalculus was my favorite subject
this year [clip. Read the whole letter
here.]
"I ordered your precalculus book, and thus far
it's been quite a learning experience. I've learned more in the
past 3 months than I learned in 4 years of high school. ....
Thanks." [an adult student]
"I'm taking Precalculus for graduate school,
and I have always hated math and been terrible at it, I was taught
only to memorize, never to understand. I'm starting to love math,
and it's because my dad (who loves math) has your book and we've
been working with it! So I wanted my own copy. Thank you for
writing such a great precalculus book!"
"I am the teacher who used your
Precalculus text with some homeschoolers over the internet the
year before last. I now have more students asking for the class.
I would like to use your text again. (I was very pleased that
the students who used your book and went on to take the SAT got
math scores very near 800. It'll be interesting to see what
happens with the new SAT exam.) ..."
"I love teaching the text and the other
instructor feels likewise. The course has been a challenge for my
students. For those who have buckled
down and done the requisite assigned work (and shift in conceptual
focus), well, the results are very, very evident." [continued here]
-- A high school teacher.
"Speaking as an
aerospace engineer, this was a great course, great professor [at
a different school], and great textbook. I would have never
found that textbook on my
own. I would not change anything with this course. It meets the
demands of the Math Analysis course in a previous era... the one
I grew up in. For the
most part, Calculus and Pre-Calculus classes have been
dramatically watered down since the 1980s. This course restores
the ancient paths.
"I think this is the best math
class she [his daughter] has had for her mathematical
understanding [continued here]"
-- A parent
Of course, the presentation of most topics resembles that of
other precalculus texts. So does the organization, at least
after Chapter
1 (which is unique). But it is particularly effective because of
its numerous distinguishing features:
An effective new approach that incorporates
graphing
calculators
as
a learning tool (not just a calculating tool).
This may be the first text to fully adjust to the fact that
calculators can do the calculations and therefore accelerate
learning about algebra, exponentials, logs, and trig, but students
must still learn and understand the math. Calculators
can help:
Concentrate attention on essential points
Increase the rate at which students
gather experience with the subject
Focus on learning math that is valuable (essential!) even
though calculators can do all the calculations. There
is still a lot to learn about math, even though calculators
can do a lot. This text clearly distinguishes between learning
about calculators and learning about math with the help of
calculators. (Dr. Esty has given numerous conference talks
about learning with the help of calculators.)
Emphasis on learning how thesymbolic
languageof math
is used. This is probably the most
distinguishing feature of the text. It is an explicit goal of
Chapter 1 that students learn how thoughts about methods are
written in modern mathematical notation. The goal of
Chapter 1 is to have students become able to learn math by
reading math. Let's face it, most students do not learn
math by reading it. This text has explicit reading lessons!
They will
Increase students' ability to generalize
properly
Increase students' ability to learn
outside of class. [There is so much more time outside of
class than in class. Wouldn't it be great if students couldlearn
(not just practice) outside class!]
Illuminating
homework in addition to the usual type of calculation
problems for practice.
(For example, most "B1" problems ask for an
illustration, or explanation, rather than a computation.)
Memorable
visual illustrations that generate correct concepts.
Emphasis on connections to lower- and higher-level
material.
(Calculus-style applications of algebra are
frequently discussed).
Two
sections
devoted to how to do word problems. Students who
can't do word problems are missing something important about
algebra -- how symbolism is used to represent operations. The
emphasis on symbolism for expressing thoughts about operations
in Chapter 1 helps students learn how to do word problems, and
they would never be ready without it. The author's research on
word problems shows that students cannot do word problems just
by taking years of algebra. They need to study writing about
operations in symbols first.
Emphasis on graphs and their interpretation, and
effective use of graphing calculators.
Emphasis on mathematical concepts that will not
become obsolete when the next generation of calculators
arrives.
Instructor-friendly and student-friendly
(this text does not require new teaching techniques or
classroom experiments)
Excellent for
teaching yourself. It is hard to learn math on your own.
You must have good (English) reading skills. In contrast to
all other texts, this one has lessons in Chapter 1 on how math
is written and how to read it. This should help you get the
most of the text even if you don't have a teacher.
A solution manual
with solutions to odd-numbered problems so you can follow how
problems are done if you have questions.
Six articles by Dr. Esty on learning precalculus with the
aid of calculators have appeared in the recent proceedings of
the International Conference on Technology in Collegiate
Mathematics (some are on-line with links below).
The importance of conceptual development that is
specifically algebraic is discussed in
"Algebraic Thinking,
Language, and Word Problems," an article by Dr. Esty and
Dr. Anne Teppo in the 1996 Yearbook: Communication in
Mathematics, published by the National Council of Teachers
of Mathematics. They have also written related articles on
problem-solving and algebraic thinking in several issues of Psychology
in Mathematics Education. | 677.169 | 1 |
Downloading ... TradesMathCalc-demo.exe
Review
Solve common machine shop math problems quickly and easily!
Solve common machine shop and other trades trigonometry and math problems at a price every trades person can afford! As a machinist or CNC programmer, you often have to use trigonometry to calculate hole positions, chamfers, sine bar stacks, dovetail measurements, bolt circles, etc. You often have t ... | 677.169 | 1 |
Basic Algebra (SSAT-Algebra)
The SSAT requires some knowledge of Algebra. Students should know what Algebra is, its uses as well as how to answer questions involving Algebra. This includes simplifying algebraic expressions, solving simple equations as well as working with word problems involving algebra. Substitution or replacing of variables with numbers and evaluating these expressions are also an integral part of Algebra for the purposes of the SSAT. | 677.169 | 1 |
AcademicsCombinatorics
Combinatorics is the study of arranging
objects to satisfy given rules. That is, we try to solve puzzles
such as:
a) Take a chessboard and remove a pair of
diagonally opposite corner squares. Suppose we have some dominos,
each of which exactly covers two adjacent squares of the chessboard.
Is it possible to exactly cover this chessboard using the
dominos?
b) Kirkman's Schoolgirl Problem (1850):
A schoolmistress takes her class of 15 girls on a daily walk.
The girls are arranged in 5 rows, with 3 girls in each row,
so that each girl has 2 companions. Is it possible to plan
a walk for 7 consecutive days so that no girl will walk in
a triplet with any of her classmates more than once?
c) Suppose a region of land is to be divided
into countries. How many colors do we need so that, however
the region is divided, we can produce a map of the region
in which no two neighboring countries are the same color?
If we can show that a certain arrangement
exists, then we are interested in how many possible arrangements
there are. In the course we study some essential techniques
of combinatorics and then look at some problems from various
areas of the field. We also consider how combinatorial techniques
and results apply to other fields, such as experimental design
and computer science.
Course Structure: The course text
is "Introductory Combinatorics" (3rd edition) by
Richard Brualdi (available in bookstore and on reserve in
the library). An approximate outline for the course
is chapters 1-3, 5, 6, 9-12 of the text. There
will be two types of homework assignment. The first
type will consist of problems which reinforce and build on
the skills we are developing in class; the second type will
be a single challenging problem. They will be set on
alternate Thursdays. The first type are due by 4pm the
following Wednesday. For the second type there is nothing
to hand in, but you should come to class the following Thursday
ready to discuss progress you have made and approaches you
have attempted.
Grading: Your grade will be based on 3 equally
weighted components; the first type of homework, a final exam
and class participation. The class participation component
will rely heavily on your engagement with the problems in
the second type of homework. | 677.169 | 1 |
Syllabus Structure and Content
3.1 INTRODUCTION
The way in which the mathematical content in the syllabuses is organised and presented in the syllabus document is described in sections 3.2 and 3.3. Section 3.3 also discusses the main alterations, both in content and in emphasis, with respect to the preceding versions. The forthcoming changes in the primary curriculum, which will have "knock-on" effects at second level, are outlined in Section 3.4. Finally, in Section 3.5, the content is related to the aims of the syllabuses.
3.2 STRUCTURE
For the Higher and Ordinary level syllabuses, the mathematical material forming the content is divided into eight sections, as follows:
Sets
Number systems
Applied arithmetic and measure
Algebra
Statistics
Geometry
Trigonometry
Functions and graphs
The corresponding material for the Foundation level syllabus is divided into seven sections; there are minor differences in the sequence and headings, resulting in the following list:
Sets
Number systems
Applied arithmetic and measure
Statistics and data handling
Algebra
Relations, functions and graphs
Geometry
The listing by content area is intended to give mathematical coherence to the syllabuses, and to help teachers locate specific topics (or check that topics are not listed). The content areas are reasonably distinct, indicating topics with different historical roots and different main areas of application. However, they are inter-related and interdependent, and it is not intended that topics would be dealt with in total isolation from each other. Also, while the seven or eight areas, and the contents within each area, are presented in a logical sequence combining, as far as possible, a sensible mathematical order with a developmental one for learners it is envisaged that many content areas listed later in the syllabus would be introduced before or alongside those listed earlier. (For example, geometry appears near the end of the list, but the course committee specifically recommends that introductory geometrical work is started in First Year, allowing plenty of time for the ideas to be developed in a concrete way, and thoroughly understood, before the more abstract elements are introduced.) However, the different order of listing for the Foundation level syllabus does reflect a suggestion that the introduction of some topics (notably formal algebra) might be delayed. Some of these points are taken up in Section 4.
Appropriate pacing of the syllabus content over the three years of the junior cycle is a challenge. Decisions have to be made at class or school level. Some of the factors affecting the decisions are addressed in these Guidelines in Section 4, under the heading of planning and organisation.
3.3 SYLLABUS CONTENT
The contents of the Higher, Ordinary and Foundation level syllabuses are set out in the corresponding sections of the syllabus document. In each case, the content is presented in the two-column format used for the Leaving Certificate syllabuses introduced in the 1990s, with the lefthand column listing the topics and the right-hand column adding notes (for instance, providing illustrative examples, or highlighting specific aspects of the topics which are included or excluded). Further illustration of the depth of treatment of topics is given in Section 5 (in dealing with assessment) and in the proposed sample assessmentmaterials (available separately).
CHANGES IN CONTENT
As indicated in Section 1, the revisions deal only with specific problems in the previous syllabuses, and do not reflect a root-and-branch review of the mathematics education appropriate for students in the junior cycle. The main changes in content, addressing the problems identified in Section 1, are described below. A summary ofall the changes is provided in Appendix 1.
Calculators and calculator-related techniques
As pointed out in the introduction to each syllabus, calculators are assumed to be readily available for appropriate use, both as teaching/learning tools and as computational aids; they will also be allowed in examinations.
The concept of "appropriate" use is crucial here. Calculators are part of the modern world, and students need to be able to use them efficiently where and when required. Equally, students need to retain and develop their feel for number, while the execution of mental calculations, for instance to make estimates, becomes even more important than it was heretofore. Estimation, which was not mentioned in the 1987 syllabus (though it was covered in part by the phrase "the practice of approximating before evaluating"), now appears explicitly and will be tested in examinations.
The importance of the changes in this area is reflected in two developments. First, a set of guidelines on calculators is being produced. It addresses issues such as the purchase of suitable machines as well as the rationale for their use. Secondly, in 1999 the Department of Education and Science commissioned a research project to monitor numeracy-related skills (with and without calculators) over the period of introduction of the revised syllabuses. If basic numeracy and mental arithmetic skills are found to disimprove, remedial action may have to be taken. It is worth noting that research has not so far isolated any consistent association between calculator use in an education system and performance by students from that system in international tests of achievement.
Mathematical tables are not mentioned in the content sections of the syllabus, except for a brief reference indicating that they are assumed to be available, likewise for appropriate use. Teachers and students can still avail of them as learning tools and for reference if they so wish. Tables will continue to be available in examinations, but questions will not specifically require students to use them.
Geometry
The approach to synthetic geometry was one of the major areas which had to be confronted in revising the syllabuses. Evidence from examination scripts suggested that in many cases the presentation in the 1987 syllabus was not being followed in the classroom. In particular, in the Higher level syllabus, the sequence of proofs and intended proof methods were being adapted. Teachers were responding to students' difficulties in coping with the approach that attempted to integrate transformational concepts with those more traditionally associated with synthetic geometry, as described in Section 1.1 of these Guidelines.
For years, and all over the world, there have been difficulties in deciding how indeed, whether to present synthetic geometry and concepts of logical proof to students of junior cycle standing. Their historical importance, and their role as guardians of one of the defining aspects of mathematics as a discipline, have led to a wish to retain them in the Irish mathematics syllabuses; but the demands made on students who have not yet reached the Piagetian stage of formal operations are immense. "Too much, too soon" not only contravenes the principle of learnability (section 2.5), but leads to rote learning and hence failure to attain the objectives which the geometry sections of the syllabuses are meant to address. The constraints of a minor revision precluded the question of "whether" from being asked on this occasion. The question of "how" raises issues to do with the principles of soundness versus learnability. The resulting formulation set out in the syllabus does not claim to be a full description of a geometrical system. Rather, it is intended to provide a defensible teaching sequence that will allow students to learn geometry meaningfully and to come to realise the power of proof. Some of the issues that this raises are discussed in Appendix 2.
The revised version can be summarised as follows.
The approach omits the transformational elements, returning to a more traditional approach based on congruency.
In the interests of consistency and transfer between levels, the underlying ideas are basically the same across all three syllabuses, though naturally they are developed to very different levels in the different syllabuses.
The system has been carefully formulated to display the power of logical argument at a level which hopefully students can follow and appreciate. It is therefore strongly recommended that, in the classroom, material is introduced in the sequence in which it is listed in the syllabus document. For theHigher level syllabus, the concepts of logicalargument and rigorous proof are particularlyimportant. Thus, in examinations, attempted proofsthat presuppose "later" material in order to establish"earlier" results will be penalised. Moreover, proofsusing transformations will not be accepted.
To shorten the Higher level syllabus, only some of the theorems have been designated as ones for which students may be asked to supply proofs in the examinations. The other theorems should still beproved as part of the learning process;students should be able to follow the logical development, and see models of far more proofs than they are expected to reproduce at speed under examination conditions. The required saving of time is expected to occur because students do not have to put in the extra effort needed to develop fluency in writing out particular proofs.
Students taking the Ordinary and (a fortiori)Foundation level syllabuses are not required to prove theorems, but in accordance with the level-specific aims (Section 2.4) should experience the logical reasoning involved in ways in which they can understand it. The general thrust of the synthetic geometry section of the syllabuses for these students is not changed from the 1987 versions.
It may be noted that the formulation of the Foundation level syllabus in 1987 emphasised the learning process rather than the product or outcomes. In the current version, the teaching/learning suggestions are presented in theseGuidelines (chiefly in Section 4), not in the syllabus document. It is important to emphasise that the changed formulation in the syllabus is not meant to point to a more formal presentation than previously suggested for Foundation level students.
Section 4.9 of this document contains a variety of suggestions as to how the teaching of synthetic geometry to junior cycle students might be addressed.
Transformation geometry still figures in the syllabuses, but is treated separately from the formal development of synthetic geometry. The approach is intended to be intuitive, helping students to develop their visual and spatial ability. There are opportunities here to build on the work on symmetry in the primary curriculum and to develop aesthetic appreciation of mathematical patterns.
Other changes to the Higher level syllabus
Logarithms are removed. Their practical role as aids to calculation is outdated; the theory of logarithms is sufficiently abstract to belong more comfortably to the senior cycle.
Many topics are "pruned" in order to shorten the syllabus.
Other changes to the Ordinary level syllabus
The more conceptually difficult areas of algebra and coordinate geometry are simplified.
A number of other topics are "pruned".
Other changes to the Foundation level syllabus
There is less emphasis on fractions but rather more on decimals. (The change was introduced partly because of the availability of calculators though, increasingly, calculators have buttons and routines which allow fractions to be handled in a comparatively easy way.)
The coverage of statistics and data handling is increased. These topics can easily be related to students' everyday lives, and so can help students to recognise the relevance of mathematics. They lend themselves also to active learning methods (such as those presented in Section 4) and the use of spatial as well as computational abilities. Altogether, therefore, the topics provide great scope for enhancing students' enjoyment and appreciation of mathematics. They also give opportunities for developing suitably concrete approaches to some of the more abstract material, notably algebra and functions (see Section 4.8).
The algebra section is slightly expanded. The formal algebraic content of the 1987 syllabus was so slight that students may not have had scope to develop their understanding; alternatively, teachers may have chosen to omit the topic. The rationale for the present adjustment might be described as "use it or lose it". The hope is that the students will be able to use it, and that suitably addressed it can help them in making some small steps towards the more abstract mathematics which they may need to encounter later in the course of their education.
Overall, therefore, it is hoped that the balance between the syllabuses is improved. In particular, the Ordinary level syllabus may be better positioned between a more accessible Higher level and a slightly expanded Foundation level.
