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Find an Eloy Algebra 1Students will be required to use different technological tools and manipulatives to discover and explain much of the course content. The math sections of the SAT measure a student's ability to reason quantitatively, solve mathematical problems, and interpret data presented in graphical form. Th |
Steps to Achieving the Highest Levels of Mathematics
Overview
Because of the sequential nature of learning mathematics, course placement is based on student effort, teacher recommendation, standardized test scores, and parent/student input. To remain on grade-level, students need to participate in three math credits during their freshman and sophomore years, especially to complete Algebra I, Parts I and II and Euclidean Geometry. Students will need a graphing calculator; all are encouraged to use the Texas Instruments series. The TI-81-86 graphing series is recommended for Algebra I pt. I, and beyond. All students are strongly encouraged to study mathematics beyond tenth grade at the most challenging levels.
Mathematics: Meeting New Challenges Grade 7
Mathematics in grade seven continues to develop the topics learned in elementary school, with an emphasis on problem solving using algebraic skills. Students review basic understanding of fractions and decimals; a sound grasp of multiplication facts is a must. Students participate in the American Mathematics Competition Examination, as well as taking the NECAP and MAP assessments. Based on NECAP scores, districts assessments, and teacher recommendation, students can enroll in Algebra I: Part 1 and earn high school credit.
Pre-algebra Grade 8
Qualifying students may participate in this course in grade 7. Topics covered include numbers and operations, powers and exponents, order of operations, scientific notation, prime factorization, rational and irrational numbers, ratios, and percent of change. In algebra, students identify inverse operations, distributive property, graphing equations, and inequalities, scale models, identify congruent and similar figures, transformations, Pythagorean Theorem, ratios, circles, and classify and sketch solids. In data analysis and probability, students find outcomes and odds, and draft appropriate data displays. Problem-solving is integrated throughout the course. District assessments include NECAP and MAP. The eighth grade participates in the American Mathematics Competition-8.
Algebra I: Part I 1 credit Grades 8-12 Math credit
Prerequisite(s): Pre-algebra and teacher recommendation
This course develops ability in the real number system. Combining like terms and balancing equations leads to expertise in solving and graphing linear functions. Students use graphing calculators extensively as an aid in learning about slope as a rate of change and in solving linear systems. Problem solving skills are integrated into all topics and students complete the first seven chapters of the text, Algebra I (McDougall, Littell-Larson Ed.)
Algebra I: Part II 1 credit Grades 9-12 Math credit.
Prerequisite(s): Algebra I: Part I and teacher recommendation
This course extends a student's ability to work with algebraic expressions and functions. The rules for exponents are learned, leading students to more sophisticated equations (quadratic, exponential, radical) and graphs (parabolas, exponentials, hyperbolas). Graphing calculators are used extensively to understand and learn graphing translations. Factoring and division techniques are developed in order to solve higher degree equations. Permutations and combinations are taught as part of more advanced probability activities.
Euclidean Geometry 1 credit Grades 9-12 Math credit
Prerequisite(s): Algebra 1: Part I
Students demonstrate high level reasoning by writing proofs and solving problems dealing with points, lines, angles, triangles, quadrilaterals, circles, and other shapes. Students study area, perimeter, and volume and the connections between the three dimensions. Students will complete a variety of two- and three-dimensional hands-on projects. The texts used are Geometry (Houghton, Mifflin) and Flatland (Abbott).
Algebra II 1 credit Grades 10-12 Math credit
Prerequisite(s): Algebra I: Part II
This course extends the study of previous algebra courses and assumes a strong working knowledge of those topics. It encompasses the study of functions including logarithmic functions, irrational and complex numbers, polynomial equations, analytic geometry, conic sections, and series and sequences. The text is Algebra II (McDougall, Littell).
Pre-calculus 1 credit Grades 11-12 Math credit
Prerequisite(s): Algebra II and Geometry
This course completes the preparation for college-level calculus. Students develop skills in advanced function analysis and the use of these functions for modeling applications. Concepts in trigonometry are extended to include circular and inverse functions. Analytic trigonometry is studied to apply in vector, parametric, and polar applications. Conic sections are reviewed and extended as are topics in discrete mathematics. Students use graphing calculators on a daily basis.
AP Calculus 1½ credits Grades 11-12 Math credit
Prerequisite(s): Pre-calculus and teacher recommendation
This full-year course prepares students for The College Board Advanced Placement Examination, level AB, which is equivalent to one semester of college calculus. This course includes a brief review of the algebraic and transcendental functions and a study of topics in the differential and integral calculus. Students taking this class participate in the AP Calculus exam. The primary text is Calculus: Graphical, Numerical, Algebraic, 3rd ed. (Finney, Demana, Waits, Kennedy).
Math Workshop 1 credit Grades 9-10 Elective credit
Prerequisite(s): Teacher recommendation
This class is designed to prepare a student for algebra at the high school level. The course is a review of necessary and fundamental arithmetic skills. Students learn to cope with the frustrations of mathematics and pursue a variety of strategies to unlock the principles and procedures of mathematics. Organizational and study skills are emphasized in this elective course.
Introductory Algebra 1 credit Grades 9-10 Math credit
Prerequisite(s): Teacher recommendation
In this course, students investigate algebra using different methods and strategies to solve problems. Algebraic concepts are applied to real-world situations. Students learn the language of algebra to solve simple equations, work with algebraic expressions, and communicate mathematical thinking to others. Students use graphing and other data analysis to organize and understand mathematics. The text used is Algebra: Concepts and Applications (Glencoe McGraw-Hill).
Discovering Geometry 1 credit Grades 10-12 Math credit
Prerequisite(s): Algebra I: Part I or Introductory Algebra
This course is an introduction to the practical aspects of geometry. Topics include the properties of angles, triangles, quadrilaterals, circles and other two-dimensional shapes, area, perimeter, volume, ratio and proportion, geometric construction, and right angle trigonometry. Students complete a variety of two- and three-dimensional hands-on projects. The text used is Discovering Geometry: An Intuitive Approach (Key Curriculum).
Consumer Math 1 credit Grades 11-12 Math credit
Prerequisite(s): Teacher recommendation
Topics in this course relate to problems that consumers face in everyday life. Topics include: housing, income and expenses, taxes, consumer credit, banking and loans, insurance, and investments. Solid arithmetic skills are important. A calculator is strongly recommended. The text is Consumer Mathematics (Houghton, Mifflin). |
logarithmic function
A function which acts on its argument with a logarithm.
matrix
A rectangular array of, usually, real or complex numbers, organized into rows and columns. When specifying the size of a matrix, the number of rows is stated first. For example, here is a 2 by 4 real matrix:
The numbers in a matrix are called entries, and are specified by the row and then column in which they appear. In the example above, for instance, A1,2 is the entry in the first row and second column, i.e. 4.98. Two matrices of the same size (with the same number of rows and columns) can be added componentwise, that is (A + B)i, j = Ai, j + Bi, j. Matrix multiplication is a little more complicated. A matrix M can be multiplied on the right by another matrix T only if T has the same number of rows as M has columns, and the result will have as many rows as M and as many columns as T. The entry of M T appearing in row i and column j is the sum of the pairwise products of the entries in row i of M and column j of T. In other words, if M is an n by m matrix, T must be an m by l matrix, and
Notice that this operation is not, in general, commutative. A matrix that has the same number of rows and columns is called a square matrix, and these are particularly interesting as they can be added and multiplied, and the results will have the same dimensions. The most standard use of matrices is to represent linear operators, but they have a wide variety of other uses, and are interesting to study in their own right. Matrices can have a large number of different types of entries, including various kinds of numbers, elements of abstract fields and other algebraic structures, functions, and so forth.
monotone function
Also called monotonic function. See order-preserving function.
nth-term test
A test for the divergence of a series. See the related article for a complete description.
Related article: Series
natural logarithm
A logarithm with base e, the Euler number. Often written "ln" rather than "log" to distinguish it from logarithms using other bases.
normal
A line intersecting a curve (or surface) perpendicular to the tangent line (or tangent plane) at the point of intersection. The normal to a surface expressed as a function of several variables xi is given by the gradientpower series
An infinite series of the form
See the related article for a complete description.
Related article: Series |
Ships in the Fog with Sketchpad (Intermediate)
Description
Learn how to use The Geometer's Sketchpad to model situations for problem solving. In "Ships in the Fog", participants will find applications to use in classes ranging from Algebra I to Precalculus. Beginning with graphing points, we will translate points to establish a vector path, create a table of values, and test conjectures to solve the problem. Take a look at Sketchpad from a different perspective!
This is an intermediate-level Sketchpad webinar, so some previous knowledge and use of Sketchpad is assumed.
Presenter |
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It's all about computers: when they do the calculating, people can work on harder questions, try more concepts, and play with a multitude of new ideas. Conrad Wolfram discusses a new project to build a completely new math curriculum with computer-based computation at its heart - alongside a campaign to refocus math education away from historical hand-calculating techniques and toward relevant and conceptually interesting topics.
Presented at the Learning Without Frontiers Conference, January 25th 2012, London
So are you saying that applied maths should be taught at schools? Well, applied maths is basically engineering, computer science, actuarial studies, etc. which are specialized fields and more suitable to be studied at university. If you teach applied maths to student, they won't have the skills to do the problems. I believe that maths at school should be pure maths with an emphasis on rigor, problem solving and understanding so students can make use of the maths in university.