CHANGES IN EMPHASIS
The brief for revision of the syllabuses, as described in Section 1.2, precluded a root-and-branch reconsideration of their style and content. However, it did allow for some changes in emphasis: or rather, in certain cases, for some of the intended emphases to be made more explicit and more clearly related to rationale, content, assessment, and via the Guidelines methodology. The changes in, or clarification of, emphasis refer in particular to the following areas.
Understanding
General objectives B and C of the syllabus refer respectively to instrumental understanding (knowing "what" to do or "how" to do it, and hence being able to execute procedures) and relational understanding (knowing "why", understanding the concepts of mathematics and the way in which they connect with each other to form so-called "conceptual structures"). When people talk of teaching mathematics for or learning it with understanding, they usually mean relational understanding. The language used in the Irish syllabuses to categorise understanding is that of Skemp; the objectives could equally well have been formulated in terms of "procedures" and "concepts".
Research points to the importance of both kinds of understanding, together with knowledge of facts (general objective A), as components of mathematical proficiency, with relational understanding being crucial for retaining and applying knowledge. The Third International Mathematics and Science Study, TIMSS, indicated that Irish teachers regard knowledge of facts and procedures as particularly important unusually so in international terms; but it would appear that less heed is paid to conceptual/relational understanding. This is therefore given special emphasis in the revised syllabuses. Such understanding can be fostered by active learning, as described and illustrated in Section 4. Ways in which relational understanding can be assessed are considered in Section 5.
Communication
General objective H of the syllabus indicates that students should be able to communicate mathematics, both verbally and in written form, by describing and explaining the mathematical procedures they undertake and by explaining their findings and justifying their conclusions. This highlights the importance of students expressing mathematics in their own words. It is one way of promoting understanding; it may also help students to take ownership of the findings they defend, and so to be more interested in their mathematics and more motivated to learn.
The importance of discussion as a tool for ongoing assessment of students' understanding is highlighted in Section 5.2. In the context of examinations, the ability to show different stages in a procedure, explain results, give reasons for conclusions, and so forth, can be tested; some examples are given in Section 5.6.
Appreciation and enjoyment
General objective I of the syllabus refers to appreciating mathematics. As pointed out earlier, appreciation may develop for a number of reasons, from being able to do the work successfully to responding to the abstract beauty of the subject. It is more likely to develop, however, when the mathematics lessons themselves are pleasant occasions.
In drawing up the revised syllabus and preparing the Guidelines, care has been taken to include opportunities for making the teaching and learning of mathematics more enjoyable. Enjoyment is good in its own right; also, it can develop students' motivation and hence enhance learning. For many students in the junior cycle, enjoyment (as well as understanding) can be promoted by the active learning referred to above and by placing the work in appropriate meaningful contexts. Section 4 contains many examples of enjoyable classroom activities which promote both learning and appreciation of mathematics. Teachers are likely to have their own battery of such activities which work for them and their classes. It is hoped that these can be shared amongst their colleagues and perhaps submitted for inclusion in the final version of the Guidelines.
Of course, different people enjoy different kinds of mathematical activity. Appreciation and enjoyment do not come solely from "games"; more traditional classrooms also can be lively places in which teachers and students collaborate in the teaching and learning of mathematics and develop their appreciation of the subject. Teachers will choose approaches with whichthey themselves feel comfortable and which meet thelearning needs of the students whom they teach.
The changed or clarified emphasis in the syllabuses will be supported, where possible, by corresponding adjustments to the formulation and marking of Junior Certificate examination questions. While the wording ofquestions may be the same, the expected solutions may bedifferent. Examples are given in Section 5.
3.4 CHANGES IN THE PRIMARY CURRICULUM
The changes in content and emphasis within the revised Junior Certificate mathematics syllabuses are intended, inter alia, to follow on from and build on the changes in the primary curriculum. The forthcoming alterations (scheduled to be introduced in 2002, but perhaps starting earlier in some classrooms, as teachers may anticipate the formal introduction of the changes) will affect the knowledge and attitudes that students bring to their second level education. Second level teachers need to be prepared for this. A summary of the chief alterations is given below; teachers are referred to the revised Primary School Curriculum for further details.
CHANGES IN EMPHASIS
In the revised curriculum, the main changes of emphasis are as follows.
There is more emphasis on
setting the work in real-life contexts
learning through hands-on activities (using concrete materials/manipulatives, and so forth)
understanding (in particular, gaining appropriaterelational understanding as well as instrumentalunderstanding)
appropriate use of mathematical language
recording
problem-solving.
There is less emphasis on
learning routine procedures with no context provided
doing complicated calculations.
CHANGES IN CONTENT
The changes in emphasis are reflected in changes to the content, the main ones being as follows.
New areas include
introduction of the calculator from Fourth Class (augmenting, not replacing, paper-and-pencil techniques)
(hence) extended treatment of estimation;
increased coverage of data handling
introduction of basic probability ("chance").
New terminology includes
the use of the "positive" and "negative" signs for denoting a number (as in +3 [positive three], -6 [negative six] as well as the "addition" and "subtraction" signs for denoting an operation (as in 7 + 3, 24 9)
explicit use of the multiplication sign in formulae (as in 2 ×r , l ×w).
The treatment of subtraction emphasises the "renaming" or "decomposition" method (as opposed to the "equal additions" method the one which uses the terminology "paying back") even more strongly than does the 1971 curriculum. Use of the word "borrowing" is discouraged.
The following topics are among those excluded from the revised curriculum:
unrestricted calculations (thus, division is restricted to at most four-digit numbers being divided by at most two-digit numbers, and for fractions to division of whole numbers by unit fractions)
(Some of these topics were not formally included in the 1971 curriculum, but appeared in textbooks and were taught in many classrooms.)
NOTE
The reductions in content have removed some areas of overlap between the 1971 Primary School Curriculum and the Junior Certificate syllabuses. Some overlap remains, however. This is natural; students entering second level schooling need to revise the concepts and techniques that they have learnt at primary level, and also need to situate these in the context of their work in the junior cycle.
3.5 LINKING CONTENT AREAS WITH AIMS
Finally, in this section, the content of the syllabuses is related to the aims and objectives. In fact most aims and objectives can be addressed in most areas of the syllabuses. However, some topics are more suited to the attainment of certain goals or the development of certain skills than are others. The discussion below highlights some of the main possibilities, and points to the goals that might appropriately be emphasised when various topics are taught and learnt. Phrases italicised are quoted or paraphrased from the aims as set out in the syllabus document. Section 5 of these Guidelines indicates a variety of ways in which achievement of the relevant objectives might be encouraged, tested or demonstrated.
SETS
Sets provide a conceptual foundation for mathematics and a language by means of which mathematical ideas can be discussed. While this is perhaps the main reason for which set theory was introduced into school mathematics, its importance at junior cycle level can be described rather differently.
Set problems, obviously, call for skills of problem-solving; in particular, they provide occasions for logical argument. By using data gathered from the class, they even offer opportunities for simple introduction to mathematical modelling in contexts to which the students can relate.
Moreover, set theory emphasises aspects of mathematics that are not purely computational. Sets are about classification, hence about tidiness and organisation. This can lead toappreciation of mathematics on aesthetic grounds and can help to provide a basis forfurther education in the subject.
An additional point is that this topic is not part of the Primary School Curriculum, and so represents a new start, untainted by previous failure. For some students, therefore, there are particularly important opportunities for personal development.
NUMBER SYSTEMS
While mathematics is not entirely quantitative, numeracy is one of its most important aspects. Students have been building up their concepts of numbers from a very early stage in their lives. However, moving from familiarity with natural numbers (and simple operations on them) to genuine understanding of the various forms in which numbers are presented and of the uses to which they are put in the world is a considerable challenge.
Weakness in this area destroys students' confidence andcompetence by depriving them of theknowledge, skillsand understanding needed for continuing theireducation and for life and work. It therefore handicaps their personal fulfilment and hencepersonaldevelopment.
The aspect of "understanding" is particularly important or, perhaps, has had its importance highlighted with advances in technology.
Students need to become familiar with the intelligent and appropriate use of calculators, while avoiding dependence on the calculators for simple calculations.
Complementing this, they need to develop skills in estimation and approximation, so that numbers can be used meaningfully.
APPLIED ARITHMETIC AND MEASURE
This topic is perhaps one of the easiest to justify in terms of providing mathematics needed for life, workand leisure.
Students are likely to use the skills developed here in "everyday" applications, for example in looking after their personal finances and in structuring the immediate environment in which they will live. For many, therefore, this may be a key section in enabling studentsto develop a positive attitude towards mathematics as avaluable subject of study.
There are many opportunities for problem-solving, hopefully in contexts that the students recognise as relevant.
The availability of calculators may remove some of the drudgery that can be associated with realistic problems, helping the students to focus on the concepts and applications that bring the topics to life.
ALGEBRA
Algebra was developed because it was needed because arguments in natural language were too clumsy or imprecise. It has become one of the most fundamental tools for mathematics.
As with number, therefore, confidence andcompetence are very important. Lack of these underminethepersonal development of the students by depriving them of the knowledge, skills and understanding needed forcontinuing their education and for life and work.
Without skills in algebra, students lack the technical preparation for study of other subjects in school, and in particular their foundation for appropriate studies lateron including further education in mathematics itself.
It is thus particularly important that students develop appropriate understanding of the basics of algebra so that algebraic techniques are carried out meaningfully and not just as an exercise in symbol-pushing.
Especially for weaker students, this can be very challenging because algebra involves abstractions andgeneralisations.
However, these characteristics are among the strengths and beauties of the topic. Appropriately used, algebra can enhance the students' powers of communication, facilitate simplemodelling and problem-solving, and hence illustrate the power of mathematics as a valuablesubject of study.
STATISTICS
One of the ways in which the world is interpreted for us mathematically is by the use of statistics. Their prevalence, in particular on television and in the newspapers, makes them part of the environment in which children grow up, and provides students with opportunities for recognition and enjoyment of mathematics in the worldaround them.
Many of the examples refer to the students' typical areas of interest; examples include sporting averages and trends in purchases of (say) CDs.
Students can provide data for further examples from their own backgrounds and experiences.
Presenting these data graphically can extend students'powers of communication and their ability to shareideas with other people, and may also provide anaesthetic element.
The fact that statistics can help to develop a positiveattitude towards mathematics as an interesting andvaluable subject of study even for weaker students who find it hard to appreciate the more abstract aspects of the subject explains the extra prominence given to aspects of data handling in the Foundation level syllabus, as mentioned earlier. They may be particularly important in promotingconfidence and competence in both numerical and spatial domains.
GEOMETRY
The study of geometry builds on the primary school study of shape and space, and hence relates to mathematics in the world around us. In the junior cycle, different approaches to geometry address different educational goals.
More able students address one of the greatest of mathematical concepts, that of proof, and hopefully come to appreciate theabstractions andgeneralisations involved.
Other students may not consider formal proof, but should be able to draw appropriate conclusions from given geometrical data.
MATHEMATICS
Explaining and defending their findings, in either case, should help students to further their powersof communication.
Tackling "cuts" and other exercises based on the geometrical system presented in the syllabus allows students to develop their problem-solving skills.
Moreover, in studying synthetic geometry, students are encountering one of the great monuments to intellectual endeavour: a very special part of Western culture.
Transformation geometry builds on the study of symmetry at primary level. As the approach to transformation geometry in the revised Junior Certificate syllabus is intuitive, it is included in particular for its aesthetic value.
With the possibility of using transformations in artistic designs, it allows students to encounter creative aspectsof mathematics and to develop or exercise their own creative skills.
It can also develop their spatial ability, hopefully promotingconfidence and competence in this area.
Instances of various types of symmetry in the natural and constructed environment give scope for students' recognition and enjoyment of mathematics in the worldaround them.
Coordinate geometry links geometrical and algebraic ideas. On the one hand, algebraic techniques can be used to establish geometric results; on the other, algebraic entities are given pictorial representations.
Its connections with functions and trigonometry, as well as algebra and geometry, make it a powerful tool for the integration of mathematics into a unified structure.
It illustrates the power of mathematics, and so helps to establish it with students as a valuable subject of study.
It provides an important foundation for appropriatestudies later on.
The graphical aspect can add a visually aestheticdimension to algebra.
TRIGONOMETRY
Trigonometry is a subject that has its roots in antiquity but is still of great practical use to-day. While its basic concepts are abstract, they can be addressed through practical activities.
Situations to which it can be applied for example, house construction, navigation, and various ball games include many that are relevant to the students' life, work and leisure.
It can therefore promote the students' recognition andenjoyment of mathematics in the world around them.
With the availability of calculators, students may more easily develop competence and confidence through their work in this area.
FUNCTIONS AND GRAPHS
The concept of a function is crucial in mathematics, and students need a good grasp of it in order to prepare a firm foundation for appropriate studies lateron and in particular, a basis for further education inmathematics itself.
The representation of functions by graphs adds a pictorial element that students may find aesthetic as well as enhancing their understanding and their abilityto handle generalisations.
This topic pulls together much of the groundwork done elsewhere, using the tools introduced and skills developed in earlier sections and providing opportunities forproblem-solving and simple modelling.
For Foundation students alone, simple work on the set-theoretic treatment of relations has been retained. In contexts that can be addressed by those whose numerical skills are poor, it provides exercises in simple logical thinking.
NOTE
The foregoing argument presents just one vision of the rationale for including the various topics in the syllabus and for the ways in which the aims of the mathematics syllabus can be achieved. All teachers will have their own ideas about what can inspire and inform different topic areas. Their own personal visions of mathematics, and their particular areas of interest and expertise, may lead them to implement the aims very differently from the way that is suggested here. Visions can profitably be debated at teachers' meetings, with new insights being given and received as a result.
The tentative answers given here with regard to whycertain topics are included in the syllabus are, of course, offered to teachers rather than junior cycle students. In some cases, students also may find the arguments relevant. In other cases, however, the formulation is too abstract or the benefit too distant to be of interest. This, naturally, can cause problems. Clearly it would not be appropriate to reduce the syllabus to material that has immediately obvious applications in the students' everyday lives. This would leave them unprepared for further study, and would deprive them of sharing parts of our culture; in any case, not all students are motivated by supposedly everyday topics.
Teachers are therefore faced with a challenging task in helping students find interest and meaning in all parts of the work. Many suggestions with proven track records in Irish schools are offered in Section 4. As indicated earlier, it is hoped that teachers will offer more ideas for an updated version of the Guidelines. | 677.169 | 1 |
Delphi For Fun - Gary Darby; Intellitech Systems Inc.
Delphi is based on the Pascal programming language developed in the early 1970s by Niklaus Wirth and named after mathematician Blaise Pascal. This site explores the use of programming as a tool in math problem solving, discussing interesting problems,
...more>>
Delta Blocks - Hop David
A way to model different 3-D tessellations and a tool for studying geometry, crystallography, and polyhedra. Delta blocks were inspired by M. C. Escher's print "Flatworms," which he said demonstrates that one can build a house not only with the usualDennis Stanton
Dennis Stanton is a professor at the University of Minnesota studying combinatorics and hypergeometric functions. Many of his papers are available online in PostScript and PDF formats. There are also exams and solutions from previous classes, and a complete
...more>>
Design Science - Design Science, Inc.