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Um,.. Albert Einstein, Stephen Hawking, both people that were only able to ASK QUESTIONS in mathematics due to their deep understanding in maths. Thus deep understanding was only caused by learning maths. How else is someone meant to learn maths. We must be able to tackle completely theoretical problems before we are good enough to tackle real life problems
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One thing which does not necessarily include computation or at least complex computation is mathematical proof. Something like a proof module might go well with these proposals, especially to teach the understanding of mathematical concepts. |
Bartle's "The Elements of Real Analysis"
Bartle's "The Elements of Real Analysis"
I am taking a class that will be using the secnd edition of Bartle's "The Elements of Real Analysis". However, I have the first edition of the book and don't want to buy the second one if I don't need to. Does anyone know the difference between the 1st and 2nd editions?
Edit: Does anyone know if the Preface for the 2nd ed. is online (legally) somewhere? If so I'm sure he will comment on the difference there. |
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within Formula One racing. Here students learn about the models which are used to develop race strategy, since every F1 team must decide how much fuel their cars will start each race with, and the laps on which they will stop to refuel…
This resource, from Mathematics for Engineering Exemplars, introduces mathematical models for the risk assessment of dropped load, which are used to analyse the safety of structures within nuclear power stations. Here students learn about the formulae which engineers use to calculate the maximum dynamic stress and strain produced…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical and electrical engineering in the power industry. When planning a wind farm it is important to know the expected power and energy output of each wind turbine to be able to calculate its economic viability.
This field of mechanical engineering and explores the design and construction of wheels, to be used to challenge a land speed record. These principles also apply in engines and gear-boxes, which are typically full of rotating machinery…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when designing a pumping system. The operating pressure of a pumping system can vary due to various factors, so all the relevant operating conditions need to be assessed to ensure the selected pump is capable of achieving the entire operating…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within a civil engineering environment. Here students apply standard deflection formulae to solve some typical beam deflection design problems. These formulae form the basis of the calculations that would be undertaken in real life for…
This resource, from Mathematics for Engineering Exemplars, shows how to build a mathematical model of liquid draining through a tank and how to use the model to determine the time required for a tank to completely drain.
Bernoulli's conservation of energy equation, which requires integration and differentiation, is applied…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within public health engineering to supply clean water in a rural mountain area. Here students learn about the formulae used to calculate the optimum size of pipes which will ensure good pressure of water throughout the network.
Detailed…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the mechanical and civil engineering industry. Here students learn how calculations for displacement, velocity and acceleration, caused during loading, are used to ensure that they are not so large as to adversely affect the performance…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when designing highway machinery. Because a driver has to remain in the same machine for almost eight hours each day, the vibration amplitudes of the operator's seat, which should be kept as low as possible, are a key factor when…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of sports technology to compare the potential for injury to the knee or ankle when cycling and when jogging.
Students model a situation involving oscillations, looking at inertial forces, Newton's Laws of Motion,…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within mechanical, electrical and electronics engineering. One of the principal applications of Root Mean Square values is with alternating currents and voltages. This activity demonstrates the calculations required to evaluate RMS using…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when investigating the volume of registration of engineers. Statistical calculations and graphical representations are used to explore the variations, over time, of membership by area of expertise.
Detailed notes and examples are provided…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when designing and developing engines. As well as considering the power requirements for a given application, the vibration of the system should be considered. The engine installation in a machine must ensure that the natural frequency…
This resource from Mathematics for Engineering Exemplars shows the application of mathematics in mechanical engineering and construction machinery. Here students encounter the formulae used to calculate the power of the engine which was used to power the JCB Dieselmax LSR car to a world land speed record of 350mph in August 2006.
Detailed…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics for the operation of escalators on the London underground. Students consider a variety of issues which include passenger numbers and flow, as well as carbon emissions, escalator speed and energy efficiency.
Detailed notes and examples…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when building an underground storage tank, with an elliptical cross section. Health and safety requirements apply and the depth to which the tank must be buried is established using the 2D geometry of an ellipse, trigonometric functions…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical engineering. Here students learn that lack of proper insulation results in large energy losses which, over time, cost a lot of money. Models are used to calculate the value of the critical insulation radius…
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the aeronautical industry. Students are given a scenario which involves the recovery of stranded mountaineers by a rescue helicopter and the considerations required for a successful outcome. Trigonometry, formula transposition and… |
Annotation
Publisher Description This Pupil Book: * Guarantees progression with colour-coded levelling and level boosters to help pupils work at the right level and progress with ease. * Enables pupils to develop vital functional skills and put maths into context with the help of the integrated functional maths questions and exciting real-world spreads. * Promotes personalised learning and self assessment using pupil-friendly learning objectives for every chapter. * Eases the class into understanding new concepts with worked examples. * Stretches and challenges the knowledge and skills of pupils using extension activities. * Provides rigorous maths practice with the hundreds of levelled questions. * Captures pupils' attention using the colourful design. * See the Teacher's Pack for more support and answers.
Review '!even at this early stage (only a week in) I have been really impressed with the scheme so far. Our NQTs love the lesson plans and say they really help with ideas and with them finding out what sort of level to teach a topic. The lower set pupils love the workbooks, and they have been a great motivator. The books are clear and easy to read and are excellent practise for filling in SATs papers. Our only problem is that we struggle to get them to stop working and move on to their next lesson! We had a very heated discussion with one Year 9 boy who was insisting that he took his book home to carry on, and was very angry when we said he couldn't take it home! These pupils who are usually fairly unmotivated are working through at a real pace.' Cass Jackson, Barr Beacon Language College
Author Biography
Keith Gordon has 30 years teaching experience in South Yorkshire including 24 as Head of Department. He has 20 years examining experience including 11 years as a principal examiner and 6 years as Chief Examiner. Brian Speed is the former Head of Mathematics in a Rotherham Comprehensive School as well as former Chief Examiner for GCSE Mathemeatics for a major examining board. He is currently the Education Consultant for a major examination board. He still runs large seminars to GCSE pupils up and down the country talking about gaining that grade C |
In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d'analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d'analyse. For this translation, the authors have also added commentary, notes, references, and an index. |
The following types of calculators are permitted: basic calculators, scientific calculators, non-programmable graphing calculators
(click here for more information).
SI study group
Supplemental instruction (SI) offers free
out-of-class study groups to help you succeed in this
class. There will be three one-hour weekly sessions and you may choose to
go to one, two, or all three sessions.
Students who regularly attend SI will save time studying, better master
the course content, and likely earn a better
grade. Further information can be obtained from
the Faculty of Science web site.
Special Need students
Any student with a disability who may need
accommodations should discuss these with the course instructor after
contacting the Coordinator of the
Disability Resource Office, RC 251.15, at 585-4631.
To help you organize your studies, a detailed syllabus and a list of supplementary problems
will be provided. You should attempt to work all of the problems from the
list very thoroughly. Some of them will be solved during the lab hours. If you have difficulties, do not hesitate to contact me during the office hours or by e-mail.
Detailed Syllabus
Day
Section/Subject
Supplementary Problems
Dec. 5
5.1 Areas between Curves
5.4 Work
5.1 Exercises 21 - 32.
5.4 Exercises 7 - 12.
Dec. 2
5.1 Areas between Curves
5.1 Exercises 1 - 20.
Dec. 30
4.4 Indefinite Integrals and the Net Change Theorem
4.5 The Substitution Rule
4.4 Exercises 36 - 42, 46 - 56.
4.5 Exercises 61 - 66.
Nov. 28
4.3 The Fundamental Theorem of Calculus, part II
4.4 Indefinite Integrals and the Net Change Theorem
4.5 The Substitution Rule
4.3 Exercises 19 - 38, 39 - 42, 53, 61, 62.
4.4 Exercises 19-35.
4.5 Exercises 35 - 51.
Nov. 25
4.3 The Fundamental Theorem of Calculus
4.3 Exercises 7 - 18, 49 - 52, 64, 68, 69.
Nov. 23
4.2 The Definite Integral (the midpoint rule, properties of the
definite integral) |
Course Catalog 2010-2011
MAT-31096 Matrix Algebra 1, 5 cr
Person responsible
Lessons
Requirements
Two partial examinations or final examination
Completion parts must belong to the same implementation
Learning outcomes
After passing the course the student:
- knows the main concepts of matrix algebra and linear algebra and is able to perform calculations and make valid conclusions.
- is able to make the most important matrix decompositions
- can use the matrix decompositions in the right context
-knows the main definitions of Matlab uses and understands the basis of the algorithms used in Matlab.
Content
Content
Core content
Complementary knowledge
Specialist knowledge
1.
Basics of linear algebra
Use of Matlab
Applications:
- use of angle between vectors as a measure of similarity |
Themes
Georg Kiefer
This app is able to calculate the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of two
numbers. Very useful mathematical app for school and college!
This app will add a few search access points on your device. If you do not want to use this new search page, you can either ignore...
This app is the pro version of 'Area and Volume Calculator', completely without advertisement.
Area Calculator: You are able to calculate the area for the most important geometric figures. You can calculate the area of circle, ellipse, rectangle, square, trapezoid, triangle,...