Math publishing and presentation tools for the web: MathType, the professional version of Equation Editor, for Windows or Mac; WebEQ, for building interactive math web pages; MathFlow, math publishing for the enterprise; and MathPlayer, to display MathML
...more>> | 677.169 | 1 |
Class1
Course: MATH 212, Fall 2009 School: Goshen Rating:
Word Count: 226
Document Preview
1: Name:
Class January 9, 2008 To Do for Friday, January 11, 2008 1. Read Sections 5.6, Integration by Parts 2. Complete this handout to turn in. You may do this handout using your text or notes. You may discuss general differentiation and integration strategies with others, but you are to do the problems on your own without looking at anyone else's work. This handout represents some of the topics and techniques 174, Winter 2000 1. Answer the following questions: a) b) c) d) e)Initial: _What are the primary advantages of double heterostructures (DH) for lasers? Why is the absorption region of a typical Si photodiode much thicker than that of a typical
EE 174 4/7/2003HW#1 Due 4/16/03 (in class) No Late HW will be acceptedSpring 2003 Prof. Ming Wu1) For a quantum receiver (i.e., the signal is 1 if one or more photons are detected and 0 if no photons are detected), the sensitivity is 10 photons
Limiting Privacy Breaches in Privacy Preserving Data MiningAlexandre EvmievskiCornell University [email protected] GehrkeCornell University [email protected] has been increasing interest in the problem of building
Calculus II Class 2, January 11, 2008 Topic:Section 5.5: Substitution and Section 5.6: Integration by Parts Important Concepts: Symmetry in integrals. Importance of the "constant of integration". The rule for integration by parts. Which function
Lab 6 You are to begin with an abstract class called Policeman that might describe some of the policeman on a police force. The constructor contains the first name, last name, and years of service of an individual on the force. import java.text.*; pu
Review of International Studies (1997), 23, 271291 Copyright British International Studies AssociationCold War, post-Cold War: does it make a difference for the Middle East?EFRAIM KARSHWhile the euphoric predictions of a `New World Order' and t
APOLLOS EYE: A CULTURAL GEOGRAPHY OF THE GLOBE Denis Cosgrove UCLAHettner Lecture I June 2005 The globe is Geographys icon (Fig.) Although academic geographers commonly express irritation at the popular expectation that they should possess an encycl
Modern Italy Vol. 12, No. 1, February 2007, pp. 1738Remaking Italy? Place Configurations and Italian Electoral Politics under the Second RepublicJohn AgnewThe Italian Second Republic was meant to have led to a bipolar polity with alternation in
letters to natureas described29. Protein oxidation in erythroid tissues from anaemic Prdx1 2/2 and agematched wild-type mice was determined by incubating lysates in the presence or absence of 2,4-dinitrophenylhydrazine (DNPH) to derivatize oxidized
Endocytosis: clathrin-mediated membrane buddingErnst J Ungewickell1 and Lars Hinrichsen2Clathrin-dependent endocytosis is the major pathway for the uptake of nutrients and signaling molecules in higher eukaryotic cells. The long-held tenet that cla | 677.169 | 1 |
Mathematical Applications in Agriculture the specialized math skills you need to be successful in today's farming industry with MATHEMATICAL APPLICATIONS IN AGRICULTURE, 2nd Edition. Invaluable in any area of agriculture-from livestock and dairy production to horticulture and agronomy--this easy to follow book gives you steps by step instructions on how to address problems in the field using math and logic skills. Clearly written and thoughtfully organized, the stand-alone chapters on mathematics involved in crop production, livestock production, and financial management allow you... MORE to focus on those topics specific to your area while useful graphics, case studies, examples, and sample problems to help you hone your critical thinking skills and master the concepts. Invaluable in any area of agriculture or as a hands-on learning tool in introductory math courses, the 2nd Edition of MATHEMATICAL APPLICATIONS IN AGRICULTURE demonstrates industry-specific methods for solving real-world problems using applied math and logic skills students already have. | 677.169 | 1 |
College Algebra-enhanced Edition - 6th edition
Summary: Accessible to students and flexible for Accessible to students and flexible for instructors, COLLEGE ALGEBRA, SIXTH EDITION, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphi...show moreng calculators. Additional program components that support student success include Eduspace tutorial practice, online homework, SMARTHINKING Live Online Tutoring, and Instructional DVDs. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Sixth Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new | 677.169 | 1 |
MATLAB & Simulink Student Version 2012a
Description
Get the essential tools for your courses in engineering, math, and science.
MATLAB® is a high-level language and interactive environment that lets you focus on your course work and applications, rather than on programming details. It enables you to solve many numerical problems in a fraction of the time it takes to write a program in a lower-level language such as Java™, C, C++, or Fortran. You can also use MATLAB to analyze and visualize data using automation capabilities, thereby avoiding the manual repetition common with other products.
The MATLAB in Student Version provides all the features and capabilities of the professional version of MATLAB software, with no limitations. There are a few small differences between the Student Version interface and the professional version of MATLAB:
The MATLAB prompt in Student Version is EDU>>
Printouts contain this footer: Student Version of MATLAB
For more information on this product please visit the MathWorks website:
IMPORTANT NOTE:Proof of student status is required for activation of license
Features
Contains R2012a versions of:
MATLAB
Simulink
Symbolic Math Toolbox
Control System Toolbox
Signal Processing Toolbox
Signal Processing Blockset
Statistics Toolbox
Optimization Toolbox
Image Processing Toolbox
Student Version also comes with complete user documentation on the CD Rom.
IMPORTANT NOTE:Proof of student status is required for activation of license
New to this Edition
The 2012a release includes 2 important new features:
Target Hardware support directly from Simulink: Of special interest to educators is the addition of Simulink Control Design and Simulink features to enable project-based learning. Student Version now includes built-in Windows support to run Simulink models on low-cost target hardware, including LEGO MINDSTORMS NXT and BeagleBoard. With a click your model moves from simulation onto hardware, further increasing your return on Model-Based Design with Simulink | 677.169 | 1 |
Scope and form:
Duration of Course:
F2B
The exam date is only used to specify the deadline for the report (c.f. evaluation)
Type of assessment:
Evaluation of exercises/reports Five homework sets and three quizzes during the semester, and a final report on a project exercise. The homework and the quizzes counts together for 60% of the grade, and the report counts 40% of the grade.
Aid:
All Aid
Evaluation:
7 step scale, internal examiner
Qualified Prerequisites:
General course objectives:
The aim of this course is to provide the students with basic tools and competences regarding the analysis and applications of curves and surfaces in 3D. The main idea of the course is very well described by the following exerpt from the cover of the textbook: "Curves and surfaces are objects that everyone can see, and many questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques." One integral part of the course is to apply computer experiments with Maple in eachone of the three steps: To ask natural geometric questions, to formulate them in precise mathematical terms, and to answer them using techniques from calculus. The course also aims to give the students a firm background for further studies in the manifold engineering applications of differential geometric tools and concepts.
Learning objectives:
A student who has met the objectives of the course will be able to:
Calculate the curvature, the torsion, and the Frenet-Serret basis for a given space curve.
Apply the first and second fundamental form to analyze curves on surfaces in space.
Recognize isometries and conformal maps between simple surfaces.
Determine the principal curvatures and principal directions at every point of a given surface.
Calculate the Gauss curvature and the mean curvature at every point of a given surface.
Explain the invariant geometric significance of the Gauss curvature.
Explain the connection between the second fundamental form, the Weingarten map and the principal curvatures and directions.
Explain the connection between the total curvature, the normal curvature, and the geodesic curvature of a curve on a given surface.
Recognize geodesic curves from data about the normal curvature and the total curvature of the curves.
Apply the general surface theory to surfaces of revolution and to ruled surfaces.
Apply the Gauss-Bonnet theorem to estimate the Euler characteristic of a given surface.
Apply the general theory to a simple geometric problem and present the solution in the form of a report.
Content:
Curves and surfaces in 3D - with particular focus on metric and curvature properties. How to find the shortest path on a surface. How to bend a surface. How to calculate the number of holes of a compact surface. Individually chosen applications of differential geometry which span a diversity of possibilities including roler coaster constructions, geographic map projections, relativity (special or general), protein geometry, to mention but a few. The specific list of contents includes: Curves with constant width, the Frenet-Serret 'apparatus' for curves in 3D, first and second fundamental forms for surfaces, Gaussian curvature and mean curvature, equiareal maps, isometries, surfaces of constant curvature, geodesics, fundamental results of Gauss, Codazzi-Mainardi, and Gauss-Bonnet.
Course literature:
Andrew Pressley: Elementary Differential Geometry, Springer, 2001 | 677.169 | 1 |
Pre-Algebra Essentials For Dummies
Paperback
Click on the Google Preview image above to read some pages of this book!
Many students worry about
starting algebra. Pre-Algebra Essentials For Dummies provides
an overview of critical pre-algebra concepts to help new algebra
students (and their parents) take the next step without fear. Free of
ramp-up material, Pre-Algebra Essentials For Dummies contains
content focused on key topics only. It provides discrete explanations
of critical concepts taught in a typical pre-algebra course, from
fractions, decimals, and percents to scientific notation and simple
variable equations. This guide is also a perfect reference for parents
who need to review critical pre-algebra concepts as they help students
with homework assignments, as well as for adult learners headed back
into the classroom who just need to a refresher of the core concepts.
The Essentials For Dummies Series
Dummies is proud to present our new series, The Essentials For
Dummies. Now students who are prepping for exams, preparing to
study new material, or who just need a refresher can have a concise,
easy-to-understand review guide that covers an entire course by
concentrating solely on the most important concepts. From algebra and
chemistry to grammar and Spanish, our expert authors focus on the
skills students most need to succeed in a subject.
About The Author
Mark Zegarelli is a math tutor and author of several books, including Basic Math & Pre-Algebra For Dummies.
Reviewed By Toni Whitmont, Booktopia Buzz Editor
To read more reviews by Toni Whitmont, click here to visit the Booktopia Newsletter Archive.
We all know and love the Dummies series. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers and entire course by concentrating solely on the most important concepts. From alegbra and chemistry to grammar and Spanish, these expert authors focus on the skills students most need to succeed in a subject.
This Essentials series is perfect for final year school students, people doing bridging courses for university and mature age students needing a refresher. | 677.169 | 1 |
cheap scientific calculator that does matrix operations
cheap scientific calculator that does matrix operations
I do not have a calculator that does matrix stuff that would be great for my classes this semester. I don't want to spend $100+ on a graphing calculator since I use matlab at home strictly now. Im looking to solve simultaneous equations, matrix operations like det,eigen,mult,...etc
There is an excellent software calculator called Mathwizard that does Matrices,algebra,calculus,scientific calculator and plot graph.check it out. you can also find mobile applications that does matrices,algebra,calculus,differential equations , and plot graphs | 677.169 | 1 |
Computer Science Facilities
Pearsons Hall, Room 110
The department of mathematics and computer science runs a lab devoted to math and computing. The lab contains 11 dual-core workstations which run specialized mathematical and computer science software alongside standard publishing and spreadsheet programs. Mathematics software includes Maple and Octave, and the computer science software includes development environments for Java, C++, Scheme, Python, and many other programming languages.
We encourage math and computer science majors to learn LATEX (a program for typesetting mathematics documents), so our lab workstations run WinEdit, a text editor designed to work with LATEX. The lab also houses a Linux server and an eight node Beowulf cluster built as a joint project between students and faculty. The lab's location is Pearsons 110; it is open to all Drury students from 8 a.m. to midnight each weekday.
Next door to the lab is a lounge for mathematics and computer science majors. The lounge contains a dual-core workstation, a whiteboard, a sofa, a refrigerator, a microwave, a coffeemaker, and a television. | 677.169 | 1 |
11.1 From Arithmetic to Algebra 11.2 Evaluating Algebraic Expressions 11.3 Adding and Subtracting Algebraic Expressions 11.4 Using the Addition Property to Solve an Equation 11.5 Using the Multiplication Property to Solve an Equation 11.6 Combining the Properties to Solve Equations
Textbook– Sound copy, mild reading wear. May or may not have untested CD or Infotrac. May contain highlighting, underlining or writing in text. No international shipping.
$4.1522 +$3.99 s/h
Good
Aeden Stclair Marietta, OH
Used text book. Normal wear
$7.88 +$3.99 s/h
VeryGood
Extremely_Reliable Richmond, TX
Buy with confidence. Excellent Customer Service & Return policy.
$21.21 +$3.99 s/h
LikeNew
BookCellar-NH Nashua, NH
007330959128.50 +$3.99 s/h
New
Aeden Stclair Marietta, OH
New
$103.39 +$3.99 s/h
LikeNew
ZOF San Gabriel, CA
used - like new 7th Edition. Great condition! Possible minimal highlights Buy from trusted seller! Expedited Shipping may be available for few dollars more! Paperback | 677.169 | 1 |
Rent Textbook
Buy New Textbook
Used Textbook
We're Sorry Sold Out
eTextbook
We're Sorry Not Available
More New and Used from Private Sellers
Starting at $49To facilitate those instructors that use a more hands-on approach to teaching, an extensive Exploration Activities manual accompanies the text. The manual contains a variety of explorations for each section, which are referenced in the text by an icon in the margin. Some explorations deal directly with the content of the chapter, often making use of relevant manipulatives or other hands-on activities. Other explorations extend the content of the section either mathematically or by building a connection to the K - 8 classrooms. Most of the explorations can be done individually or with groups and should take about 30 - 45 minutes to complete. | 677.169 | 1 |
mathematicsUsing Maple, available from Adept Scientific (Letchworth, Herts), instructors can easily create interactive mathematical applications that help their colleagues and students solve problems, visualise solutions and explore conceptsAll Press ReleasesMathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students' understanding of music through mathematics.
Using Maple, available from Adept Scientific (Letchworth, Herts), instructors can easily create interactive mathematical applications that help their colleagues and students solve problems, visualise solutions and explore concepts.
Lanika announces Maplesoft's major new initiative to support teaching and learning. The Möbius Project makes it easy to create rich, interactive mathematical applications, share them with everyone, and grade them to assess understandingFor the third consecutive year, President Barack Obama used his State of the Union address to call for increased investment in science and technology. More than 40,000 Wisconsin students heed this call each day.
The Hong Kong Polytechnic University (PolyU) signed today (22 January) an agreement with the Australian Mathematics Trust (AMT) to launch the "Mathematics Challenge for Young Australians" (MCYA) in Hong KongThrough a careful treatment of number theory and geometry, Number, Shape, and Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofsMyAcademicWorkshop™ is a differientated online assesment system that helps place students into appropriate mathematics courses and helps increase student engagement and sense of accomplishment for students struggling in mathematics.
This book presents advanced mathematical descriptions and methods to help readers achieve more thorough results under more general conditions than what has been possible with previous results in the existing literature.
Physical Oceanography: A Mathematical Introduction with MATLAB® demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frameCarnegie Mellon Hosts 30th Annual Charles Drew Science Fair on March 10, 2012. The fair was created by Adolphus Patterson and C. Richard Gilcrese to encourage students to take an interest in careers in science, technology, enigneering, & math (STEM)."We're looking forward to having Big Ideas Learning join The Balancing Act on Lifetime TV. The Balancing Act Lifetime viewers will have a chance to learn how to help their children master mathematical benchmarks at each level."
Students do not need more STEM- Science, Technology, Engineering, and Mathematics -, they need immersion in the invention/innovation design process. Support Fluke - the wealth building game of accidental inventions.
Preparing the UK's next generation of engineers and technicians has taken a leap forward with the official opening of a state-of-the-art technology centre at leading independent training provider, S&B Automotive Academy in Bristol, UK. | 677.169 | 1 |
$ 14.79Schaum's has Satisfied Students for 50 Years.Now Schaum's Biggest Sellers are in New Editions!For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better,...
$ 8.79
Preempt your anxiety about PRE-ALGEBRA!Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve...
$ 14.79...
$ 10.29
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Practice Makes Perfect: Algebra, provides students with the same clear, concise approach...
$ 11.79
Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to...
$ 9.79
With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra...
$ 6.99
Passing grades in two years of algebra courses are required for high school graduation. Algebra II Essentials For Dummies covers key ideas from typical second-year Algebra coursework to help students get up... | 677.169 | 1 |
Purchasing Options:
Description
This text explores the beauty of topology and homotopy theory in a direct, engaging, and accessible manner while illustrating the power of the theory through many, often surprising, applications. It offers a comprehensive presentation that uses a combination of rigorous arguments and extensive illustrations to facilitate an understanding of the material. The author covers basic topology, ranging from the axioms of topology to proofs of important theorems. He also discusses the classification of compact, connected manifolds, ambient isotopy, and knots, which leads to coverage of homotopy theory.
Related Subjects
Name: An Illustrated Introduction to Topology and Homotopy (Hardback) – Chapman and Hall/CRC
Description: By Sasho Kalajdzievski. This text explores the beauty of topology and homotopy theory in a direct, engaging, and accessible manner while illustrating the power of the theory through many, often surprising, applications. It offers a comprehensive presentation that uses a...
Categories: Geometry, Mathematical Analysis, Mathematical Physics | 677.169 | 1 |
More from this developer
Description
Can help in a class like Linear Algebra. Solve a system of equations or find the inverse or determinant of a matrix. Use spaces between numbers in a row and a new line between rows. Numbers can be decimals or fractions; 0.75, .75, 3/4, and 1.5/2 are valid. Updates: Help Keypad /.- buttons Fixed determinants Clear button | 677.169 | 1 |
MathMagic is a feature-rich software application that supplies users with the necessary tools for creating and editing mathematical equations effortlessly. It can be used for various purposes, whether you are a student or a professor.
MathMagic Personal Edition 7.4.3.48 is a Trial. Please read this article and discover
what exactly does Trial mean.
Whether you're happy or not testing and using MathMagic Personal Edition 7.4.3.48, be our guest and let's solve all the problems related to this software together. Feel free to use:
MathMagic Personal Edition 7.4.3.48 | 677.169 | 1 |
MATH 0960 Accelerated Beginning Algebra
Lecture/Lab/Credit Hours 6 - 0 - 6
This course is for students who need to review basic algebra skills. It is a fast-paced course that contains all of the content of both MATH 0930 Beginning Algebra Part 1 and MATH 0931 Beginning Algebra Part 2 in a single course. Topics include positive and negative real-numbers, solving linear equations and inequalities along with their applications, integer exponents, operations with polynomials, factoring, rational expressions, equations of lines, and graphing of equations and inequalities10 or MATH 0930 with a grade of P, or MCC placement test | 677.169 | 1 |
atin g the importance of math in all areas of real life....