This mathematical app is a collection of Prime Number Tools. You are able to:
- find all prime numbers in an interval (for example between 1 and 100)
- check if a number is a prime number or a composite number
- find all the prime factors of every number
Very useful app for students!
Creating...
The best tool for school, college and work!
This mathematical app consists of a Trigonometric Calculator and Trigonometric Formulas.
Trigonometric Calculator: You are able to calculate values for the most important trigonometric functions: Sine, Cosine, Tangent, Arcsine, Arccosine, Arctangent.
Trigonometric Formulas: You can see the most...
The Pythagorean Theorem Calculator will instantly solve the Pythagorean equation. The Pythagorean Theorem states that a²+b²=c² and can be used to find the length of the hypotenuse of a right triangle. Simply input the length of sides A and sides B and the calculator will calculate the length... |
A clear, concise, modern text for the introductory Numerical Analysis market, stressing computer skills and real applications. Aims to give students who are unfamiliar with, inexperienced and uncertai... |
Bridges the gap between digital principles and practice in order to teach practical applications of theoretical knowledge in solving digital design problems. Highlights fundamental concepts in digital technology plus a large variety of integrated devices. Requires a basic knowledge of algebra and an understanding of electric circuits. Its comprehensive style makes difficult concepts easy to grasp. |
Welcome to our Classjump website for Intermediate Algebra! This website is a tool to help connect our classroom to home. Throughout the year, use this website to find class notes, homework assignments, important due dates and information regarding access to the online version of the textbook. These tools will be especially useful if you are absent or know that you will be gone in advance!
We only have about 55 minutes together each day, so it is extremely important that you come to class prepared and ready to engage in learning each and every day. This website will help to keep you prepared, so please check it regularly (like your Facebook!). Intermediate Algebra is a co-taught class in order to provide the best learning opportunities for students. I will be co-teaching Intermediate Algebra with Jesse Ziebarth, so please feel free to contact either of us with any questions or concerns. I look forward to an exciting and wonderful year!
Math lab serves as a support class for students enrolled in one of my sections of Intermediate Algebra w/ Statistics.
Each day, we will start off by checking and working through homework problems from the previous day. Students are expected to come to lab each day with every problem from their assignment ATTEMPTED. Students will work in their assigned groups in order to practice collaboration and teach each other before we come together as a whole class.
We will then extend the lesson from the previous day either through extra practice or some sort of activity, usually involving groupwork.
Time permitting, we will spend the end of the period previewing the lesson students will have in Intermediate Algebra later that day so they can get a jump start on learning that material.
Students will not be receiving extra homework in lab. All work will be done in class.
For any other information, such as the online version of the textbook and contact information, please look under the Intermediate Algebra with Statistics ClassJump page. |
National Math Panel: Major Topics of School Algebra
The National Mathematics Advisory Panel (NMP) Final Report and Reports of the Task Groups and Subcommittees The National Mathematics Advisory Panel conducted a systematic and rigorous review of the best available scientific evidence for the teaching and learning of mathematics and provided recommendations that lay out concrete steps to improve mathematics education, with a specific focus on preparation for learning algebra. The Panel worked in task groups and subcommittees to address areas of mathematics teaching and learning including Conceptual Knowledge and Skills, Learning Processes, Instructional Practices, Teachers and Teacher Education, and Assessment. Five task groups carried out detailed syntheses of research evidence that addressed each group's major questions and met standards of methodological quality. Three subcommittees were charged with completion of a particular advisory function for the Panel. The research findings cited in these reports underpin the mathematics practices and content included on the Doing What Works website.
Multimedia Overview
National Mathematics Advisory Panel
Watch this brief overview to learn about the purpose and findings of the National Mathematics Advisory Panel and research-based recommendations for improving mathematics instruction. Find out why it's important for schools to focus on teaching critical mathematics skills to better prepare students for entry into algebra.
(3:41 min)
Explore these recommended practices:
<<Topics of Algebra Teach the comprehensive set of major topics in algebra recommended by the National Mathematics Advisory Panel.
<<Multiple Paths Expect that all students will learn school algebra through a coherent progression of topics.
Related Links
Achieve has mapped out what students need to know and be able to do in mathematics in grades K-12, connecting the expectations throughout the grades with those for the end of high school. The American Diploma Project (ADP) benchmarks outline a progression of mathematics content for the Elementary Grades K-6 and Secondary Grades 7-12 to ensure that students master the content needed to succeed in college and careers.
The Society was founded in 1888 to further mathematical research and scholarship. AMS promotes mathematical research and its uses, strengthens mathematical education, and fosters awareness and appreciation of mathematics and its connections to other disciplines and to everyday life. Programs and services include meetings and conferences, support for Young Scholars programs and the Mathematical Moments program of the Public Awareness Office, resources for researchers and authors, and a Washington office that connects the mathematical community with the broader scientific community and with decision-makers who determine science funding. In addition, the site provides links to mathematics articles such as Professional Development of Mathematics Teachers.
CBMS is an umbrella organization consisting of seventeen professional societies, all of which have as one of their primary objectives the increase or diffusion of knowledge in one or more of the mathematical sciences. Its purpose is to promote understanding and cooperation among these national organizations so that they work together and support each other in their efforts to promote research, improve education, and expand the uses of mathematics. The group serves as a point of representation for the mathematical sciences to government agencies, other professional societies, and private foundations. Other activities include convening forums for the discussion of issues of broad concern to the mathematical sciences community such as the National Mathematics Advisory Panel Forum held in October 2008.
The mission of the MAA is to advance the mathematical sciences, especially at the collegiate level. Core interests of the group include: 1) supporting mathematical education and learning by encouraging effective curriculum, teaching, and assessment at all levels; 2) supporting research and scholarship; 3) providing professional development that fosters scholarship, professional growth, and cooperation among teachers, other professionals, and students; 4) influencing institutional and public policy through advocacy for the importance, uses, and needs of the mathematical sciences; and 5) promoting the general understanding and appreciation of mathematics. MAA encourages students of all ages, particularly those from underrepresented groups, to pursue activities and careers in the mathematical sciences.
The U.S. Department of Education Mathematics and Science Partnerships program funds professional development activities intended to increase the academic achievement of students in mathematics and science by enhancing the content knowledge and teaching skills of classroom teachers. Partnerships between high-need school districts and the science, technology, engineering, and mathematics (STEM) faculty in institutions of higher education are at the core of these improvement efforts. Other partners may include state education agencies, public charter schools or other public schools, businesses, and nonprofit or for-profit organizations concerned with mathematics and science education.
MSRI's mission is the advancement and communication of fundamental knowledge in mathematics and the mathematical sciences, to the development of human capital for the growth and use of such knowledge, and to the cultivation in the larger society of awareness and appreciation of the beauty, power, and importance of mathematical ideas and ways of understanding the world. From its beginning in 1982, the Institute has been primarily funded by the NSF with additional support from other government agencies, private foundations, and academic and corporate sponsors. This site provides links to workshops, streaming video, and other algebra-related resources, including workshop lectures by Hung-Hsi Wu on the topics of The Mathematics K-12 Teachers Need to Know and Preparing Teachers to Teach Algebra.
NAGB was created by Congress in 1988 to formulate policy for the National Assessment of Educational Progress (NAEP). The Governing Board monitors external contracts; prepares and recommends procedures for reporting and disseminating NAEP results; reviews and recommends test content for NAEP; and recommends policies to guide other NAEP activities. Among the Governing Board's responsibilities are developing objectives and test specifications and designing the assessment methodology for NAEP. The Mathematics Framework for the 2009 National Assessment of Educational Progress describes a design for the main NAEP assessments at the national, state, and district levels, including mathematics content and types of assessment questions.
NCSM is a mathematics leadership organization for educational leaders, which provides professional learning opportunities necessary to support and sustain improved student achievement. NCSM envisions a professional and diverse learning community of educational leaders that ensures every student in every classroom has access to effective mathematics teachers, relevant curricula, culturally responsive pedagogy, and current technology. |
Opa Locka GeEach lesson uses what was learned before. If you don't understand one of the foundational steps, you will get lost later on. Kelvin uses multiple techniques to help students understand the basics and does a thorough review so those building blocks stay fresh.
...Sample testing will be provided to evaluate student readiness to take this test. The math portion of the ACT test is 60 questions to be done within 60 minutes. The subjects and % of each included are; Pre Algebra (23%)/ Elementary Algebra (17%) = 40%
The next section is Intermediate Algebra (1...
...Pre algebra deals with the basic concepts needed in order to advance to algebra. Some of the basic concepts found in prealgebra are the following:
linear equations
Probability
Number sense
Geometry
Solving for x
In order to understand algebra, a student must be able to figure out equations tha... |
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Online Algebra Solver
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Financial literacy for students
Why is the world descending into a financial meltdown? Lack of financial math knowledge on the part of consumers and financial institutions has a lot to do with it. Here's a resource that aims to improve the situation.... |
Math
The Connected Mathematics Program (CMP2) used by the sixth and seventh grades and the College Preparatory Mathematics (CPM) algebra I curriculum used by the eighth grade are rich with areas inviting additional insights and open to diverse methods of problem-solving, creating an open-ended structure that is more permissive of individual differences. While much of the content of these programs is parallel to that of standard middle school textbooks, how students learn and the role of the teacher in their learning may be significantly different.