Less
Platform: WINDOW S & MACINTOSH Publish er: TOPICS Packa ging: JEWEL CASE Give your youngster a head start with Snap! Geometry the colorful CD-ROM software that focuses on higher mathematics. Designed especially for pre-teens and teens ages 11 to 16 this disc is chock full of lessons and games while stressing real-life uses of geometric fundamentals. With its solid blend of activities and education Snap! Geometry works all the angles!Snap! Learn something new each day with Snap! Everyday Fun & Learning Software. Let Snap! help you acquire new skills with the help of your PC. With great products at great prices. It's a Snap! System Requirements:PC: Pentium II 233 MHz 32 MB RAM (64MB recommended) 2MB HD 8X CD-ROM drive sound card 16-Bit (high color) or greater graphics Apple QuickTime...
Less
Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed...
Less connectionsClear show how to use various graphing calculators to solve problems more quickly. Perhaps most important--this book effectively prepares readers for further courses in mathematics.
Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications.The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of...
Less
Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this text like you. The book also provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics.
This book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. Recent findings on the diagnostics and control of chaos are presented, and suggestions are made for setting up a simple laboratory. Included is a list of topics for further discussion that may serve not only for personal practice or homework, but...
Less
- Prepare your middle school student for higher level math courses with the Horizons Pre-Algebra Set from Alpha Omega Publications! This year-long course takes students from basic operations in whole numbers, decimals, fractions, percents, roots, and exponents and introduces them to math-building concepts in algebra, trigonometry, geometry, and exciting real-life applications. Divided into 160 lessons, this course comes complete with one consumable student book, a student tests and resources book, and an easy-to-use teacher's guide. Every block of ten lessons begins with a challenging set of problems that prepares students for standardized math testing and features personal interviews showing how individuals make use of math in their everyday lives. - Introduce your junior...
Less
Give geometry a go with students in grades 7 and up using Helping Students Understand Geometry. This 128-page book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. The book supports NCTM standards and includes chapters on topics such as coordinates, angles, patterns and reasoning, triangles, polygons and quadrilaterals, and circles Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces - Benz, Walter THIS IS A BRAND NEW UNOPENED ITEM. Desc connectionsTurn Math Frustration Into Math Fun!Product InformationA unique learning adventure for children aged 7-11 developed by educationexperts! I Love Math is a spectacular animated time-travel adventure. No matter what yourchild's level of math prehension I Love Math will reinforce skills in keycurriculum areas increase understanding of concepts such as fractions geometryand measurements and develop the real-world math and critical- thinking skillsessential to success in school and beyond.Kids have fun with six exciting games thousands of math problems more than1000 animations and is for one or two players.I Love Math blends a solid curriculum- oriented content and incentive- drivengameplay - all brought to life by zany characters and wacky situations. Skills Learned Addition and subtraction Emerging Applications of Algebraic Geometry THIS IS A BRAND NEW UNOPENED ITEM. Buy SKU: 240879661 If you want additional information Math
$88.98
Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems (Encyclopedia of Mathematics and its Applications)
+ $5.24 shipping
/variational-principles-in/3oeMnHlh0baEUuUF3wIMCA==/info
Amazon Marketplace
Fantastic prices with ease & comfort of Amazon.com!
(
In stock
)
This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the field, with examples and exercises suitable for graduate students entering research. The method of presentation will appeal to readers with diverse backgrounds in functional analysis, differential geometry and partial differential equations. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. Since much of the material has a strong geometric flavor, the authors have supplemented the text with figures to illustrate the...
Less
Stunning all-new 2CD release from Fischer-Z front man John Watts. Abandoning the clean production of his past few albums, Watts tackles each song armed only with his guitar and minimal percussion. Raw emotion and humor still inhabit his lyrics, and this double disc features some of his finest songs in years. Also features an additional booklet of his poetry that he composed at the same time as the 16 songs here. Silver Sonic. 2006
In the Beginning... makes learning the Bible fun! Children can actively participate in a curriculum that is child-targeted, relevant, and teaches the Bible creatively. It helps provide an emotionally, physically, and spiritually safe environment for kids, and fosters family involvement through take-home sheets, which include a family activity to reinforce the key concept from the lesson.This box includes four individual quarter kits for Fall, Winter, Spring, and Summer. Each quarter kit contains:Three Identical Large Group/Small Group Lesson CDs- Director's materials, Administrator's materials, Activity Stations materials, Large Group and Small Group lessons, lesson visuals and application materials, and child take-home sheets.One Sunday School Lesson CD-Teacher's Notes, Activity Station...
Less
Dan In Real Life (2007) Steve Carell, Juliette BinocheDirector: Peter HedgesCo-stars: Dane Cook, Alison Pill, Dianne Wiest, John Mahoney98 minutes, ColorDVD: Region 1Early in Peter Hedges's "Dan in Real Life," the title character, at a bookstore, meets the woman he will fall in love with. Mistaking him for an employee, she breathlessly tries to describe the kind of book she's looking for. (He responds by gathering up a random assortment of volumes that includes the poems of Emily Dickinson, "Anna Karenina" and "Everybody Poops.") "I want something funny," she says. "But not laugh-out-loud funny. And definitely not making-fun-of-peop le funny. I want something human funny." It does not take long to recognize this as a declaration of the film's own intentions. Its moral is "expect to be Math Tee, TShirt, Shirt
The Flower Of Life is the gateway to the mysteries of Sacred Geometry Sacred geometry Tee, TShirt, Shirt
$39.94
Content Area Mathematics for Secondary Teachers: The Problem Solver
Free Shipping
/content-area-mathematics/bmYy6w-VmJvZt19TWO34WA==/info
Amazon
Get free shipping on orders over $25!
(
In stock
)
Free Shipping
Content Area Mathematics for Secondary Teachers: The Problem Solver provides pre-service and in-service educators with a concise, but rigorous review of classical mathematical theory and effective problem solving strategies required to help grade 7-12 students master math content. Developed especially for math teachers, by math teachers, The Problem Solver provides a one-stop review of need-to-know fundamental mathematics content in the following areas: general properties of the real numbers, goups and fields, geometry, trigonometry, functions, vectors, conic sections, statistics, calculus, linear algebra and discrete mathematics. Authors Cook and Romalis have compiled accessible theory and test-drive applications from university level Middle and Secondary level content area mathematics...
Less
Modern Kundalini yoga Stimulate the chakras through breathing, movement and mantras Clear the mind and body Taught by classical pianist and performer Maya Fiennes Made exclusively by Gaiam Maya Fiennes combines her talents as a successful classical pianist and performer with her upbeat personality to create a unique style of Kundalini yoga for modern living. In this 60-minute practice, she takes you through a series of exercises to stimulate the powerful centers in the body, the chakras. Through breathing techniques, movements and mantras, Maya demonstrates how to clear the mind and body, allowing viewers to tap into the universal forces and manifest anything in life. 60 minutes. Made in the USA.
Give The Gift of Education! And Conquer anxiety forever. // We all know how hard it is to study and understand math. Why can't it be easier? How can I help my children, grandchildren or myself succeed in math and succeed in life? We can help! Our series covers all major areas of math and makes learning math simple and fun. Learn at your own pace and have the luxury of reviewing as often as you like, without the embarrassment and expense of asking a tutor. // The MATH MADE EASY programs are a unique combination of step-by-step instruction which are designed by creative and experienced mathematicians and approved by math educators nationwide. They are enhanced by colorful computer graphics and real life applications. Used by millions of students all across America in schools and homes | 677.169 | 1 |
1598639 Math: Algebra (Master Math Series)
Get ready to master the principles and operations of algebra! Master Math: Algebra is a comprehensive reference guide that explains and clarifies algebraic principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced topics that will help prepare you for pre-calculus and calculus, the book helps clarify algebra using step-by-step procedures and solutions, along with examples and applications Master Math: Algebra will help you master everything from simple algebraic equations to polynomials and graphing | 677.169 | 1 |
Intermediate Algebra - 4th edition
Summary: Algebra can be like a foreign language. But one text delivers an interpretation you can fully understand. Building a conceptual foundation in the ''language of algebra,'' iNTERMEDIATE ALGEBRA, 4e provides an integrated learning process that helps you expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Packed with real-life applications of math, it blends instructional approaches that include vocabulary, practice, and well-defined pedagogy w...show moreith an emphasis on reasoning, modeling, communication, and technology skills. The authors' five-step problem-solving approach makes learning easy. More student-friendly than ever, the text offers a rich collection of student learning tools, including Enhanced WebAssign online learning system. With INTERMEDIATE ALGEBRA, 4e, algebra makes sense | 677.169 | 1 |
Search Mathematical Communication:
Mathematical Communication
Welcome to MathDL Mathematical Communication
Topic Teaching Tip(s):
Courses in which students communicate about mathematics | Including writing in math classes | Including oral communication in math classes | General principles of mathematical communication
This website is by and for educators whose students write, give presentations, or communicate informally about mathematics. Some educators would like students to learn to communicate as mathematicians; others would like students to talk or write about math in order to better learn math. This site supports both goals by offering pedagogical advice, materials, and links to helpful resources. | 677.169 | 1 |
Perfect for either undergraduate mathematics or science history courses, this account presents a fresh and detailed reconstruction of the development of two mathematical fundamentals: numbers and infinity. One of the rare texts that offers a friendly and conversational tone, it avoids tedium and cont... read more
Customers who bought this book also bought:
Our Editors also recommend:
A Source Book in Mathematics by David Eugene Smith The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhereElementary Number Theory: Second Edition by Underwood Dudley Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.
History of the Theory of Numbers by Leonard Eugene Dickson Save 10% when you buy all 3 volumes of this set. Includes "Volume I: Divisibility and Primality," "Volume II: Diophantine Analysis," and "Volume III: Quadratic and Higher Forms."Product Description:
Perfect for either undergraduate mathematics or science history courses, this account presents a fresh and detailed reconstruction of the development of two mathematical fundamentals: numbers and infinity. One of the rare texts that offers a friendly and conversational tone, it avoids tedium and controversy while maintaining historical accuracy in defining its concepts' profound mathematical significance. The authors begin by discussing the representation of numbers, integers and types of numbers, and cubic equations. Additional topics include complex numbers, quaternions, and vectors; Greek notions of infinity; the 17th-century development of the calculus; the concept of functions; and transfinite numbers. The text concludes with an appendix on essay topics, a bibliography, and an index | 677.169 | 1 |
September 2007 This is the second installment of a new feature in Plus : the teacher package. Every issue contains a package bringing together all Plus articles about a particular subject from the UK National Curriculum. Whether you're a student studying the subject, or a teacher teaching it, all relevant Plus articles are available to you at a glance.
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics , biology , earth science , meteorology ) and engineering disciplines (e.g. computer science , artificial intelligence ), but also in the social sciences (such as economics , psychology , sociology and political science ); physicists , engineers , statisticians , operations research analysts and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. Mathematical models can take many forms, including but not limited to dynamical systems , statistical models , differential equations , or game theoretic models .
The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is subtracted from the desired value to create the error signal, which is amplified by the controller.
A signal-flow graph (SFG) is a special type of block diagram [ 1 ] —and directed graph —consisting of nodes and branches. Its nodes are the variables of a set of linear algebraic relations. An SFG can only represent multiplications and additions.
Little Green Book Nearly everything that occurs in the universe can be considered a part of some system, and that certainly includes human behavior and, potentially, human attitudes as well. But this does not mean that systems theory, and thus graph algebra, is appropriate for use in all situations. There are many competing approaches to the study of social and political phenomena, and systems theory using graph algebra is only one such approach.
From the publisher's description of the book: Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied. Key Features:
(This is the first in a series on the use of Graph Algebraic models for Social Science.) Linear Difference models are a hugely important first step in learning Graph Algebraic modeling. That said, linear difference equations are a completely independent thing from Graph Algebra.
(This is the second of a series of ongoing posts on using Graph Algebra in the Social Sciences.) First-order linear difference equations are powerful, yet simple modeling tools. They can provide access to useful substantive insights to real-world phenomena. They can have powerful predictive ability when used appropriately. Additionally, they may be classified in any number of ways in accordance with the parameters by which they are defined. And though they are not immune to any of a host of issues, a thoughtful approach to their application can always yield meaningful information, if not for discussion then for further refinement of the model.
Data must be selected carefully. The predictive usefulness of the model is grossly diminished if outliers taint the available data. Figure 1, for instance, shows the Defense spending (as a fraction of the national budget) between 1948 and 1968. Note how the trend curve (as defined by our linear difference model from the last post : see appendix for a fuller description) is a very poor predictor. Whatever is going on here isn't a first-order process.
This is sort-of related to my sidelined study of graph algebra. I was thinking about data I could apply a first-order linear difference model to, and the stock market came to mind. After all, despite some black swan sized shocks, what better predicts a day's closing than the previous day's closing? So, I hunted down the data and graphed exactly that: | 677.169 | 1 |
Mathland The Expert Version
9780521468022
ISBN:
0521468027
Publisher: Cambridge University Press
Summary: Mathland is a problem-solving adventure. Pupils are given a problem to solve by an inhabitant of Mathland - the answer determines the next page they go to. The problems come from all areas of maths (apart from statistics) and are intended to stimulate both analytical and empirical approaches. | 677.169 | 1 |
Introductory Algebra and Trigonometry With Applications
9780471368762
ISBN:
0471368768
Pub Date: 1999 Publisher: Wiley & Sons, Incorporated, John
Summary: Introductory Algebra and Trignometry with Applications by Paul Calter and Carol Felsinger Rogers This textbook introduces all the important topics for a student who needs preparatory, review, or remedial work in mathematics. Adapted from Calter's Technical Mathematics, it uses an intuitive approach and gives information in very smallsegments. Careful page layout and numerous illustrations make the material easy to fo...llow. Features of Introductory Algebra and Trigonometry with Applications include the following.Graphing Calculator: The graphing calculator has been fully integrated throughout the text, and calculator problems are given in the exercises. The book does not present any particular calculator. Keystrokes are shown in the early chapters, with verbal descriptions given thereafter.Common Error Boxes: Many of the mistakes that students repeatedly make have been identified and are presented in the text as Common Error boxes.Summary of Facts and Formulas: All important formulas are boxed and numbered in the text and are listed in the Summary of Facts and Formulas at the end of the book.Examples: The many fully worked examples are specifically chosen to help the student do the exercises.Exercises: A large number of exercises is given after each section, graded by difficulty and grouped by type.Chapter Review Exercises: Every chapter ends with a set of Chapter Review Exercises. In contrast to the exercises, most are scrambled as to type and difficulty, requiring the student to be able to identify type.Applications: Applications drawn from many fields are included in the examples, the exercises, and the Chapter Review.Writing Questions: The "writingacrossthecurriculum" movement urges writing in every course as an aid to learning. In response, this text provides a writing question at the end of every chapter.Team Projects: As an aid to collaborative learning, a team project is included at the end of most chapters.Thorough Support Material: Among valuable components found at the end of the book are the Summary of Facts and Formulas, Conversion Factors, Answers to Selected Exercises, Index to Applications, Index to Writing Questions, Index to Team Projects, and General Index.For the Instructor: An Instructor's Manual contains workedout solutions to every evennumbered problem in the text. This most valuable supplement is available to any instructor using the textbook.For more information on this book or any of Prentice Hall's other new technology titles, visit our Web site at | 677.169 | 1 |
0495558885
9780495558880
111178230X
9781111782306 features and patient explanation to give students a book that preserves the integrity of mathematics, yet does not discourage them with material that is confusing or too rigorous. Long respected for its ability to help students quickly master difficult problems, this book also helps them develop the skills they'll need in future courses and in everyday life. This new edition has the mathematical precision instructors have come to expect, and by bringing in new co-author, Jeff Hughes, the authors have focused on making the text more modern to better illustrate to students the importance of math in their world. «Show less... Show more»
Rent College Algebra 10th Edition today, or search our site for other Frisk | 677.169 | 1 |
Overview
Because of the fact that we will be extending so
many areas, this is a perfect opportunity to solidify everything that
you have done before, or to get little tastes of things you haven't
seen before. We'll start with some basics of real
numbers, then earn the basics of what and why complex numbers are.
After that we will see interplay with geometry, linear algebra,
and then head toward topics from calculus: series,
differentiation and end with the richest area of all - integration.
Grading
Half of your grade will come from problem sets.
Another tenth will come from a final project and each of two
midterm exams. The final fifth will come from the final exam.
Problem Sets
After we finish each chapter problem sets will be
collected. They will be returned with a letter grade based on the
following factors: number of exercises correctly completed,
difficulty of exercises correctly completed, number of exercises
completed by classmates, and some subjective determination on my part
as to what seems appropriate. Each problem set will be scaled
using a linear function of the number of exercises completed (problems
correctly completed by only one student will earn two points).