Our mathematics courses support a philosophy of teaching and learning in which the teacher is a facilitator of learning rather than a dispenser of knowledge, and the students are active participants in constructing and explaining mathematics. Activities promote mathematical reasoning, problem-solving, and communication skills. Students work in small and large groups as well as individually to explore concepts, make conjectures, and form generalizations. They learn to respect and value other opinions as they create and eagerly present a variety of approaches and solutions to problems. In so doing, students have an opportunity to experience mathematics in meaningful and challenging ways while obtaining a solid conceptual basis for further study in mathematics.
The CMP series in both sixth and seventh grade consists of several units, each developing a major mathematical concept through a series of investigations. The problems are designed to allow students to uncover the mathematics that is embedded in the situation. The sixth grade year begins with Prime Time, where students explore number theory and concepts involving factors, multiples, primes, and composites. From there, the first of three units focusing on rational numbers, Bits and Pieces 1, provides opportunities for understanding fractions, decimals and percents. Subsequent units on rational numbers interspersed between other topics deal with operations and applications. Other topics include a geometry unit that promotes reasoning about shapes, as well as properties of these shapes and their angles, as well as a measurement unit that emphasizes area and perimeter relationships of both regular and irregular, curved, and straight-sided figures.
In seventh grade, the students study pre-algebra, beginning with Variables and Patterns, which is an introduction to algebra, using tables, graphs and symbols as representations. Similarity concepts are developed in Stretching and Shrinking before exploring rate, ratio, proportion, percent, and proportional reasoning in Comparing and Scaling. Through activities from Accentuate the Negative, students develop an understanding and use of integers before Moving Straight Ahead highlights linear relationships expressed in words, tables, graphs, and symbols. The study of volume and 3-D measurement in Filling and Wrapping extends our study of geometry before concluding the year with What do You Expect, a unit on probability.
Eighth grade algebra begins by briefly reviewing arithmetic operations with integers, order of operations, and some aspects of geometry, especially area. Quickly though, students move into writing and solving equations, solving and graphing systems of equations, examining geometric and algebraic ratios through a variety of activities, and finally factoring quadratics. The end of the year will bring problems that begin to tie algebraic concepts together by formalizing our work with relations, functions, non-linear graphs, and solving inequalities. Lastly, the students will revisit quadratic equations more formally and work out a derivation of the quadratic formula.
Although those represent some of the mathematical topics for each year, the changes we hope to see in your children go beyond acquiring the fundamentals of algebra. We hope that they develop a greater sense of involvement and excitement about mathematical thinking, a greater sense of confidence and trust in their own abilities, a greater ability to clearly explain their thoughts and procedures both in writing and in conversation, and a greater awareness of the diverse skills and approaches that are embraced in mathematics and that can be discovered in each student. |
Mathematics
We offer two services in the area of mathematics to the students who attend the Career Center.
First, each student has a period per week of math that starts of the beginning of their Sophomore year and ends at the conclusion of the first semester of their junior year. The purpose of these sessions are two-fold. 1) to have students discover the connection between mathematics and their specific trade/technical area. 2) to assist the student in their preparation of and pursuit to be able to demonstrate proficiency in the state assessment (PSSA) taken in the early spring of their junior year.
Secondly, we give a full course in mathematics for a credit for any student whose home school has made such a request.
These lessons are aligned are aligned to the eligible content items and consist of 10 multiple choice questions with one open-ended math prompt. This will give the student the opportunity to practice integrated math skills in the PSSA format.
M11.A.1.1.1 Lesson 1: Find Square Root
M11.A.1.1.2 Lesson 2: Scientific Notation
M11.A.1.3.1 Lesson 3: Irrational Numbers on a Number Line
M11.A.2.1.1 Lesson 4: Rates and Percents
M11.A.2.1.2 Lesson 5: Use Direct and Inverse Proportions
M11.A.2.1.3 Lesson 6: Use Proportional Relationships
M11.A.3.1.1 Lesson 7: Use Order of Operations
M11.A.3.2.1 Lesson 8: Use Estimation
M11.B.2.1.1 Lesson 9: Measure Angles in Degrees
M11.B.2.2.1 Lesson 10: Surface Area Prisms
M11.B.2.2.2 Volume of Prisms
M11.B.2.2.3 Irregular Figures
M11.B.2.3.1 Affect of How Linear Dimensions
M11.C.1.1.1 Properties of a Radius
M11.C.1.2.2 Properties of Quadrilaterals
M11.C.1.4.1 Lesson 16: Using Pythagorean Theorem
M11.C.3.1.2 Slope
M11.D.3.2.1 Slope of the Line
Lesson Log & Plans (most recent on top)
---------------------------------------------------------------------- Thursday, April 1, 2010 1:00 pm (Auto and Diesel Technology) M11.A.1.1.2 Lesson 2: Scientific Notation The students made it to #10 of lesson 2. Do number 11 next time and then start lesson 3.
Thursday, April 1, 2010 10:15 am (Auto Technology) M11.A.1.3.1 Lesson 3: Irrational Numbers on a Number Line The students finished lesson 2 and made it through number 2 of lesson 3.
Thursday, April 1, 2010 9:35 am (Construction and Diesel Technology) M11.A.1.1.2 Lesson 2: Scientific Notation The students began lesson 2 and made it through #8. Next time finish the lesson and start lesson 3. ----------------------------------------------------------------------
Wednesday, March 24, 2010 1:40 pm (Cosmetology) M11.A.1.3.1 Lesson 3: Irrational Numbers on a Number Line The students finished #4 of lesson 3. They will finish lesson 3 next time.
Wednesday, March 24, 2010 10:15 am (Cosmetology) M11.A.1.3.1 Lesson 3: Irrational Numbers on a Number Line The students finished #5 of lesson 3. They will finish lesson 3 next time.
Wednesday, March 24, 2010 9:40 am (Industrial Technology & Computer Networking) M11.A.1.3.1 Lesson 3: Irrational Numbers on a Number Line The students finished #3 of lesson 3. They will finish lesson 3 next time. ---------------------------------------------------------------------- Tuesday March 30, 2009 1:40 pm 30, 2010, 2010 1:00 pm (Welding) M11.A.1.1.2 Lesson 2: Scientific Notation The students completed the first ten problems lesson 1 and made it to #5 of lesson 2.
Tuesday, March 30, 2010, 2010 10:15 am 23, 2010 9:35 am (Welding) M11.A.1.1.2 Lesson 2: Scientific Notation The students finished lesson 2. We talked about irrational and rational numbers just before the end of the class. Next time, review rational and irrational numbers and begin lesson 3. (remember to work in tolerances this month)
---------------------------------------------------------------------- Monday, March 29, 2010 1:40 pm (Allied Health) M11.A.1.1.2 Lesson 2: Scientific Notation The students finished lesson 2. Next time begin lesson 3. Monday, March 29, 2010 1:00 pm (Police Science) M11.A.1.1.2 Lesson 2: Scientific Notation The students made it to number 7 on lesson 2. Finish it next time and then begin lesson 3 Monday, March 29, 2010 10:15 am (Allied Health) M11.A.1.1.2 Lesson 2: Scientific Notation The students made it to number 7 on lesson 2. Finish it next time and then begin lesson 3
Monday, March 29, 2010 9:40 am (Police Science)| M11.A.1.1.2 Lesson 2: Scientific Notation The students made it to number 9 on lesson 2. Finish it next time and then begin lesson 3Wednesday, March 24, 2010 1:40 pm (Cosmetology) M11.A.1.1.2 Lesson 2: Scientific Notation The students finished #10 of lesson 2. They will finish lesson 2 next time. Two were absent.
---------------------------------------------------------------------------------------------------------- Tuesday March 23, 2009 1:40 pm (CAH & TMS) M11.A.1.1.1 Lesson 1: Find Square Root The students completed the first 10 problems of lesson 1. Next time do number 11 before moving on to lesson 2.
Tuesday, March 23, 2010, 2010 1:00 pm (Welding) M11.A.1.1.1 Lesson 1: Find Square Root The students completed the first ten problems of lesson 1. Next time review number 11a and then complete lesson 1 and move to scientific notation.
Tuesday, March 23, 2010, 2010 10:15 am (CAH & TMS) M11.A.1.1.1 Lesson 1: Find Square Root The students completed the first 10 of lesson 1. Next time they will finish it and move to scientific notation.
Tuesday, March 23, 2010 9:35 am (Welding) M11.A.1.1.2 Lesson 2: Scientific Notation The students began the final nine weeks working on lesson 2 and made it through number 8. They will begin there next time.
Thursday, March 4 4 4, 2010 10:15 am (Auto and Diesel Technology) The students worked on the final PSSA practice problems 1-20.
Thursday, March 4, 2010 9:35 am (Construction Technology) The students worked on the final PSSA practice problems 1-20.
Wednesday, March 3, 2010 1:40 pm (Cosmetology) The students worked on the final PSSA practice problems 1-20. And, they worked on estimating the number of inches of hair to cut.
Wednesday, March 3, 2010 1:00 pm (Industrial Technology & Computer Networking) The students worked on the final PSSA practice problems 1-20.