Submitting no problem set by the day it is due will earn a score
of zero. I strongly recommend consulting
with me as you work on these problem sets. I also recommend
working together on them, however I want to carefully emphasise that
each must
write up their own well-written solutions. A good rule for this
is it is encouraged to speak to each other about the problem, but you
should not read each other's solutions. A violation of this
policy will result in a zero for the entire assignment and reporting to
the Dean of Students for a violation of academic integrity.
Final Project
Your final project will constitute writing up a
detailed explanation (filling in the gaps) of a topic in the text that
we will omit (or another topic selected by you and approved by me) ,
and a completion of a problem set (graded as above) from the exercises
in that section.
Exams
The exams will consist of a few straightforward
problems designed to emphasise a personal understanding of the basicsAcademic Dishonesty
While working on homework with one another is
encouraged, all write-ups of solutions must be your own. You are
expected to be able to explain any solution you give me if asked.
The
Student Academic Dishonesty Policy and Procedures
of observance of religious holidays the opportunity to make up missed
work.
You are responsible for notifying me by September 11 of plans to
observe
a holiday.
Schedule (loose and subject to variations)
August 29 Introduction
31
Chapter 1 (1-3, 4, 5)
September 2
7
9
12
14 Chapter 2 (1, 2, 6, 7, 8)
16 PS1 due
19
21
23
26
28
Chapter 3 (1, 2, 4, 5) PS2 due
30
October 3 exam (Chapter 1-2)
5
7
12
14
17 Chatper 4 (2.3, 2.4, 2.5, 1, 2)
19
21 PS3 due
24
26
28
31
November 2 Chapter 5 (1, 2, 3, 4, half of 5) PS4 due
4
7 exam (Chapter 3-4)
9
11
14
16
18 Chapter 6 (1, 2, 4, 5)
21 PS5 due
28
30
December 2
5 Chapter 7 (1, 2)
7
9
12 Review, PS6-7 due, Final Project due
Monday, December 19 12N - 3p
Final Exam (half 5-7, half 1-4)
Learning Outcomes
Upon successful completion of this course, a student will be able to
Express complex numbers in the important equivalent forms - rectangular, polar and exponential. | 677.169 | 1 |
The Math Place
What is The Math Place? The Math Place is a free
tutoring service specifically designed for students enrolled in Learning
Center mathematics courses (ULC 147 & 148),
and MTH 115, 121, 122, 141, 142
Students should feel free
to drop in any time the Math Place is open for help with their math work.
How Can Students Use It? Students can bring problems
or questions to the Math Place and the tutors will provide assistance.
Students should rememberto bring their textbook
and notes in order to aid the tutors in explaining the relevant material. | 677.169 | 1 |
This book is a guided tour of geometry, from Euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems, and it links geometry to other branches of mathematics. It is a teaching text, with a large number of exercises woven into the exposition. Topics covered include: ruler and compass r s1tructions, transformations, triangle and circle theorems, classification of isometries and groups of isometries in dimensions 2 and 3, Platonic solids, conics, similarities, affine, projective and Mobius transformations, non-Euclidean geometry, projective geometry, the beginnings of algebraic geometry.
Stock Availability:
This title will be ordered from the publisher and usually ships by us within 15 days. Allow a few extra days for delivery | 677.169 | 1 |
Tabula Bookmark
Publisher Description
Tabula is a new software program for math instruction that joins the conveniences of a presentation program with the tools specific to teaching geometry. Tabula also excels at modeling math concepts with geometry.
A novel set of manipulation and transformation tools facilitates and extends activities that use paper, scissors, straight edge, and other hands-on items. Students can use Tabula to apply concepts in projects involving tiling patterns, tessellation, perspective drawing, and more. Tabula can be used in 5th grade through high school geometry.
Soft-Files is not responsible for the content of "Tabula" software description. We encourage you to determine whether this product or your intended use is legal. We do not encourage or condone the use of any software in violation of applicable laws. | 677.169 | 1 |
MAS170 Practical Calculus
In this course we learn how to define and evaluate derivatives and
integrals for functions which depend on more than one variable,
with an emphasis on functions of two variables, for which the main
ideas already appear. We also think about what it means to
approach a limit or to add up a sum with infinitely many terms,
but throughout the emphasis is on explicit examples and getting
answers.
Differential equation for continuous compound interest. Solution by
inspection and by separation of variables. Radioactive decay,
half-life. Newton's law of cooling. Other examples of separable
equations.
4. Partial derivatives (4 lectures)
Functions of two variables, their graphs, level curves and tangent
planes. Partial derivatives, their graphical interpretation and
evaluation. Jacobians, higher derivatives. Increments, the Chain Rule
and its applications, including to Laplace's equation.
5. Double integrals (5 lectures)
Review of the Fundamental Theorem of Calculus. Two-dimensional
integrals as volumes under graphs, their evaluation by double
integration, in either order. Change of variables, including to polar
coordinates. ∫−∞∞ e−[1/2]x2 dx.
6. Infinite series (5 lectures)
Infinite series of positive terms. Basic examples including
geometric
and harmonic series. Sum as a limit of partial sums. Numerical and
graphical illustration. Absolute convergence. Manipulating Maclaurin
series. Finding the radius of convergence. | 677.169 | 1 |
Course Content and Outcome Guide for ALC 63
Date:
02-OCT-2012
Posted by:
Heiko Spoddeck
Course Number:
ALC 63
Course Title:
Basic Math Skills Lab
Credit Hours:
3
Lecture hours:
0
Lecture/Lab hours:
0
Lab hours:
90
Special Fee:
$36
Course Description
In conjunction with the instructor, students choose a limited number of topics in Basic Math (MTH 20) and/or Introductory Algebra (MTH 60 and 65) to review over the course of one term. Instruction and evaluation are self-guided. Students must spend a minimum of 90 hours in the lab. Completion of this course does not meet prerequisite requirements for other math courses.
7.3Classify points by quadrant or as points on an axis; identify the origin
7.4Label and scale axes on all graphs
7.5Interpret graphs in the context of an application
7.6Create a table of values from an equation
7.7Plot points from a table
8.0INTRODUCTION TO FUNCTION NOTATION
8.1Determine whether a given relation presented in graphical form represents a function
8.2Evaluate functions using function notation from a set, graph or formula
8.3Interpret function notation in a practical setting
8.4Identify ordered pairs from function notation
9.0LINEAR EQUATIONS IN TWO VARIABLES
9.1Identify a linear equation in two variables
9.2Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
9.3Find ordered pairs that satisfy a linear equation written in standard or slope-intercept form including equations for horizontal and vertical lines; graph the line using the ordered pairs
9.4Find the intercepts given a linear equation; express the intercepts as ordered pairs
9.5Graph the line using intercepts and check with a third point
9.6Find the slope of a line from a graph and from two points
9.7Given the graph of a line identify the slope as positive, negative, zero, or undefined. Given two non-vertical lines, identify the line with greater slope
9.8Graph a line with a known point and slope
9.9Manipulate a linear equation into slope-intercept form; identify the slope and the vertical-intercept given a linear equation and graph the line using the slope and vertical-intercept and check with a third point
9.10Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
9.11Given the equation of two lines, classify them as parallel, perpendicular, or neither
9.12Find the equation of a line using slope-intercept form
9.13Find the equation of a line using point-slope form
10.0APPLICATIONS OF LINEAR EQUATIONS IN TWO VARIABLES
10.1Interpret intercepts and other points in the context of an application
10.2Write and interpret a slope as a rate of change
10.3Create and graph a linear model based on data and make predictions based upon the model
10.4Create tables and graphs that fully communicate the context of an application problem
11.0LINEAR INEQUALITIES IN TWO VARIABLES
11.1Identify a linear inequality in two variables
11.2Graph the solution set to a linear inequality in two variables
11.3Model application problems using an inequality in two variables
Introductory Algebra II
THEMES:
1.Functions 2.Graphical understanding
3.Algebraic manipulation
4.Number sense
5.Problem solving
6.Applications, formulas, and modeling
7.Critical thinking
8.Effective communication
SKILLS:
1.0SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
1.1Solve and check systems of equations graphically and using the substitution and addition methods
1.2Create and solve real-world models involving systems of linear equations in two variables
1.2.1Properly define variables; include units in variable definitions
1.2.2Apply dimensional analysis while solving problems
1.2.3State contextual conclusions using complete sentences
1.2.4Use estimation to determine reasonableness of solution
2.0WORKING WITH ALGEBRAIC EXPRESSIONS
2.1Apply the rules for integer exponents
2.2Work in scientific notation and demonstrate understanding of the magnitude of the quantities involved | 677.169 | 1 |
The
course develops fundamental geometric tools of mathematical analysis,
in particular integration theory, and is a preparation for further
geometry/topology courses. The central statement is the famous Stokes
theorem, a classical version of which appeared for the first time
as an examination problem in Cambridge in 1854. Various manifestations
of the general Stokes theorem are associated with the names of Newton,
Leibniz, Ostrogradski, Gauss, Green. This theorem, both in its
infinitesimal and global forms, relates integral over a boundary of a
surface or of a solid domain ("circulation" or "flux") with a natural
differential operator, known in particular cases as "curl" or
"divergence". The prototype and the simplest case of the Stokes theorem
is the Newton-Leibniz formula linking the difference of the values of f
on endpoints of a segment with the integral of df . The
standard modern language for these topics is differential forms
and the exterior derivative. Differential forms are used
everywhere from pure mathematics to engineering. We give an
introduction to the theory of forms, as well as a simplifying treatment
for the traditional technique of operations with vector fields in the
Euclidean three-space. | 677.169 | 1 |
Humble Precalculus
...Student are taught how to set of and solve elementary word problems. Algebra 2 basically introduces the notion of a function, and it extends this notion to a variety of different types of functions. We see polynomial, exponential, logarithmic functons and more. | 677.169 | 1 |
... read more
Customers who bought this book also bought:
Our Editors also recommend:Geometry and Symmetry by Paul B. Yale Introduction to the geometry of euclidean, affine and projective spaces with special emphasis on the important groups of symmetries of these spaces. Many exercises, extensive bibliography. Advanced undergraduate level.
Differential Geometry by Erwin Kreyszig An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
A Course in the Geometry of n Dimensions by M. G. Kendall This text provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. 1961Invitation to Geometry by Z. A. Melzak Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983The Elements of Non-Euclidean Geometry by D. M.Y. Sommerville Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.A Modern View of Geometry by Leonard M. Blumenthal Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures.
Geometry, Relativity and the Fourth Dimension by Rudolf Rucker Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
Product Description:
the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
Reprint of the Prentice-Hall, Englewood Cliffs, New Jersey, 1965 | 677.169 | 1 |
Classification
Reviews (1)
A link to a website which has numerous PowerPoints covering a wide range of algebraic topics. The PowerPoints provide simple step-by-step instructions on how to answer questions which provides a good revision tool for students. | 677.169 | 1 |
This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces. Following the modern point of view on differential geometry, the book emphasizes the global aspects of the subject. The excellent collection of examples and exercises (with hints) will help students in learning the material. Advanced undergraduates and graduate students will find this a nice entry point to differential geometry.
In order to study the global properties of curves and surfaces, it is necessary to have more sophisticated tools than are usually found in textbooks on the topic. In particular, students must have a firm grasp on certain topological theories. Indeed, this monograph treats the Gauss-Bonnet theorem and discusses the Euler characteristic. The authors also cover Alexandrov's theorem on embedded compact surfaces in \(\mathbb{R}^3\) with constant mean curvature. The last chapter addresses the global geometry of curves, including periodic space curves and the four-vertices theorem for plane curves that are not necessarily convex.
Besides being an introduction to the lively subject of curves and surfaces, this book can also be used as an entry to a wider study of differential geometry. It is suitable as the text for a first-year graduate course or an advanced undergraduate course.
This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Readership
Undergraduate students, graduate students, and research mathematicians interested in the geometry of curves and surfaces.
Reviews
"With its readable style and the completeness of its exposition, this would be a very good candidate for an introductory graduate course in differential geometry or for self-study." | 677.169 | 1 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
How to Program? - Part 1 Part 1: Problem Solving Analyze a problem Decide what steps need to be taken to solve it. Take into consideration any special circumstances. Plan a sequence of actions that must take place in a specified order Solve the
AgendaIAT 201:Workshop D102/103Week 5TA: Daniel [email protected] Business items Review: Requirements for the next assignment Team Activity: Task analysis Team Activity: Volere templateBusiness1. Most of you have done so already, but for t
You are only allowed to read this if you are standing on your head and you have tried all four parts! 11a. [6, 4] and R = 5. 11b. (7, 1) and R = 4. 11c. [2 1/8, 2 + 1/8) and R = 1/8. 11d. The series only converges when x = 1/2, so R = 0.11. Find t
Math 114 Calculus II Spring 2009 Exam II Scores Each exam grade is listed by code name and score before curving. If you cannot nd your code name, it means it was too easy for me to break and I am instead posting your grade by the last two digits of y
Math 114 Calculus II Spring 2009 Each exam grade is listed by code name and score before curving. If you did not list a code name, I am instead posting your exam grade by the last two digits of your student ID. Final Exam Results: High: 97 Low: 28 Av
MATH and PIZZATangents to Four Unit Spheres:An Introduction to Enumerative Algebraic GeometrySpeakersDavid CoxWilliam J. Walker Professor of Mathematics at Amherst College Sponsored by Department of Mathematics University of KentuckyDate: Thu
Fall 2007 Name(printed neatly): Quiz Grade:Math 131-501Quiz 9Fri, 9/Nov/20071. In the study of markets, economists dene consumers willingness and ability to spend as the maximum amount that consumers are willing and able to spend for a specic
ENVS 680 Doing a Summer Internship You can do your actual internship during the summer and take the internship course, ENVS 680, the following fall. However, you need to do certain homework assignments for the internship course during the summer. You
EE 143 Optical Lithography Lecture, A.R. Neureuther, Sp 2006Ver: 02/01/2009OPC Scatterbars or Assist FeaturesMain Feature The isolated main pattern now acts somewhat more like a periodic line and space pattern which has a higher quality image es
Topics Covered Final Exam ReviewLast Lecture R&G - All Chapters Covered First half of the course (see midterm review) you are responsible for it; final will lean towards material covered since then. SQL (covered before and after midterm) Impleme | 677.169 | 1 |
Subject overview
Why mathematics?
Mathematics is core to most modern-day science, technology and business. When you turn on a computer or use a mobile phone, you are using sophisticated technology that mathematics has played a fundamental role in developing. Unravelling the human genome or modelling the financial markets relies on mathematics.
As well as playing a major role in the physical and life sciences, and in such disciplines as economics and psychology, mathematics has its own attraction and beauty. Mathematics is flourishing: more research has been published in the last 20 years than in the previous 200, and celebrated mathematical problems that had defeated strenuous attempts to settle them have recently been solved.
The breadth and relevance of mathematics leads to a wide choice of potential careers. Employers value the numeracy, clarity of thought and capacity for logical argument that the study of mathematics develops, so a degree in mathematics will give you great flexibility in career choice.
Why mathematics at Sussex?
Mathematics at Sussex was ranked in the top 20 in the UK in The Sunday Times University Guide 2012.
In the 2008 Research Assessment Exercise (RAE) 90 per cent of our mathematics research and 97 per cent of our mathematics publications were rated as recognised internationally or higher, and 50 per cent of our research and 64 per cent of our publications were rated as internationally excellent or higher.
The Department awards prizes for the best student results each year, including £1,000 for the best final-year student.
In 2011, US careers website Jobs ratedranked mathematician to be the second most popular job out of the 200 considered.
You will find that our Department is a warm, supportive and enjoyable place to study, with staff who have a genuine concern for their students.
Our teaching is informed by current research and understanding and we update our courses to reflect the latest developments in the field of mathematics.
MMath or BSc?
The MMath courses are aimed at students who have a strong interest in pursuing a deeper study of mathematics and who wish to use it extensively in careers where advanced mathematical skills are important, such as mathematical modelling in finance or industry, advanced-level teaching or postgraduate research.
Applicants unsure about whether to do an MMath or a BSc are strongly advised to opt initially for the MMath course. If your eventual A level grades meet the offer level for a BSc but not an MMath we will automatically offer you a place on the BSc course. Students on the MMath course can opt to transfer to the BSc at the end of the second year.
Why economics?
Addressing many of the world's problems and issues requires an understanding of economics. Why are some countries so rich and others so poor? Should Microsoft be broken up? Should the private sector be involved in providing health and education? Could environmental taxes help reduce global warming? What is the future of the euro?
Economics provides a framework for thinking about such issues in depth, allowing you to get to the heart of complex, topical problems. The methods of economics can be applied to a wide range of questions and will prove useful to you in your future career. In addition, the study of economics teaches you a variety of practical skills, including the ability to use and evaluate evidence (often statistical) in order to arrive at sound conclusions.
Why economics at Sussex?
In the 2008 Research Assessment Exercise (RAE) 100 per cent of our economics research was rated as recognised internationally or higher, and 60 per cent rated as internationally excellent or higher.