Wednesday, March 3, 2010 10:15 am (Cosmetology) The students worked on the final PSSA practice problems 1-20. And, they worked on estimating the number of inches of hair to cut.
Wednesday, March 3, 2010 9:40 am (Industrial Technology & Computer Networking) The students worked on the final PSSA practice problems 1-20.
Tuesday March 2, 2009 1:40 pm (CAH & TMS) M11.A.3.2.1 Lesson 8: Use Estimation The students continued to work on lesson 8 and made it through problem # 9.
Tuesday, March 2, 2010, 2010 1:00 pm (Welding) M11.B.2.2.1 Lesson 10: Surface Area Prisms The students began lesson 10 and got the first question done.
Tuesday, March 2, 2010, 2010 10:15 am (CAH & TMS) M11.A.3.2.1 Lesson 8: Use Estimation The students completed up to #8 of lesson 8. Begin next class with #9 (redo). If time, begin lesson 10 on surface area.
Tuesday, March 2, 2010 9:35 am (Welding) M11.A.3.2.1 Lesson 8: Use Estimation The students completed lesson 8 and began lesson 10 on finding surface area. They did the first problem and will need to redo it next time.
Thursday, February 18 February 18 M11.A.3.2.1 Lesson 8: Use Estimation The students made it to #2 of lesson 8. Next time, begin with #3.
Thursday, February 25, 2010 9:35 am (Construction Technology)
M11.A.3.2.1 Lesson 8: Use Estimation The students made it to #3 of lesson 8. Next time, begin with #4.
Wednesday, February 24, 2010 1:40 pm (Cosmetology) M11.A.3.2.1 Lesson 8: Use Estimation The students will start lesson 8 next time. They were prepping for a test and did not come today.
Wednesday, February 24, 2010 1:00 pm (Industrial Technology & Computer Networking) M11.A.3.2.1 Lesson 8: Use Estimation The students made it to #7 of lesson 8. Next time, begin with #6.
Wednesday, February 14, 2010 10:15 am (Cosmetology) M11.A.3.2.1 Lesson 8: Use Estimation The students made it to #3 of lesson 8. Next time finish lesson 8 and work in some examples of estimating fractional portions of an inch.
Wednesday, February 24, 2010 9:40 am (Industrial Technology & Computer Networking) M11.A.3.2.1 Lesson 8: Use Estimation The students made it to #7 of lesson 8. Next time, begin with #8. If time, start lesson 9.
Tuesday February 24, 2009 1:40 pm (CAH & TMS) M11.A.3.2.1 Lesson 8: Use Estimation The students used the PRS clickers and worked in groups to complete lesson 8. Next time begin lesson they will begin with #4.
Tuesday February 23, 2009 1:40 pm (CAH & TMS)
M11.A.3.2.1 Lesson 8: Use Estimation The students used the PRS clickers and worked in groups to complete lesson 8. Next time begin lesson they will begin with #4.
Tuesday, February 23, 2010 1:00 pm (Welding) M11.A.3.2.1 Lesson 8: Use Estimation The students used the PRS clickers and worked in groups to complete lesson 8. Next time begin lesson they will begin with #7.
Tuesday, February 23, 2010 10:15 am (CAH & TMS) M11.A.3.2.1 Lesson 8: Use Estimation The students completed up to #4 of lesson 8. Begin next class with #5.
Tuesday, February 23, 2010 9:35 am (Welding) M11.A.3.2.1 Lesson 8: Use Estimation The students completed up to #6 of lesson 8. Begin next class by doing #6 again and then try to finish the lesson.
Monday, February 22, 2010 1:40 pm (Allied Health)
M11.A.2.1.3 Lesson 6: Use Proportional Relationships The students used the PRS clickers and worked in groups to complete lesson 6. Next time begin lesson 7. Monday, February 22, 2010 1:00 pm (Police Science) M11.A.2.1.3 Lesson 6: Use Proportional Relationships The students used the PRS clickers and worked in groups to complete lesson 6. Next time begin lesson 7. Monday, February 22, 2010 10:15 am (Allied Health) M11.A.2.1.3 Lesson 6: Use Proportional Relationships The students used the PRS clickers and worked in groups to complete lesson 6. Next time begin lesson 7.
Monday, February 22, 2010 9:40 am (Police Science)|40 pm00 pm 9:35 am40 pm (Cosmetology00 pm (Industrial Technology & Computer Networking) M 10:15 am (Cosmetology) M11.A.2.1.3 Lesson 6: Use Proportional Relationships The students used the PRS clickers and worked in groups to complete lesson 6. Next time begin lesson 7. |
Book Description: Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition. |
The Philosophy of Mathematics: An Introductory Essay by Stephan Körner A distinguished philosopher surveys the mathematical views and influence of Plato, Aristotle, Leibniz, and Kant. He also examines the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 editionProblem Solving Through Recreational Mathematics by Bonnie Averbach, Orin Chein Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. 1980History of Mathematics, Vol. II by David E. Smith Volume II of a two-volume history — from Egyptian papyri and medieval maps to modern graphs and diagrams. Evolution of arithmetic, geometry, trigonometry, calculating devices, algebra, calculus, more. Problems, recreations, and applications.
History of Mathematics, Vol. I by David E. Smith Volume 1 of a two-volume history — from Egyptian papyri and medieval maps to modern graphs and diagrams. Non-technical chronological survey with thousands of biographical notes, critical evaluations, contemporary opinions on over 1,100 mathematiciansPopular account ranges from counting to mathematical logic and covers the many mathematical concepts that relate to infinity: graphic representation of functions; pairings and other combinations; prime numbers; logarithms and circular functions; formulas, analytical geometry; infinite lines, complex numbers, expansion in the power series; metamathematics; more. 216 |
Fundamental Theorem of Calculus
In this lesson, Professor John Zhu gives an introduction to the fundamental theorem of calculus. He goes over the properties for the fundamental theorem of calculus as well as the definition of integral. He reviews four rules/ properties for calculus and performs a few example problems.
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Fundamental Theorem of Calculus
Simply evaluating integral at 2
bounds
Area under a curve
Accumulated value of
anti-derivative function
Fundamental Theorem of Calculus
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
collection is a full course of material in the form of a textbook. The textbook is FHSST Mathematics textbook contains a total of 45 chapters to be used in grades 10, 11, and 12. At the end of this description is a complete Table of Contents.
The textbook is broken into 5 sections: basics (Chapter 1), Grade 10 (Chapters 2-16), Grade 11 (Chapters 17-34), Grade 12 (Chapters 35-45), and Exercises. In this collection, you will find folders for each of these sections and chapters are found within.
Description:Algebra 1 textbook answers and problem sets designed to illustrate all chapters covered in Algebra 1. All answers are illustrated with "motion lines" and explanations. Contributed by offering instant math help for struggling algebra students.
Description:This is a very fun Geometry and STEM wiki; I teach everything with arts and sciences and humanities. It is projects based learning and discovery learning; it is a work-in-progress and encourages collaborations across all subjects and worldwide…
Last Updated:Feb-01-2012
Subject(s):
Arts
Career & Technical Education Assignment/Homework
Asset: Article/Essay
...
This is a very fun Geometry and STEM wiki; I teach everything with arts and sciences and humanities. It is projects based learning and discovery learning; it is a work-in-progress and encourages collaborations across all subjects and worldwide…
Description:
START OF THIS PROJECT GUTENBERG EBOOK A FIRST BOOK IN ALGEBRA *
Last Updated:Jun-22-2012
Subject(s):
Mathematics
Mathematics > AlgebraBook: Text Book |
Description
The first half of a modern high school algebra sequence with a focus in seven major topics: transition from arithmetic to algebra, solving equations & inequalities, probability and statistics, proportional reasoning, linear equations and functions, systems of linear equations and inequalities, and operations on polynomials. Students enrolled in this course must take the WA State High School End of Course Algebra Assessment if they have not attempted it once already. Prerequisite: Must be working toward a high school diploma.
Intended Learning Outcomes
Select and justify functions and equations to model and solve problems
Solve problems that can be represented by linear functions, equations, and inequalities
Solve problems that can be represented by a system of two linear equations or inequalities.
Solve problems that can be represented by quadratic functions and equations
Solve problems that can be represented by exponential functions and equations
Know the relationship between real numbers and the number line, and compare and order real numbers with and without the number line
Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables
Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions
Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection
Use algebraic properties to factor and combine like terms in polynomials |
TEXTBOOK*
Functions, Data, and Models: An Applied Approach to College Algebra
Sheldon P. Gordon and Florence S. Gordon
Functions, Data, and Models is a college-level algebra textbook that is written to provide the kind of mathematical knowledge and experience that students will need for courses in other fields such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experiments or from other studies. The book focuses on fundamental mathematical concepts and realistic problem-solving via mathematical modeling rather than the development of algebraic skills.
Functions, Data and Models presents college algebra in a way that differs from almost all college algebra books available today. The authors teach something new rather than covering the same ground as high school courses. By changing the content of the course, the authors are able to give students an introduction to data analysis and mathematical modeling that even students with limited algebraic skills can handle. The book contains rich exercises, many of which use real data. Also included are thought experiments or what if questions that are meant to stretch the student's mathematical thinking. |
Conley ACT
...Algebra was developed to expand math where arithmetic fell short. Similarly, Calculus expands the reaches of mathematics where Algebra alone cannot reach. Calculus is the study of rates of change for continuous functions. |
Note:
These are course-specific requirements that go above and beyond the Provider Baseline Technical Requirements.