We emphasise the practical application of economics to the analysis of contemporary social and economic problems.
We have strong links to the major national and international economic institutions such as the European Commission, the World Bank and the Department for International Development.
The Department has strong research clusters in labour markets and in development economics, and is one of Europe's leading centres for research on issues of international trade.
We offer you the chance to conduct an economics research project supervised by a faculty member.
Programme content
This degree exploits the strong relationship between mathematical modelling and economics. Alongside the mathematics core modules, you study the principles of economic analysis and its policy applications at both the macro (economy-wide) and the micro (individual/ company) levels. The economics element provides an opportunity to acquire practical skills and to apply mathematical methods.
As well as the core mathematics modules in Years 1 and 2, you will spend 25 per cent of your time studying economics modules. In the third year, you take a combination of mathematics and economics options.
On the MMath course, you carry out a project in the fourth year and choose from a range of more advanced mathematical modules recognise that new students have a range of mathematical backgrounds and that the transition from A level to university-level study can be challenging, so we have designed our first-term modules to ease this. Although university modes of teaching place more emphasis on independent learning, you will have access to a wide range of support from tutors.
Teaching and learning is by a combination of lectures, workshops, lab sessions and independent study. All modules are supported by small-group teaching in which you can discuss topics raised in lectures. We emphasise the 'doing' of mathematics as it cannot be passively learnt. Our workshops are designed to support the solution of exercises and problems.
Most modules consist of regular lectures, supported by classes for smaller groups. You receive regular feedback on your work from your tutor. If you need further help, all tutors and lecturers have weekly office hours when you can drop in for advice, individually or in groups. Most of the lecture notes, problem sheets and background material are available on the Department's website.
Upon arrival at Sussex you will be assigned an academic advisor for the period of your study. They also operate office hours and in the first year they will see you weekly. This will help you settle in quickly and offers a great opportunity to work through any academic problemsexcellent training in problem-solving skills
understanding of the structures and techniques of mathematics, including methods of proof and logical arguments
written and oral communication skills
organisational and time-management skills
an ability to make effective use of information and to evaluate numerical data
IT skills and computer literacy through computational and mathematical projects
you will learn to manage your personal professional career development in preparation for further study, or the world of work.
Core content
Year 1
You take modules on topics such as calculus • introduction to pure mathematics • geometry • analysis • mathematical modelling • linear algebra • numerical analysis. You also work on a project on mathematics in everyday life.
Year 2
You take modules on topics such as calculus of several variables • an introduction to probability • further analysis • group theory • probability and statistics • differential equations • complex analysis • further numerical analysis core ideas and analytical techniques are presented in lectures and supplemented by classes or workshops where you can test your understanding and explore the issues in more depth. These provide the opportunity for student interaction, an essential part of the learning process at Sussex. The more quantitative skills, such as using statistical software, are taught in computer workshops. On the dissertation module in the final year, you receive one-to-one supervision as you investigate your chosen research topic in depth.
Formal assessment is by a range of methods including unseen exams and coursework. In addition there are regular assignments, which allow you to monitor your progress. In the first year, you have regular meetings with your academic advisor to discuss your academic progress and to receive feedback on your assignments and understanding of the principles of economics
the skills to abstract the essential features of a problem and use the framework of economics to analyse it
the ability to evaluate and conduct your own empirical research
the confidence to communicate economic ideas and concepts to a wider audience
a range of transferable skills, applicable to a wide variety of occupations.
Core content
Year 1
You are introduced to the principles of economics and their application to a range of practical and topical issues. The aim is not to look at economic theory in isolation but to learn how it is used to analyse real issues. You also take a mathematics module, giving you some of the tools you need to understand contemporary economics.
Year 2
You develop your understanding of economics principles through the study of more advanced topics such as trade and risk. You also take a statistics module and learn how to analyse and interpret data. In addition, there are more applied modules, allowing you to see how the subject deals with empirical issues. There are opportunities for small research projects, including a group project.
Year 3
You have the opportunity to choose from a range of options such as labour or development economics. These modules go into the relevant issues in greater depth, giving you a high level of expertise. There is the opportunity to do a sustained piece of research on a chosen topic. You can also take more advanced quantitative modules – useful if you wish to do postgraduate work.
Geometry
15 credits
Autumn teaching, Year 1
Topics include: vectors in two and three dimensions. Vector algebra: addition, scalar product, vector product, including triple products. Applications in two- and three-dimensional geometry: points, lines, planes, geometrical theorems. Area and volume. Linear dependence and determinants. Polar co-ordinates in two and three dimensions. Definitions of a group and a field. Polynomials. Complex numbers, Argand plane, De Moivre's theorem. Matrices: addition, multiplication, inverses. Transformations in R^2 and R^3: isometries. Analytical geometry: classification and properties of conics.
Introduction to Economics
15 credits
Autumn teaching, Year 1
This course provides an introduction to the fundamental principles of economics. The first half of the course deals with microeconomic issues including the behaviour of individuals and firms, their interaction in markets and the role of government. The second half of the course is devoted to macroeconomics and examines the determinants of aggregate economic variables, such as national income, inflation, and the balance of payments, and the relationships between them. This course also provides students with a basic introduction to mathematical economics, covering solving linear equations, differential calculus, and discounting.
Microeconomics 1
15 credits
Spring teaching, Year 1
This module develops consumer and producer theory, examining such topics as consumer surplus, labour supply, production and costs of the firm, alternative market structures and factor markets. It explores the application of these concepts to public policy, making use of real-world examples to illustrate the usefulness of the theory.
Numerical Analysis 1
15 credits
Spring teaching, Year 1
This module covers topics such as:
Introduction to Computing with MATLAB
Basic arithmetic and vectors, M-File Functions, For Loops, If and else, While statements
Analysis 2
15 credits
Autumn teaching, Year 2
Topics covered: power series, radius of convergence; Taylor series and Taylor's formula; applications and examples; upper and lower sums; the Riemann integral; basic properties of the Riemann integral; primitive; fundamental theorem of calculus; integration by parts and change of variable; applications and examples. Pointwise and uniform convergence of sequences and series of functions: interchange of differentiation or integration and limit for sequences and series; differentiation and integration of power series term by term; applications and examples. Metric spaces and normed linear spaces: inner products; Cauchy sequences, convergence and completeness; the Euclidean space R^n; introduction to general topology; applications and examples.
First order PDEs: Method of characteristics for semilinear and quasilinear equations, initial boundary value problems.
Macroeconomics 1
15 credits
Spring teaching, Year 2
This module introduces core short-run and medium-run macroeconomics.
First you will consider what determines demand for goods and services in the short run. You will be introduced to financial markets, and outline the links between financial markets and demand for goods. The Keynesian ISLM model encapsulates these linkages. Second, you will turn to medium-term supply. You will bring together the market for labour and the price-setting decisions of firms in order to build an understanding of how inflation and unemployment are determined. Finally, you will look at supply and the ISLM together to produce a full medium-term macroeconomic model.
Microeconomics 2
15 credits
Autumn teaching, Year 2
This module develops the economics principles learned in Microeconomics 1. Alternative market structures such as oligopoly and monopolistic competition are studied and comparisons drawn with perfect competition and monopoly. Decision-making under uncertainty and over multiple time periods is introduced, relaxing some of the restrictive assumptions made in the level 1 module. The knowledge gained is applied to such issues as investment in human capital (eg education), saving and investment decisions, insurance and criminal deterrence.
Distribution theory: Chebychev's inequality, weak law of large numbers, distribution of sums of random variables, t,\chi^2 and F distributions;
Confidence intervals;
Statistical tests including z- and t-tests, \chi^2 tests;
Linear regression;
Nonparametric methods;
Random number generation;
Introduction to stochastic processes.
Macroeconomics 2
15 credits
Autumn teaching, Year 3
This module is concerned with two main topics. 'The long run' is an introduction to how economies grow, gradually raising the standard of living, decade by decade. Once we have the basic analysis in place, we can begin to explain why there are such huge disparities in living standards around the world. 'Expectations' is a deepening of the behavioural background to modelling, saving and investment decisions, emphasising the intrinsically forward-looking nature of saving and investment decisions and analysing the financial markets which coordinate these decisions.
Advanced Macroeconomics
15 credits
Spring teaching, Year 3
The module completes the macroeconomics sequence, starting with a consideration of the policy implications of rational expectations. The macroeconomy is then opened up to international trade and capital movements: the operation of monetary and fiscal policies and the international transmission of disturbances under fixed and flexible exchange rates are contrasted, and the issues bearing on the choice of exchange-rate regime are explored. The major macroeconomic problems of hyperinflation, persistent unemployment and exchange-rate crises are examined. The module concludes by drawing together the implications of the analysis for the design and operation of macroeconomic policy.
Advanced Microeconomics
15 credits
Spring teaching, Year 3
This module covers the topics of general equilibrium and welfare economics, including the important issue of market failure. General equilibrium is illustrated using Sen's entitlement approach to famines and also international trade. Welfare economics covers concepts of efficiency and their relationship to the market mechanism. Market failure includes issues such as adverse selection and moral hazard, and applications are drawn from health insurance, environmental economics and the second-hand car market.
Harmonic Analysis and Wavelets
15 credits
Autumn teaching, Year 4
You will be introduced to the concepts of harmonic analysis and the basics of wavelet theory: you will discuss the concepts of normed linear spaces and Hilbert spaces, with a focus on sequence spaces and spaces of functions, most notably the space of square-integrable functions on an interval or on the real line. You will be introduced to the ideas of best approximation, orthogonal projection, orthogonal sums, orthonormal bases and Fourier series in a separable Hilbert space.
You will then apply these concepts to the concrete case of classical trigonometric Fourier series, and both Fejer's theorem and the Weierstrass approximation theorem will be proved.
Finally, you will apply the introduced concepts for Hilbert to discuss wavelet analysis for the example of the Haar wavelet and the Haar scaling function. You will be introduced to the concepts of an orthogonal wavelet and a multiresolution analysis (with a scaling function for the case of the Haar wavelet), but will also be defined in general. The concepts of an orthogonal wavelet and a multiresolution analysis (with a scaling function) will initially be introduced for the case of the Haar wavelet, but will also be defined in general.
Introduction to Mathematical Biology
15 credits
Autumn teaching, Year 4
The module will introduce you to the concepts of mathematical modelling with applications to biological, ecological and medical phenomena. The main topics will include:
Perturbation theory and calculus of variations
15 credits
Spring teaching, Year 4
The aim of this module is to introduce you to a variety of techniques primarily involving ordinary differential equations, that have applications in various branches of applied mathematics. No particular application is emphasisedRing Theory
15 credits
Autumn teaching, Year 4
In this module we will explore how to construct fields such as the complex numbers and investigate other properties and applications of rings.
Special topics: Quaternions, valuations, Hurwitz ring, the four squares theorem.
Topology and Advanced Analysis
15 credits
Spring teaching, Year 4
This module will introduce you to some of the basic concepts and properties of topological spaces. The subject of topology has a central role in all of Mathematics and having a proper understanding of its concepts and main theorem is essential as part of an undergraduate mathematics curriculum.
Topics that will be covered in this module include:
Topological spaces
Base and sub-base
Separation axioms
Continuity
Metrisability
Completeness
Compactness and Coverings
Total Boundedness
Lebesgue numbers and Epsilon-nets
Sequential Compactness
Arzela-Ascoli Theorem
Montel's theorem
Infinite Products
Box and Product Topologies
Tychonov Theorem.
MMath Project
30 credits
Autumn & spring teaching, Year 4
The work for the project and the writing of the project report will have a major role in bringing together material that you have mastered up to Year 3 and is mastering in Year 4. It will consist of a sustained investigation of a mathematical topic at Masters' level. The project report will be typeset using TeX/LaTeX (mathematical document preparation system). The use of mathematical typesetting, (mathematics-specific) information technology and databases and general research skills such as presentation of mathematical material to an audience, gathering information, usage of (electronic) scientific libraries will be taught and acquired during the project.
E-Business and E-Commerce Systems
15 credits
Autumn teaching, Year 4
This module will give you a theoretical and technical understanding of the major issues for all large-scale e-business and e-commerce systems. The theoretical component includes: alternative e-business strategies; marketing; branding; customer relationship issues; and commercial website management. The technical component covers the standard methods for large-scale data storage, data movement, transformation, and application integration, together with the fundamentals of application architecture. Examples focus on the most recent developments in e-business and e-commerce distributed systems.
Financial Portfolio Analysis
15 credits
Spring teaching, Year 4
You will study valuation, options, asset pricing models, the Black-Scholes model, Hedging and related MatLab programming. These topics form the most essential knowledge for you if you intend to start working in the financial fields. They are complex application problems. Your understanding of mathematics should be good enough to understand the modelling and reasoning skills required. The programming element of this module makes complicated computations manageable and presentable.
Harmonic Analysis and Wavelets
15 credits
Autumn teaching, Year 4
This module introduces you to the concepts of harmonic analysis and the basics of wavelet theory. We will discuss the concepts of normed linear spaces and Hilbert spaces, with a focus on sequence spaces and spaces of functions, most notably the space of square-integrable functions on an interval or on the real line. You will be intoroduces to the ideas of best approximation, orthogonal projection, orthogonal sums, orthonormal bases and Fourier series in a separable Hilbert space, and apply these to the concrete case of classical trigonometric Fourier series. You will also use these strategies to prove both Fejer's theorem and the Weierstrass approximation theorem. Finally you will apply the concepts for Hilbert spaces to discuss wavelet analysis using the example of the Haar wavelet and the Haar scaling function. The concepts of an orthogonal wavelet and a multiresolution analysis (with a scaling function) will initially be introduced for the case of the Haar wavelet, but will also be defined in general.
Introduction to Cosmology
15 credits
Autumn teaching, Year 4
This module covers:
observational overview: In visible light and other wavebands; the cosmological principle; the expansion of the universe; particles in the universe.
cosmological models: solving equations for matter and radiation dominated expansions and for mixtures (assuming flat geometry and zero cosmological constant); variation of particle number density with scale factor; variation of scale factor with time and geometry.
inflation: definition; three problems (what they are and how they can be solved); estimation of expansion during inflation; contrasting early time and current inflationary epochs; introduction to cosmological constant problem and quintessence.
initial singularity: definition and implications.
connection to general relativity: brief introduction to Einstein equations and their relation to Friedmann equation.
Mathematical Models in Finance and Industry
15 credits
Spring teaching, Year 4
Topics include: partial differential equations (and methods for their solution) and how they arise in real-world problems in industry and finance. For example: advection/diffusion of pollutants, pricing of financial options.
Object Oriented Programming
You will be introduced to object-oriented programming, and in particular to understanding, writing, modifying, debugging and assessing the design quality of simple Java applications.
You do not need any previous programming experience to take this module, as it is suitable for absolute beginnersTechnology-Enhanced Learning Environments
15 credits
Spring teaching, Year 4
This module emphasises learner-centred approaches to the design of educational and training systems. The module content will reflect current developments in learning theory, skill development, information representation and how individuals differ in terms of learning style. The module has a practical component, which will relate theories of learning and knowledge representation to design and evaluation. You will explore the history of educational systems, as well as issues relating to: intelligent tutoring systems; computer-based training; simulation and modelling environments; programming languages for learners; virtual reality in education and training; training agents; and computer-supported collaborative learning
Specific entry requirements: A levels must include both Mathematics and Further Mathematics, grade A.
International Baccalaureate
Typical offer: 35 points overall
Specific entry requirements: Higher Levels must include Mathematics, with a grade of 6.
Advanced Diploma
Typical offer: Pass with grade A in the Diploma and A in the Additional and Specialist Learning.
Specific entry requirements: The Additional and Specialist Learning must be an A level in Mathematics (grade A). Successful applicants will also need to take A level Further Mathematics as an extra A level software development, actuarial work, financial consultancy, accountancy, business research and development, teaching, academia and the civil service. All of our courses give you a high-level qualification for further training in mathematics.
Recent graduates have taken up a wide range of posts with employers including:
actuary at MetLife
assistant accountant at World Archipelago
audit trainee at BDO LLP UK
credit underwriter at Citigroup
graduate trainee for aerospace and defence at Cobham plc
pricing analyst at RSA Insurance Group plc
assistant analytics manager at The Royal Bank of Scotland
associate tutor at the University of Sussex
health economics consultant at the University of York
risk control analyst at Total Gas & Power
supply chain manager at Unipart Group
technology analyst at J P Morgan
digital marketing consultant at DC Storm
junior financial advisor at Barclays
audit associate at Ernst & Young
claims graduate trainee at Lloyds of London
development analyst at Axa PPP healthcare
fraud analyst at American Express
futures trader at Trading Tower Group Ltd
accountant at KPMG Mathematical and Physical Sciences
The School of Mathematical and Physical Sciences brings together two outstanding and progressive departments - Mathematics, and Physics and Astronomy. It capitalises on the synergy between these subjects to deliver new and challenging opportunities for its students and faculty advice | 677.169 | 1 |
Problem Solving Approach to Mathematics for Elementary School Teachers
9780321331793
ISBN:
0321331796
Edition: 9 Pub Date: 2006 Publisher: Addison-Wesley
Summary: Setting the Standard for Tomorrow's Teachers:This best-selling text continues as a comprehensive, skills-based resource for future teachers. In this edition, readers will benefit from additional emphasis on active and collaborative learning. Revised and updated content will better prepare readers for the day when they will be teachers with students of their own. An Introduction to Problem Solving. Sets, Whole Numbers..., and Functions. Numeration Systems and Whole-Number Computation. Integers and Number Theory. Rational Numbers as Fractions. Decimals, Percents, and Real Numbers. Probability. Data Analysis/ Statistics: An Introduction. Introductory Geometry. Constructions, Congruence, and Similarity. Concepts of Measurement. Motion Geometry and Tessellations. For all readers interested in mathematics for elementary school teachers [more99 Purchased as new and in great condition. We cannot guarantee the availability of CD/DVD or other resource materials such as access code etc if the book is so described by the [more]
ALTERNATE EDITION: Annotated Instructor. Same as the student edition. Cannot guarantee the availability of CD/DVD/Access codes. Ships now if ordered before 2pm CST[less] | 677.169 | 1 |
Overview - HANDS-ON ALGEBRA
A vast assortment of ready-to-use games and activities make Hands-On Algebra! an invaluable resource for teachers of Grades 7-12 looking to make algebra more meaningful and fun. The 159 reproducible games and lessons teach all of the major concepts covered in first-year algebra recommended by the NCTM. Business and industry are requiring more employees to have a better understanding of mathematics than ever before, in particular a greater knowledge of algebra. Teaching techniques once used only for college-bound students must now be adjusted to better serve students of all ability levels.
Hand-On Algebra! was designed to help teachers of algebra meet the needs of this increasing population of students. The book covers content and contains materials sufficient for a two-semester course in Algebra I. It is appropriate for students of varying abilities: Students with dyslexia or with decoding or other processing difficulties find instruction with manipulatives beneficial. Gifted students delve more deeply into mathematical ideals.
Using a unique three-step approach-concrete to pictorial to abstract-students gain mastery over important algebra concepts and skills one activity at a time.
Each objective is presented in the following sequence: Activity 1 offers physical models in the development of the concept, with easy-to-follow instructions to help learners seek patterns. It is at this concrete level that most students discover the special relationships being developed.
Activity 2 uses pictorial models such as diagrams, tables, and graphs to help students bridge from the concrete to the abstract level of thinking, and to retain and test what they have learned.
Each activity has complete teacher directions, materials needed, and helpful examples for discussion, homework, and quizzes. The activities provide numerous opportunities for students to describe their procedures and results both orally and in written form. Most of them include timesaving reproducible worksheets or game pieces. The book is printed in a big 8.25- by 11-inch lay-flat binding for easy photocopying.
The book is divided into the following five sections: -Real Numbers, Their Operations, and Their Properties (11 objectives) -Linear Forms (8 objectives) -Linear Applications and Graphing (12 objectives) -Quadratic Concepts (12 objectives) -Special Applications (9 objectives)
Special Features The Appendix contains an assortment of four tile patterns that can be easily photocopied for student use in completing the games and activities located throughout the book.
About the Author Frances McBroom Thompson has taught mathematics at the junior and senior high school levels, and has served as a K-12 mathematics specialist. She holds a B.S. in mathematics education from Abilene Christian University in Texas, a master's degree in mathematics from the University of Texas at Austin, and a doctoral degree in mathematics education from the University of Georgia in Athens. | 677.169 | 1 |
A rigorous, concise development of the concepts of modern matrix structural analysis, with particular emphasis on the techniques and methods that form the basis of the finite element method. All relevant concepts are presented in the context of two-dimensional (planar) structures composed of bar (truss) and beam (frame) elements, together with simple discrete axial, shear and moment resisting spring elements. The book requires only some basic knowledge of matrix algebra and fundamentals of strength of materials. | 677.169 | 1 |
sábado, 28 de julho de 2012
The Mathematical Collage has been written to meet an Associate Degree general education requirement of a mathematics course with a Beginning Algebra prerequisite. The text shows that mathematics is alive in today's world and helps students see the beauty and power of mathematics. Its contents consists of chapters on the lore of numbers, finance matters, measurement geometry and trigonometry, probability and statistics, and math in sports, It also includes Mathematical Excursions, short trips into various areas where mathematics is used, such as math and the tourist, math and the internet, math and voting, math and nursing, math and the automobile, math and cooking, math and the angler, math and the World Series of Poker.
quinta-feira, 26 de julho de 2012
It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.
This volume is concerned with the alignment between the way the mathematical performance of students is assessed and the reform agenda in school mathematics. The chapters in this book have been prepared to raise a set of issues that scholars are addressing during this period of transition from traditional schooling practices toward the reform vision of school mathematics. Chapters are: (1) "Issues Related to the Development of an Authentic Assessment System for School Mathematics" (T. A. Romberg and L. D. Wilson), (2) "A Framework for Authentic Assessment in Mathematics" (S. P. Lajoie), (3) "Sources of Assessment Information for Instructional Guidance in Mathematics" (E. A. Silver and P. A. Kenney), (4) "Assessment: No Change without Problems" (J. De Lange), (5) "The Invalidity of Standardized Testing for Measuring Mathematics Achievement" (R. E. Stake), (6) "Assessment Nets: An Alternative Approach to Assessment in Mathematics Achievement" (M. Wilson), and (7) "Connecting Visions of Authentic Assessment to the Realities of Educational Practice
Contents
Preface vii
1 Issues Related to the Development of an Authentic Assessment System for School Mathematics
THOMAS A. ROMBERG AND LINDA D. WILSON
This volume, a reprinting of a classic first published in 1952, presents detailed discussions of 26 curves or families of curves, and 17 analytic systems of curves. For each curve the author provides a historical note, a sketch or sketches, a description of the curve, a discussion of pertinent facts, and a bibliography. Depending upon the curve, the discussion may cover defining equations, relationships with other curves (identities, derivatives, integrals), series representations, metrical properties, properties of tangents and normals, applications of the curve in physical or statistical sciences, and other relevant information. The curves described range from the familiar conic sections and trigonometric functions through the less well known Deltoid, Kieroid and Witch of Agnesi. Curve related systems described include envelopes, evolutes and pedal curves. A section on curve sketching in the coordinate plane is included.
domingo, 1 de julho de 2012
A survey of math for liberal arts majors. This book is a survey of contemporary mathematical topics: voting theory, weighted voting, fair division, graph theory, scheduling, growth models, finance math, statistics, and historical counting systems. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.
The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics.
quinta-feira, 28 de junho de 2012
The idea of this book was suggested to me by Kindergarten Gift No. VIII. - Paper-folding. The gift consists of two hundred variously colored squares of paper, a folder, and diagrams and instructions for folding. The paper is colored and glazed on one side. The paper may, however, be of self-color, alike on both sides. In fact, any paper of moderate thickness will answer the purpose, but colored paper shows the creases better, and is more attractive. The kindergarten gift is sold by any dealers in school supplies ; but colored paper of both sorts can be had from stationery dealers. Any sheet of paper can be cut into a square as explained in the opening articles of this book, but it is neat and convenient to have the squares ready cut. | 677.169 | 1 |
Outcome
Type
Tuition Fees
Sponsors
College: College of Physical and Engineering Science
Department: Department of Mathematics and Statistics
Instructors
Prof. Joe Cunsolo
Description
Getting Ready for Calculus is a non-credit course designed as a preparation for university-level mathematics.
This course is for you if you lack a solid mathematics background and/or skills and find that you need to take more mathematics to reach your educational and/or career goals. In designing this course, the Department of Mathematics recognizes the diverse mathematical backgrounds and concerns of students. The material in this course spans Grade 9 through to and including part of the OAC Calculus course. The course starts with a basic review of algebra from Grades 9 and 10, and then it focuses on the mathematical material from Grades 10, 11 and 12 that allows the introduction of material from the OAC Calculus course. This design allows you to develop a more solid grounding in the mathematics that is needed for university-level mathematics courses.
Call us (519-767-5010) if you have any questions regarding this unique preparatory course.
Note: This is a non-credit course | 677.169 | 1 |
Lecture 9: WildLinAlg9: Three dimensional affine geometry
Embed
Lecture Details :
Three dimensional affine geometry is a big step from two dimensional planar geometry. Here we introduce the subject via a 3d coordinate system, showing some ZOME models, explaining how to draw such a coordinate system in the plane, and seeing how points in space are naturally associated to triples of [x,y,z] of numbers. We discuss points, lines and planes in 3D, and point out the important distinction between affine space and a vector space.
NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry---see his WildTrig YouTube series under user `njwildberger'. There you can also find his series on Algebraic Topology, History of Mathematics and Universal Hyperbolic Geometry.
Course Description :
This course on Linear Algebra is meant for first year undergraduates or college students. It presents the subject in a visual geometric way, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine algebraic geometry. Flexibility in choosing coordinate frameworks is essential for understanding the subject. Determinants also play an important role, and these are introduced in the context of multi-vectors in the sense of Grassmann. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry. | 677.169 | 1 |
Short description Key Stage 4 (KS4) maths eBooks comprise three principle sections. These are, notably: (Read more) maths eBooks are produced such as that as well as a Publications Guide, and three principle publications corresponding to the principle sections (Number and Algebra, Geometry and Measures and Statistics Data) there are individual modules produced within each principle section which are published as eBooks.
Rounding Numbers, Accuracy and Bounds, Estimation and Checking is a module within the Number and Algebra principle section our Key Stage 4(KS4) publications. (Less) | 677.169 | 1 |
By the end of the course students should be able to:
- apply numerical methods to solve a variety of mathematical problems with relevance to engineering;
- demonstrate an understanding of the limitations and applicability of the methods
- demonstrate skills in solving similar problems using MATLAB programs
L4 and L5 Numerical solution of ODE&ęs
Introduction to solution of Ordinary Differential Equations, derivation and application of the Euler Method. Application of Euler, Euler-Cauchy and Runge-Kutta Methods. [Associated MATLAB exercises run in labs during same period]
L8 and L9 Numerical differentiation
Nature of the problem: situations in which it arises in civil engineering problems. Finite difference formulae. The concept of finite differences, two, three and higher point formulae. Errors. Central, backward and forward differences. Method order. Application of difference formulae to estimate derivatives. Examples. Polynomial fitting by least squares. Algebraic differentiation. Problems likely to be encountered.
L10 Revision
Applications and worked examples, to further demonstrate use of methods for solving Civil Engineering problems with guidance on checking correct implementation and common errors to avoid.
Tutorials: Titles & Contents
Some exercises in this module are undertaken in the Computer Laboratory using MATLAB. The aim is to build on the course Computer Tools for Civil Engineers 2 (CTC2) to give further experience and confidence in the use of numerical analysis packages on computers. Other examples are worked into revision exercises.
Computer Exercise 1: Non-linear Equations
This computer lab exercise is undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of non-linear equations using Fixed Point, Newton-Raphson, Bisection and False Position methods. Example scripts are provided for some of these, others must be developed from scratch. These are then applied to the solution of various mathematical problems, with investigation of issues such as convergence and tolerances. The lab exercises are designed to teach the student that problems which look difficult from an algebraic viewpoint can be simple numerically, and vice versa.
Computer Exercise 2: ODE&ęs
This computer lab exercise is also undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of ODE&ęs. The methods used are Euler, Euler-Cauchy and Runge Kutta. Example scripts are provided for some of these, others must be developed from scratch. These are then applied to the solution of various mathematical problems, some set in the context of Civil Engineering problem, with investigation of issues such as numerical errors and convergence and tolerances.
Assessment of the coursework is undertaken in the fifth week of labs, with a set of short questions testing ability to apply the above methods to some similar problems. It is conducted using MATLAB, with submission via the course intranet pages on WebCT.
There are also revision exercises for completion by hand run in weekly tutorial sessions. These will cover the same material as that of the teaching course, but provide the hands-on experience that students require to gain confidence in application of the methods, learning to resolve difficulties, correct misunderstandings, etc. The examples provided are typical of the questions asked during the examinations. | 677.169 | 1 |
MAA Review
[Reviewed by Fernando Q. Gouvêa , on 02/11/2001]
The Old Testament book of Ecclesiastes reminds us that "of the making of many books there is no end" and "there is nothing new under the sun." And when it comes to mathematics textbooks this often seems to be the case. Here, on the other hand, is something truly different.
Introductory books on number theory seem, these days, to always begin at the same place and cover similar territory. Whatever differences one finds between books have to do with details of approach and style or with what is done in the more advanced chapters, after the obligatory chapters dealing with divisibility, congruences, linear diophantine equations, primitive roots, and quadratic reciprocity.
Now, of course there's nothing wrong with that sequence; in fact, one can certainly argue that it represents some of the most important foundational ideas in the subject. On the other hand, number theory is such a large subject, and so much of it is initially accessible without too many pre-requisites, that one would expect to see a different take on the subject every once in a while. And that, happily, is what we have here, both in content and in style of presentation.
Burger's book proposes to introduce students to a range of number-theoretical ideas, theorems, and problems by having the students themselves discover the results and prove the theorems. Thus, the book presents the material largely through a sequence of problems surrounded by some expository text which usually focuses on the significance of the theorems rather than on their proofs. The chapters, actually called "modules," typically end with "Big Picture Questions" which invite the student to attempt to consider what has been done so far, where it might be going, and why it is interesting.
The main thread through the book is diophantine approximation. For the first ten modules, the focus is on approximating irrational numbers by rationals while controlling the size of the denominator of the approximants. This is a rich area of number theory, connected to continued fractions, Farey sequences, and transcendence theory. It is also an area that is accessible to undergraduates, so it is a particularly good choice for this kind of book. The modules build towards some significant results: a description of the Markoff spectrum, solving the Pell equation, and the work of Liouville and Roth on transcendental numbers.
The next two chapters are basically a detour through arithmetical algebraic geometry. They look at Pythagorean triples from a geometric point of view and quickly visit the theory of elliptic curves. Then come chapters on Minkowski's "geometry of numbers" and applications to simultaneous diophantine approximation and the four squares theorem. After a module on "distribution modulo 1," the final modules deal briefly with p-adic numbers, ending with a discussion of Hensel's Lemma and the local-global principle.
As that summary suggests, the first half of the book feels tightly integrated around a basic theme, building towards some significant theorems. The second half is more like a quick tour, with stops at several interesting locations but no extensive development and no culminating theorems. This may make sense in a course setting, where one would be virtually certain of finishing the first ten modules but might want to pick and choose among the last ten.
Overall, this is a very nice guide through this material. The first ten modules are the best and most interesting part of the book, well worth working through. The section on "arithmetical algebraic geometry" is probably the weakest, but the book picks up steam again when it goes into the "geometry of numbers" section. The module on "distribution modulo 1" has an interesting theorem at its center, though perhaps the proof given here is not the most illuminating one. (On the other hand, the proof I really find more illuminating has far more pre-requisites.) The section on the p-adics should be lots of fun for the students, and goes just deep enough to suggest that there is some substance to the subject.
Since the book is designed to be given to students in a seminar-style course, it does not contain solutions of any of the problems. For some problems, hints are provided; these vary from very meager to quite detailed. There are discussions, at the back of the book, of some, but not all, of the "Big Picture Questions." All this is just right for a course where students are expected to work through the material and develop their own proofs and examples, but it lays a heavy burden on the instructor. No "teacher's solution manual" is provided. If you propose to lead your students into this jungle, you had better have a pretty good idea of the lay of the land before you start, or you'll all end up lost together. This is particularly true when it comes to the "big picture."
For professors with the requisite background, this may be just the right book to use in an upper-level undergraduate seminar. Students working through this book will learn some nice material, and will probably also emerge from the course with a much greater confidence in their ability to do mathematics.
Fernando Q. Gouvêa is Associate Professor of Mathematics at Colby College in Waterville, ME. He works in number theory (focusing especially on modular forms and Galois representations) and also has a strong interest in the history of mathematics.
BLL* — The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. | 677.169 | 1 |
textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve new problems. | 677.169 | 1 |
It may be a good idea to get a Rubik's cube, as many examples we will see may be easier to understand with a cube in front of you. There are several online cube solvers (I particularly like this one), and they may be used as well, but I still recommend you get a physical copy.
The book presents many examples using the mathematics software SAGE. SAGE, developed by William Stein, is open source and may be freely downloaded. Consider installing it in your own computers so you can practice on your own. SAGE is very powerful and you will probably find it useful not just for this course.
(It was recently proved that Rubik's cube can be solved in 20 moves or less, and 19 moves do not suffice in general.)