The school or student is responsible for providing:
This class uses Apex Learning online curriculum. Each student will run a system checkup during the Getting Started activity to insure their computer has all the required features and settings; Refer to the Apex Learning System check-up:
Materials to be ordered via the DLD
The DLD Registrar may order the following materials via the DLD upon registering the student:
No additional materials required for this course.
Description
This first semester of algebra 1 course covers real numbers, introduction to algebra, writing and solving equations, proportional reasoning, writing and solving inequalities, graphs and functions, as well as graphing equations. Because high school students have unique needs and experiences, CompassLearning ensures that students know where they, are while challenging them to grow. Odyssey High School Math focuses on foundational skills to support learners, emphasizes repetition and practice of key skills, reinforces study habits, including note-taking, to sharpen students� comprehension, and covers National Mathematics Advisory Panel�s concepts for success in algebra.
Syllabus / Outline
The interesting thing about this class is that we learn lots of math and numbers. Its interesting to learn this online because I never thought that I would learn math online. First I like that my teacher is there to help via email with my work. Next I like that the work is brought out to me in my class. Lastly I like that my math isn't super super hard. my least favorite thing is that since i'm no good at math I end up falling behind and I feel that I'm a bad math student. I would like to tell others that this class is very fun if you can understand math. |
Book summary
More than any other book in this field, this book ties together discrete topics with a theme. Written at an appropriate level of understanding for those new to the world of abstract mathematics, it limits depth of coverage and areas covered to topics of genuine use in computer science. Chapter topics include fundamentals, logic, counting, relations and digraphs, trees, topics in graph theory, languages and finite-state machines, and groups and coding. For individuals interested in computer science and other related fields looking for an introduction to discrete mathematics, or a bridge to more advanced material on the subject. [via] |
Mathematics is the art and science of abstraction;
it is the systematic study of quantity, structure, space, and change;
to paraphrase Newton, it is the language in which the universe is written.
The study of mathematics provides the abilities to
analyze data, discover patterns, and reason logically.
Computer Science is the fusion of abstraction and technology;
it is the study of representing, processing, and communicating information,
the design and analysis of algorithms,
and the implementation of solutions through both hardware and software.
The study of computer science is both theoretical and practical,
and provides the abilities to develop and to maintain software.
Contact
For additional information, please contact: |
[via]
One of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, convincing answer; others hem and haw and stare at the floor. The real response to the question should be, "Yes, you will, because algebra gives you power" the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on.
Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, Algebra I For Dummies can provide the help you need.
This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works.
In Algebra I For Dummies, you'll discover the following topics and more:
All about numbers rational and irrational, variables, and positive and negative
Figuring out fractions and decimals
Explaining exponents and radicals
Solving linear and quadratic equations
Understanding formulas and solving story problems
Having fun with graphs
Top Ten lists on common algebraic errors, factoring tips, and divisibility rules.
No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, Algebra I For Dummies can give you the tools you need to succeed [via]
Volume I of a pair of classic texts and standard references for a generation this book is the work of an expert algebraist who taught at Yale for two decades. Volume I covers all undergraduate topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence. [via]
. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.
This text provides a supportive environment to help students successfully learn the content of a standard algebra course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success. [via]
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included. [via]
More editions of Commutative Algebra with a View Toward Algebraic Geometry:
This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters identify important themes and establish the notation used throughout the book, and subsequent chapters explore the normal and arithmetical structures of groups as well as applications. Includes 679 exercises. 1978 edition.
Presents the fundamentals of linear algebra in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. This substantial revision includes greater focus on relationships between concepts, smoother transition to abstraction, early exposure to linear transformations and eigenvalues, more emphasize on visualization, new material on least squares and QR-decomposition and a greater number of proofs. Exercise sets begin with routine drill problems, progress to problems with more substance and conclude with theoretical problems. [via]
Noted for its expository style and clarity of presentation this substantial revision reflects a new generation of students' changing needs. Proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Features a wide variety of interesting contemporary applications which have been extensively revised and updated. Includes new material on least squares and QR-decomposition and greater emphasis on visualization. [via]
From the reviews: "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --ZENTRALBLATT FÜR MATHEMATIK [via]
Considered a classic by many, A First Course in Abstract Algebra is an in-depth, introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. The sixth edition of this text continues the tradition of teaching in a classical manner while integrating field theory and a revised Chapter Zero. New exercises were written, and previous exercises were revised and modified. [via]
Galois theory is a fascinating mixture of classical and modern mathematics, and in fact provided much of the seed from which abstract algebra has grown. It is a showpiece of mathematical unification and of "technology transfer" to a range of modern applications.
Galois Theory, Second Edition is a revision of a well-established and popular text. The author's treatment is rigorous, but motivated by discussion and examples. He further lightens the study with entertaining historical notes - including a detailed description of Évariste Galois' turbulent life. The application of the Galois group to the quintic equation stands as a central theme of the book. Other topics include the problems of trisecting the angle, duplicating the cube, squaring the circle, solving cubic and quartic equations, and the construction of regular polygons
For this edition, the author added an introductory overview, a chapter on the calculation of Galois groups, further clarification of proofs, extra motivating examples, and modified exercises. Photographs from Galois' manuscripts and other illustrations enhance the engaging historical context offered in the first edition.
Written in a lively, highly readable style while sacrificing nothing to mathematical rigor, Galois Theory remains accessible to intermediate undergraduate students and an outstanding introduction to some of the intriguing concepts of abstract algebra. [via]
The Study Guide is based on David Lay's many years in the classroom, and has been updated so students can take full advantage of the new projects and data in the Updated Second Edition of the text. This guide gives the worked-out solutions to model problems that correspond with exercises in the text, along with study tips, hints to students, instructions for using MATLAB along with the text, additional MATLAB exercises, and expanded coverage of some text material. Maple and Mathematica appendices have been added, and the TI appendix has been updated to include coverage of the TI-86. [via]
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a "brick wall.". Finally, when discussed in the abstract, these concepts are more accessible. Students' conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology. David Lay changed the face of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition. With this update, he builds on this philosophy through increased visualization in the text, vastly enhanced technology support, and an extensive instructor support package. He has added additional figures to the text to help students visualize abstract concepts at key points in the course. A new dedicated CD and Website further enhance the course materials by providing additional support to help students gain command of difficult concepts. The CD, included in the back of the book, contains a wealth of new materials, with a registration coupon allowing access to a password-protected Website. These new materials are tied directly to the text, providing a comprehensive package for teaching and learning linear algebra. [via]
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text. [via]
A student-oriented approach to linear algebra, now in its Second Edition
This introductory-level linear algebra text is for students who require a clear understanding of key algebraic concepts and their applications in such fields as science, engineering, and computer science. The text utilizes a parallel structure that introduces abstract concepts such as linear transformations, eigenvalues, vector spaces, and orthogonality in tandem with computational skills, thereby demonstrating clear and immediate relations between theory and application.
Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups. [via] |
Introduction to MATLAB and SCILAB
Powerful platforms for high-performance mathematical computation and graphical representation provide immense benefits with their ability to handle immense amounts of data in a flexible manner. Capabilities for rapid model design, development, the ability to manipulate "what-if" stimuli and statistical analysis have made these platforms popular worldwide. Gain an intermediate skill level to write scripts, perform calculations, use the command line, import data from files, plot data, integrate with C++ or Java and build GUIs.
Future-Term Courses and Enrollments
Courses are offered three terms per year: spring, summer, fall. Information about upcoming courses is available when enrollment opens each term. |
BLACKBOARD
Resources
on Mathematics Instruction
National Council of Teachers of
Mathematics, (2000) Principles and Standards for School Mathematics.
Reston, VA: National Council of Teachers of Mathematics. For information on
purchasing the publication in book, CD-ROM, or Portable Document Format, please
visit
or call toll-free (800) 235-7566.
For information on the
Mathematics Test of the GED 2002, contact Kenn Pendleton of the GED Testing
Service, American Council on Education, One Dupont Circle NW, Suite 250,
Washington, DC 20036-1163; telephone (202) 939-9498; fax (202) 775-8578; e-mail
kenn_pendleton@ ace.nche.edu; or visit the web site
A new book, Adult Numeracy
Development: Theory, Research, Practice, is available from Hampton Press.
Edited by Iddo Gal, it contains 16 chapters written by adult educators and
researchers. Chapters include "Numeracy and Adult Learning: Implications of
Research for Instruction;" "Understanding NCTM Standards;"
"Instructional Principles for Adult Numeracy Education;" and "Teaching
Mathematics to Adults with Specific Learning Difficulties." Orders can be
placed with the publisher, phone (800)-894-8955, via e-mail: [email protected], or via online sellers such as
Amazon.com.