Contents: The usual syllabus for this course lists
Introduction to abstract algebraic systems – their motivation, definitions, and basic properties. Primary emphasis is on group theory (permutation and cyclic groups, subgroups, homomorphism, quotient groups), followed by a brief survey of rings, integral domains, and fields.
Joyner's textbook emphasizes group theory through permutation representations. The theory is illustrated by several permutation games. Other natural examples of groups come from geometric considerations. We will see many additional examples.
(An interesting example of groups arising from geometric considerations are the plane symmetry groups, which one can see nicely illustrated in La Alhambra. I visited Granada in 2005 and have uploaded to Google+ some pictures from the trip, where you can see further examples.)
Prerequisites: 187 (Discrete and foundational mathematics). Knowledge of 301 (Linear algebra) will be useful, though I will review the matrix theory we will need.
Grading: There will not be exams. Instead, the grade will be determined based on homework.
I will frequently assign problems (many will come directly from the book) and provide deadlines. Some of these problems are routine, others are more challenging, a few may give you extra credit points due to their difficulty. Although collaboration is allowed, each student should write their own solutions. If a group of students collaborate in a problem, they should indicate so at the beginning of their solutions. Also, if additional references are consulted, they should be listed as well. It may happen that while reading a different book you see a solution for a homework problem. This is fine, as long as it is not done intentionally, and I trust your honesty in this regard. For some problems, I may specify that no collaboration is allowed.
No problems will be accepted past their deadline, and deadlines are non-negotiable.
I will pay particular attention not only to the correctness of the arguments, but also to how the arguments are presented. Your final grade will be determined based on the total score you accumulate through the term.
It may be that you do not see how to completely solve a problem, but you see how to solve it, if you could prove an intermediate result. If so, indicate this clearly, as it may result in partial credit. On the other hand, the fact that you write something does not mean you will get partial credit.
In addition, you will be assigned a project (to work in groups of two or at most three), to be turned in at the latest by the scheduled time of the final exam. This will constitute 20% or your total grade.
Attendance to lecture is not required but highly recommended.
As the term progresses, I will be getting pickier on how you write your solutions. Introduce and describe all your notation. Use words as necessary; strings of equations and implications do not suffice. You may lose points even if you have found the correct answer to a problem but it is not written appropriately. Do not turn in your scratch work, I expect to see the final product. I am not requiring that you typeset (or LaTeX) your solutions, but I expect to be able to read them without any difficulty. Additional remarks are encouraged; for example, if a problem asks you to prove a result and you find a proof of a stronger statement, this may result in additional extra credit points.Your final project must be typeset; I encourage you to consult with me through the semester in terms of how it looks and its contents.
Once your total score is determined, II will use this website to post any additional information, and encourage you to use the comments feature. If you leave a comment, please use your full name, which will simplify my life filtering spam out.
Post navigation
3 Responses to 305 – Abstract Algebra I
[...] Although I have several ideas in mind, feel free to suggest your own topic. As mentioned on the syllabus, I expect groups of two or three per project. The deadline for submission is the scheduled time of [...]
[...] we now have computers and projection equipment on each classroom. I am using this quite a bit in my abstract algebra class. Except that, during the first few weeks, it was more often than not that the keyboard would [...] order type $\beta$, or the col […] | 677.169 | 1 |
Students are reminded that for those classes requiring a calculator, they need to purchase a TI-84+ (preferred)or a TI-84 Silver Edition Graphing Calculator. Now is the time to watch for back-to-school sales of these products! Please also know, the Pius XI Math Department participates in Texas Instruments' Rewards Program to get technology into the classroom. As such, students are asked to submit the TI Technology Rewards Points Symbol to their teacher this fall.
While the physical world we live in is finite, bounded, limited and measurable, the realm of mathematics is the opposite – infinite, unbounded, limitless and immeasurable. Because students arrive at Pius XI at many different levels of understanding, different skill levels and abilities, the mathematics department offers a full range of courses from Pre-Algebra to Advanced Placement Calculus. While a comprehensive four-year program is recommended for all students, those at a higher level are encouraged to participate in a unique peer-tutoring program to foster strong bonds among all levels of ability.
Students are introduced to both the historical and cultural roots of mathematics, as they learn to communicate this knowledge in oral and written form using mathematical vocabulary and symbols. In addition, skills in analysis, social interaction and decision-making are developed through the discovery process. On a technical level, graphing calculators and computers are integrated into select classes, and Geometry students can expect to use computers on a regular basis. The classroom environment overall promotes intellectual curiosity and a desire to become lifelong learners.
Incoming freshmen are placed in one of two levels of algebra, or accelerated geometry or PreAlgebra based on their placement score and the recommendation of the middle school teacher. Prospective students are invited to participate in the Eighth-Grade Math Competition.
Students will learn to:
Understand numbers and the important and powerful ways in which they are used, thus developing their numerical literacy skills.
Organize work and present mathematical procedures and results clearly, concisely, and correctly.
Communicate using numeric, algebraic and geometric approaches, deciding which is most appropriate given the specific information.
Select appropriate problem-solving strategies and apply them to a variety of situations.
Interpret theoretical and real-world data, make predictions and assess the validity of their predictions. | 677.169 | 1 |
Linear Algebra by Georgi E. Shilov Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, and moreChallenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.Products in Algebra
Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problemsOur Price: $11.95
On Sale!$8.96
Algebra by Larry C. Grove This graduate-level text is intended for initial courses in algebra that proceed at a faster pace than undergraduate-level courses. Subjects include groups, rings, fields, and Galois theory. 1983 edition. Includes 11 figures. Appendix. References. Index.
Our Price:$19.95
The Algebra of Logic by Louis Couturat In an admirably succinct form, this volume offers a historical view of the development of the calculus of logic, illustrating its beauty, symmetry, and simplicity from an algebraic perspective. 1914 edition.
Our Price:$37.50
The Algebraic Structure of Group Rings by Donald S. Passman "Highly recommended" (Bulletin of the London Mathematical Society) and "encyclopedic and lucid" (Bulletin of the American Mathematical Society), this book offers a comprehensive, self-contained treatment of group rings. 1985 edition.
Our Price:$29.95Our Price:$25.95Our Price:$16.95
Boolean Algebra by R. L. Goodstein This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
A Course in Linear Algebra by David B. Damiano, John B. Little Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter features multiple examples, proofs, and exercises. Includes solutions to selected problems. 1988 edition.
Our Price:$26.95
Elementary Matrix Algebra by Franz E. Hohn This treatment starts with basics and progresses to sweepout process for obtaining complete solution of any given system of linear equations and role of matrix algebra in presentation of useful geometric ideas, techniques, and terminology.
Our Price:$49.95Our Price:$12.95
Foundations of Galois Theory by M. M. Postnikov A virtually self-contained treatment of the basics of Galois theory. This 2-part approach begins with the elements of Galois theory and concludes with the unsolvability by radicals of the general equation of degree n is greater than 5. | 677.169 | 1 |
Information About:
Department of Math News
Kent State Dedicates New Math Emporium
Posted Sep. 19, 2011
Members of the Kent State University community celebrated the opening of the new Kent State Math Emporium on Tuesday, Sept. 13. The Math Emporium, a state-of-the-art computerized learning center, is located on the second floor of the University Library and is designed to help students learn math.
Robert G. Frank, Kent State provost and senior vice president
for academic affairs, cuts the ribbon dedicating the Math
Emporium. Among those helping is Andrew Tonge (far left),
chair of the Department of Mathematical Sciences at Kent State.
"The university has developed a specialized learning experience to equip students with the mathematical knowledge they will need on their path to graduation," says Robert G. Frank, Kent State provost and senior vice president for academic affairs. "The students will learn math by interacting with a team of instructors and the Web-based math software called ALEKS. The Math Emporium promises to make a significant impact on our first-year retention. For some students, it will give them confidence in their math skills to pursue careers that require math, such as nursing and finance."
At the Math Emporium, students will learn through an innovative, engaging and easy-to-use program designed to help them become comfortable and proficient in basic mathematics. The Math Emporium serves as the classroom for four classes: Basic Algebra 1, 2, 3 and 4. Prior to the beginning of school, students take a placement assessment to determine which math courses they need. Students who need additional math preparation to succeed in college will be matched with the appropriate course of study in the Math Emporium.
"Students will focus on learning exactly what they need to know at their own pace while their instructional team provides individualized coaching," says Andrew Tonge, chair of the Department of Mathematical Sciences. "The Math Emporium uses an adaptive software program, ALEKS, to determine what students already know. It then offers each student an individualized choice of paths forward. This enables them to complete the curriculum efficiently by always studying only material they are ready to learn. All students can then manage their study time to focus on actively learning precisely the information they need, with the aid of online help tools and an interactive e-book, together with one-on-one assistance from an instructional team."
"The Math Emporium's potential effect on student success is very exciting," Frank says. "In addition to this Math Emporium on our Kent Campus, we will have similar facilities on our Regional Campuses."
The Math Emporium features state-of-the-art technology with 247 computer stations in an 11,154-square-foot space. The facility also features bright, vibrant colors and comfortable furniture, making it an attractive and appealing environment.
The Math Emporium is staffed from 7:30 a.m. to 9 p.m. Monday through Thursday; 7:30 a.m. to 6 p.m. on Friday; 10 a.m. to 6 p.m. on Saturday; and noon to 8 p.m. on Sunday. Students also can access the program from any Web browser. | 677.169 | 1 |
You are here
Mathematics Secondary Media
Algebra 2 lesson: By developing a function to describe the annual cost of a refrigerator and given a function describing concentration of drug in the body, students relate the behavior of the graph of a rational function with the phenomenon it describes. Asymptotes and particular points become important information about the application.
Algebra 2 lesson: Using the CBL and the graphing calculator, students work in groups to collect data describing the freefall of an object over time. The data collected includes data not relevant and that must be eliminated, and data is shifted near the y-axis to make the intercept meaningful. The students describe the meaning of the coefficients. The experiment is run again with an object that has drag (like a hat) and a model is found. The follow-up problem works with the football data from the lesson: Football and Braking Distance: Model Data with Quadratic Functions.
Algebra 2 lesson: Using the definition of complex numbers and operations with complex numbers, students add, multiply, and graph with complex numbers using some sample items from the NC Algebra II Indicators. Once familiar with the operations and graphing, students iterate complex numbers in functions to determine whether the iteration stabilizes. With some experimentation, rules are developed that show patterns in stabilization that carry into graphs by special coloring schemes. The result is a fractal. Examples from the Julia Set and the Mandelbrot Set are shown.
Algebra 2 lesson: Concepts of composition are used to develop functions that describe volumes of pyramids with specific bases and combinations of special discounts when purchasing a car. The connection between study time and number of courses leads to a function using inverse function that can help students determine the number of courses to take for available weekly study time.
Algebra 2 lesson: Using rulers, students measure distances on a diagram to find a shortest path. They create ordered pairs and a scatterplot. With the motivation that the scatterplot has a clear message, the students develop a function that measures the distances using the distance formula. Based on the function, the shortest distance can be estimated and then considered on the diagram. A follow-up problem involving determining the best place to put a new Post Office is included.
Algebra 2 lesson: Data representing the period of a swinging pendulum versus the length of the pendulum can be best modeled by a square root function. Data and an appropriate model are both given to the students. Questions from the NC Algebra II Indicators require students to solve equations involving radical expressions. Solutions are also investigated from both a graphical and an analytical point of view.
Algebra 2 lesson: Students are given data to describe the trajectory of a football tossed from the tallest bleachers of a stadium. The data is fit with a quadratic function using least squares criteria. Given data extracted from page 288 of Glencoe's Algebra II book, students investigate braking distance versus speed of a car. Using quadratic least squares, the student finds a best-fit function for the data. Data is given on reaction distance versus speed of the car. When reaction distance is added to braking distance to find total stopping distance, students fit another quadratic function. A Follow Up Problem relates number of sides of a polygon with the number of vertices to create a quadratic function. | 677.169 | 1 |
Course Descriptions
Mathematics Course Descriptions
MAT-designated courses (with the exception of MAT101 and MAT102) qualify as Liberal Arts or Mathematics electives.
MAT101
Elementary Algebra with Lab - 3 Credits
This course develops the fundamental processes of algebraic thinking and provides students with the skills for further study in higher level algebra based courses. This course is integrated with an online mathematics program and mandatory computer lab sessions designed to further enhance the classroom experience. Topics include a study of the real number system, solving and graphing linear equations and inequalities in one and two variables, exponents, scientific notation, operations on polynomials, ratios, proportions, and basic factoring in a problem solving context. Course requires subscription to a supplementary online program. Graphing calculator will be provided for occasional use in class.
Prerequisite: Department recommendation.
MAT102
Intermediate Algebra - 3 Credits
This course builds upon algebraic skills learned in MAT101 or a similar experience and provides students with additional skills needed for further study in higher level algebra based courses. This course is integrated with an online mathematics program designed to further enhance the classroom experience. Topics include further development of the study of linear functions, solving absolute value equations and inequalities, solving linear systems for break-even analysis, working with polynomial functions, and further development of factoring skills, applications of quadratic functions, and simplifying rational and radical expressions. Course requires subscription to a supplementary online program.
Prerequisite: C or better in MAT101 or Department PermissionMAT106
Business Mathematics (elective offered in Spring of 2013) - 3 credits
This course, intended for the business major, surveys topics in elementary algebra, personal finance, probability, and statistics and is integrated with an online homework and tutorial program designed to assist students in achieving their goals of high level performance in and out of the classroom. Topics focus on real-life situations, decision making skills, and problem solving. Topics include solving algebraic equations, solving ratio and proportion problems, and applications involving percentage, simple interest, simple discounts, consumer credit, compound interest, future and present value, applied probability, descriptive statistics, investments, mortgages, and taxes. Some working knowledge of elementary algebra is expected. Course requires subscription to a supplementary online program. Scientific or graphing calculator strongly recommended.
A survey of mathematics topics all students need to meet with success in today's society. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Topics include a study of number systems, essential algebraic & geometric principles, sets and logic, counting principles, statistics, graphing, and data analysis. Optional topics may include networks, money, and voting principles. Course requires subscription to a supplementary online program. Scientific calculator recommended. Course is designed to prepare students for success on standard workplace competency assessments.
MAT120
College Algebra - 3 CreditsPrerequisite: C or better in MAT102 or Department Permission.
MAT130
Pre-Calculus and Trigonometry - 3 Credits
This course is a study of functions deeply embedded with real-life activities and integrated with an online mathematics program designed to further enhance the classroom experience. Topics include an overview of algebraic, exponential, logarithmic, rational, radical, and trigonometric functions as they are applied to daily life experiences. Course requires subscription to a supplementary online program. Graphing calculator required.
Prerequisite: MAT120, or MAT102 with Department Permission, or Department Recommendation.
MAT220
Statistics - 3 CreditsMAT223
Statistics II - 3 credits
This course is a continuation of introductory statistics with applications. Topics covered include inferences involving two populations, analysis of variance, linear regression analysis, multiple regression, forecasting, time series analysis, and elements of nonparametric statistics. This course is integrated with a state of the art online program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program. Scientific or graphing calculator and access to a spreadsheet program is recommended.
Prerequisite: MAT 220 or Department permission.
MAT230
Quantitative Analysis - 3 CreditsPrerequisite: MAT120 College Algebra or MAT130 Pre-Calculus.
MAT250
Calculus I - 3 Credits
This course introduces differential and integral calculus of one variable. Topics include analytic geometry, functions, limits, derivatives, applications of derivatives, and anti-derivatives. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program.
Prerequisite: MAT130 Pre-Calculus or Department permission.
MAT251
Calculus II - 3 Credits
This course is a continuation of MAT250. Topics include the definite integral, the Fundamental Theorem of Calculus, exponential and logarithmic functions, techniques of integration, and applications. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program. | 677.169 | 1 |
Mathematics
This subject is required each year through tenth grade, or longer if
theModern Curriculum Press Mathematics: Level D
Subject: Arithmetic
Course Number: 56340
Suggested Grade Level: 4th
Authors: Richard Monnard and Authors: Royce Hargrove
Number of Pages: 351
Publisher: Pearson Education, Inc.
Academic Credit: None
Copyright: 1994
Elective Fee: None
Prerequisites: None
Course Materials: Workbook, teacher's guide, and 15 tests*
* Item published by Christian Liberty Press
Course Description: This course begins by reviewing facts regarding addition and subtraction and then presents topics such as multiplication of whole numbers, division by a one-digit number and by whole numbers, and working with decimals and fractions. Students are also introduced to measurement, graphing, probability, and geometry. A number of word problem sets are included.
Course Description: This course re-teaches and then reviews many of the concepts presented in Arithmetic 3 including the four basic arithmetic operations and multiplication and division of two-digit numbers. Area measure, estimation, elementary geometry, writing decimals as fractions, and solving equations are also taught. Fractions receive considerable attention, as do "proper and improper," finding the least common denominator, adding, subtracting, and multiplying. | 677.169 | 1 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.