Adult Learning Maths (ALM) is an
international research forum that brings together researchers and practitioners
in adult mathematics and numeracy to promote the learning
of mathematics by adults. To join or to learn more, contact Dr. Katherine
Safford, Saint Peter's College, Kennedy Boulevard, Jersey City, NJ 07306, or
e-mail her at [email protected]. ALM's web
site is at
Adult Numeracy Network is a
community dedicated to quality mathematics instruction at the adult level. For
more information, visit the AN2 web site at:
The Numeracy E-Mail List is an
electronic discussion list for ideas and discussion on the teaching of numeracy
and basic mathematics to adult learners. To subscribe, write to: [email protected].
In the message area, type: subscribe numeracy.
Family Math, by J. Stenmark, V. Thompson, &R. Cossey, is available
from Lawrence Hall of Science, University of California, Berkeley, CA 94720.
Call (800) 897-5036, or go to the web site
The
Labor Market and the GED
Beyond the GED: Making Conscious
Choices About the GED and Your Future, a set of teaching materials for GED
teachers, is now available from NCSALL. Written by GED teacher Sara
Fass and Focus on Basics editor Barbara Garner, and piloted by Sara in her
class, the materials consist of three units: "The Labor Market,"
"Pursuing Higher Education," and "What the Research
Tells Us." Lesson plans, reading materials, and handouts are provided. To
order, send a request with a check for $5 to cover the cost of photocopying and
mailing to Sam Gordenstein, World Education, 44 Farnsworth Street, Boston, MA02210-1211. Please include contact information such as phone number or
e-mail address.
NCSALL
Reports Available
New research reports are
available from NCSALL. Order by sending a list of the reports you want (by
number) and a check or money order for the correct amount to Sam Gordenstein,
World Education, 44 Farnsworth Street, Boston, MA02210-1211. Please include contact information such as phone number or
e-mail address. The charges cover photocopying
and mailing. The reports can also be ordered over the web, |
Solving Math Word Problems
Solving Math Word problems is not easy! A lot of students have difficulty with Math problems but employing some basic techniques will help you. Math word problems are nothing but numerical functions formated as word. Make your math word problems easy now by working with our expert tutors. Word problems are found in all topics in math like we have algebra word problems, geometry word problems and so on.You can get help in all topics of math like geometry help, calculus help, trigonometry help and so on.Learn math with step by step explanation, get your math homework help and math answers now!!!
How to Solve Math Word Problems?
Ask until it gets clear
Math Word Problems are all about the concepts so it is important that you are clear on the 'process' of how to solve a Math problem. It is important to ask questions and get clarity on the concepts. Once a new topic is introduced you should write it down, review it and in case of any doubts bring it up with your tutor. This process of continuously revising what you learn will gear you up to solve problems.
Read it carefully
It is important to read the word problem you intend to solve slowly and carefully in order to understand what is it that you need to solve. At times you miss out on important information when you give it a quick reading.
Break the problem into parts
Before you get around to solving a Math word problem it is important to break it into parts. Clearly define what you need to do, what all information has been given in the problem and what you already know. Once you have that written down it gets easier to solve the problem.
Help with Math Word Problems
Solve your math word problems for free with expert online tutors and make your math easy. Our online tutors help you to understand the math problems with step by step explanation and get math answers for the problems at the soonest possible time. Get your math help now and make your math a pleasant indulgence rather than a headache. Try a free demo session to see how our sessions work and feel the difference. |
quickest way to be able to acquire mathematical knowledge at (graduate)-university level, but the $best$bestSeries}$DivergentSeries beableto money athand to be able to understand its content. I'd like to understand it, however!
Yet another learning Roadmap request: From high-school to mid-undergraduate studies...
Dear Math-Overflow community, prerequisite knowledge at hand to be able to understand its content. I'd like to understand it, however! |
MATH 2432
This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at Credit Hours 4 Course Title Calculus II Prerequisite(s) MATH 2431 with a "C" or better Corequisite(s)None Specified Catalog Description
This course includes the study of techniques of integration, applications of the definite integral, an introduction to differential equations, polar graphs, and power series.
Expected Educational Results
As a result of completing this course, the student will be able to: 1. Evaluate integrals using techniques of integration. 2. Use integrals to solve application problems. 3. Solve separable differential equations and apply to elementary applications. 4. Investigate the convergence of series and apply series to approximate functions and definite integrals. 5. Apply polar representations including graphs, derivatives, and areas.
General Education Outcomes
I. This course addresses the general education outcome relating to communication by providing additional support as follows: A. Students improve their listening skills by taking part in general class discussions and in small group activities. B. Students improve their reading skills by reading and discussing the text and other materials. Reading mathematics requires skills somewhat different from those used in reading materials for other courses in that students are expected to read highly technical material. C. Unit tests, examinations, and other assignments provide opportunities for students to practice and improve mathematical writing skills. Mathematics has a specialized vocabulary that students are expected to use correctly. II. This course addresses the general education outcome of demonstrating effective individual and group problem-solving and critical-thinking skills as follows: A. Students must apply mathematical concepts to non-template problems and situations. B. In applications, students must analyze problems, often through the use of multiple representations, develop or select an appropriate mathematical model, utilize the model, and interpret results. III. This course addresses the general education outcome of using mathematical concepts to interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problem-solving skills by using the definite integral to solve application problems. B. Students must be able to solve applied problems that can be modeled by differential equations. C. Students must use power series techniques to approximate function values to a specified degree of accuracy. IV. This course addresses the general education outcome of locating, organizing, and analyzing information through appropriate computer applications (including hand-held graphing calculators). As a result of taking this course, the student should be able to use technology to: A. Approximate definite integrals using Simpson's rule or a built-in integration feature. B. Approximate points of intersection of curves for use in determining approximate limits of integration in application problems. C. Investigate series representations of functions, their graphs, and the convergence or divergence of series. D. Approximate values of functions and definite integrals using Taylor series. V. This course addresses the general education outcome of using scientific inquiry by using techniques of Calculus including integration or differentiation to apply scientific inquiry to problem solving.
Course Content
1. Techniques of Integration 2. Applications of the Definite Integral 3. Differential Equations 4. Series 5. Polar representations ENTRY LEVEL COMPETENCIES Upon entering this course the student should be able to do the following: 1. Investigate limits using algebraic, graphical, and numerical techniques. 2. Investigate derivatives using the definition, differentiation techniques, and graphs. The classes of functions studied include algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and implicit. 3. Apply the derivative as a rate of change, optimize functions, use Newton's Method, and sketch curves. 4. Define the definite integral and approximate definite integrals using Riemann sums. 5. State and apply the Fundamental Theorem of Calculus. 6. Graph and use parametric equations.
Assessment of Outcome Objectives
The Calculus Committee or a special assessment committee appointed by the Chair of the Math, Computer Science, and Engineering Executive Committee, will accumulate and analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding. |
Elementary Linear Algebra
9780132296540
ISBN:
0132296543
Edition: 9 Pub Date: 2007 Publisher: Prentice Hall
Summary: This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof |
College Algebra, Eleventh Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Eleventh Edition, the authors recognize that st...
For courses in Introductory Accounting.Essentials of Accounting is a workbook that provides a self-teaching and self-paced introduction to financial accounting for active users of business data. This text presents the ideas and terminology essential to understanding balance sheets, income statement...
For courses in Introductory Accounting.Core Concepts of Accounting captures the full text (but not the programmed approach) of Essentials of Accounting, while including important accounting concepts and terms.
Edited by two of the most respected international relations scholars, International Politics places contemporary essays alongside classics to survey the field's diverse voices, concepts, and issues. Challenging students to use original scholarship to recognize and analyze patterns in ... |
More About
This Textbook
Editorial Reviews
Booknews
A resource and guide for all who make decisions that affect the mathematics education of students from prekindergarten through grade 12. Recommendations are grounded in the belief that students should learn important mathematical concepts and processes with understanding. Principles for school mathematics are presented, related to equity, teaching, learning, assessment, and technology, and standards are elucidated for school mathematics at different grade levels. Each chapter describes standards for number and operations, algebra, geometry, measurement, data analysis and probability, problem solving, reasoning and proof, communication, connections, and representation |
. T. (P) Caribbean Mathematics: Bk. 1
Average rating
4 out of 5
Based on 6 Ratings and 6 Reviews
Book Description
The first book in a concentric, graded mathematics course offering coverage of the syllabi for grades 7, 8 and 9 as preparation for later CXC work. Three types of exercises are provided for children of different abilities, with additional mixed revision exercises at the end of each section.
About A. Shepherd (Author) : A. Shepherd is a published author of children's books and young adult books. Some of the published credits of A. Shepherd include STP National Curriculum Mathematics, STP National Curriculum Mathemati... more View A. Shepherd's profile
About C.E. Layne (Author) : C.E. Layne is a published author. Some of the published credits of C.E. Layne include Certificate Mathematics (Caribbean S.), STP Caribbean Mathematics (Caribbean S.). View C.E. Layne's profile
About Ewart Smith (Author) : Ewart Smith is a published author and an editor of children's books and young adult books. Some of the published credits of Ewart Smith include AQA Modular Maths, AQA Modular Maths. View Ewart Smith's profile
About F.S. Chandler (Author) : F.S. Chandler is a published author of children's books and young adult books. Some of the published credits of F.S. Chandler include AQA Modular Maths, AQA Modular Maths. View F.S. Chandler's profileVideos
You must be a member of JacketFlap to add a video to this page. Please Log In or Register. |
Secondary Mathematics Education Lab
The Secondary Mathematics Laboratory is housed on the second floor in Stright 211. This curriculum library is designed to help present and future teachers with designing lessons that teach mathematics effectively to students in grades 7–12.
The lab has textbooks from the 1960s to the present. It also has many manipulatives that students, teachers, and faculty members can use for enhancing their lessons. There is also a portable SMART Board that students and faculty can use for practice or preparation.
Most of the books and materials can be checked out. However, the most recent texts are used daily by students, so those texts are required to stay in the lab. If you would like any additional information about the lab or would like to use its resources, contact Dr. Brian Sharp. |
PURPOSE:
Students will develop an understanding of and the applications for linear equations and their graphical
displays.
DESCRIPTION: The unit on graphing linear equations will begin with
students learning to manipulate an equation into slope-intercept form. This will be accomplished through
classroom discussion and guided practice from an overhead projector and the chalkboard. Students will then
have independent practice with a lesson from their algebra text. Another series of lessons will follow on
graphing equations and the various methods of graphing a linear equation.
The proposed lesson will follow
after becoming familiar with slope intercept form, manipulating an equation, and graphing equations.
Students will participate in a cooperative learning activity of matching a graphic display with an
equation. A Kagan Activity; corner; will then be used for students to practice graphing an equation. After
the review students will reinforce the concepts learned through the use of a graphing calculator. Future
concepts such as parallel and perpendicular lines will also be introduced. Through the use of a LitePro
and one computer, students will be introduced in the classroom to the computer program, Green Globs and
Graphing Equations. Students will then move to the computer lab and work individually on the tutorial
and game. Upon completion of the game, students will then complete an Internet lesson on the applications
of the concepts learned. Students will communicate their understanding of the concepts learned through a
journal entry as well as other methods.
This is a building block in algebra;
therefore, this concept will carry on for many more lessons and possibly years.
ACTIVITIES:
(Note:
This is a unit plan that may cover several days to several weeks. Not all of the following
activities/standards will appear in the video clips used.)
After a brief into and a
review of linear equations students will be given an equation and a graphical display of a different
linear equation. Students must find the graphical display which matches their equation. Upon finding
their match, students will work in groups of three or four to verify each otherís match. A code is
on the back of each and the correct match will be revealed by the teacher.
Mathematics: 2, 3, 6, 8
Working in groups of three or
four, students will each take an equation and create the graphic display for their equation. Then
students will regroup so that one from each original group will now be working with others with the
same equation; students will do a peer assessment. Students return to their original group and take
turns showing their group members how they arrived at their graphic display. All students are to
complete each graphic as it is explained. This is a Spencer Kagan activity entitled, corners. Each
studentsí graphics are turned in to the teacher.
Mathematics: 2, 3, 6, 8
Using graphing calculators
students will extend their investigations of linear equations. Students will draw conclusions about
slope and y-intercept. The concept of parallel and perpendicular lines will be introduced.
Mathematics: 2, 3, 6, 8, 9
Grades 6-8: 4, 7, 9
Grades 9-12: 8, 10
The computer program Green
Globs & Graphing Equations (Sunburst) will be used to reinforce the concept of
slope-intercept form. The software will be introduced in the classroom with the use of an LCD
Projector. In a lab setting students will be given 20 levels of lines to identify the equation. For
each line given, students are to give the equation in slope-intercept form. If a student does not
get the equation correct, a red line is graphed for his/her equation so that the student can see if
they have the slope correct or maybe the intercept is what is wrong. Students are given unlimited
chances on writing the equation for the line; however, they must get an equation correct for each
level the first time in order to advance to the next level. I have created a record-keeping sheet in
which students keep up with how many times they incorrectly write an equation. After completing the
lesson, students will then play the game Green Globs in which they are to write an equation
for lines that will hit as many globs as possible with one line in order to get points. Students
become very interested in slope and intercepts at this point, and they also become very competitive.
The program has a record keeping system for the top ten scores.
Mathematics: 1, 2, 3, 6
Grades 6-8: 4, 5, 8
Using the Internet as a
resource, students will gather data to create a graphic display and experience a real world
application of the use of linear equations. Students will be supplied with other possible sites they
may visit which will reinforce the algebraic concepts covered in this lesson.
Mathematics: 2, 3, 5, 8, 9, 10
Grades 6-8: 4, 8, 10
Grades 9-12: 7, 9
As a summation students will
write an entry in their journal that demonstrates their understanding of the the concepts learned.
ASSESSMENT:
The matching of a linear equation with the graphic display. Peer-assessment will occur during the Kagan
Activity, corners. Self-assessment will be done from the visual display of the overhead calculator. A
rubric will be used for Green Globs & Graphing Equations tutorial. The Internet lesson and
journal entry will be assessed by the teacher. Students will also be assessed through out the course on
this concept.
TIMELINE & COURSE OUTLINE:
This unit will come early in the course and this activity will be used after students are successful at
manipulating equations. My students were reenacting this activity to an extent. I did not do the Internet
lesson the same way earlier. This lesson can be taught in a 90-minute block and students may use open lab
time to further research the sites given.
COMMENTS:
I have used the computer program Green Globs for several years with great success. Students
donít complain about graphing equations; they actually enjoy it. The game feature allows students to
demonstrate their understanding of the concept in a competitive way.
Technology Resources: I chose the computer program, Green Globs,
after first seeing it demonstrated at a technology conference. The program is individual and has a broad
range of tutorials. The cost of the computer program is reasonable and very well worth the money. Students
are more enthused about learning mathematics and actually enjoy it.
The use of the overhead graphing
calculator and student graphing calculators gives students the opportunity to instantly see results
therefore draw conclusions and introduce future concepts.
I like using the LitePro projector
to take the students on a virtual field trip in the classroom prior to turning them loose on their own
with the computer. This takes care of a lot of questions later.
Teaching Strategy:
Allowing students to work in groups makes it less threatening and also gives each student a support group.
So many times students donít like math because they are afraid they will fail and are therefore
threatened by the subject. Giving students a support group to fall back on is like having a safety net and
thus makes them more willing to try solutionsI feel that the use of a
computer program to enhance learning is a strong part of this lesson. Democracy is a crucial
part of this lesson as well because students must be able to share power, make decisions, and demonstrate Individual
Responsibility of the responsibility. Having students actively involved in their learning and
assessing each other puts part of the responsibility on them and makes them have ownership of their
learning. The use of the graphing calculator is a reinforcement of the concepts learned as well as a Reflection
and introduction of future concepts.
Student Characteristics: All students learn at different rates and through
different modes so for that reason I have tried to make this lesson as well-rounded as possible in that we
still do concrete and abstract activities as well as thinking. The students in this class were not all
what I would call typical math students and with the use of the technology in this lesson those students
were given an opportunity to fail and retry until success was found.
How the Activity Has Evolved Over
Time: I have used the computer program for several years and
added the pre-activities to the lesson to facilitate learning for the slower students and reintroduce the
concepts to all students. The Internet lesson was added so that students would see a real-world
application of the mathematical concepts. The journal entry is also a way of having students demonstrate
understanding through writing. |
Description: An introduction to the techniques used by mathematicians to solve problems. Skills such as Externalization (pictures and charts), Visualization (associated mental images), Simplification, Trial and Error, and Lateral Thinking learned through the study of mathematical problems. Problems drawn from combinatorics, probability, optimization, cryptology, graph theory, and fractals. Students will be encouraged to work cooperatively and to think independently. Prerequisites: Recommended preparation: MATH 1010(101) or the equivalent. Not eligible for course credit by examination. Not open for credit to students who have passed any mathematics course other than MATH 1010(101), 1011(104), 1030(103), 1070(105), 1040(107), 1050(108) or 1060(109). Offered: Fall Intersession Spring Suummer Credits: 3
These are the most recent data in the math department database for Math 102Q in Storrs Campus.
There could be more recent data on our class schedules page, where you can also check for sections at other campuses. |
Calculus ABCs:
Absolutely Basic Competency
Introduction
Freshman Calculus covers a wide range of topics. As students struggle to
learn concepts, techniques, and applications, it is possible for certain basic
skills to get lost in the shuffle. To ensure that students who pass freshman
calculus can do the basics, the Department of Mathematics has identified
standards for "Absolutely Basic Competency"--what we call the Calculus
ABCs. There are separate standards for MA131 and MA132, covering only
prerequisite material (see below). In both of these courses, students must
demonstrate mastery of these basic skills in order to receive a grade of C or
better.
Requirement
Passing a Calculus ABCs Test is a minimum requirement for getting a
grade of C or better in the course: passing means you may earn any grade (A
to F) in the course (based on other coursework), while not passing means you
may earn no higher than a D+ (regardless of other coursework). This
requirement is part of MA131 and MA132 each semester they are taught, and also
applies to placement tests for those courses administered at Clarkson.
A passing score is 90% or better; all problems are graded right/wrong
(essentially no partial credit). ABCs tests will be offered as needed during
the first half of the semester. Each student may take up to five tests in
order to pass; if needed, they may take one last ABCs test during final exam
week (in addition to the regular course final exam).
Advice
Take the test seriously--for many students this is a real challenge.
Practice using the sample tests (see below) and learn the
material solidly before taking the test.
Do not just show up and hope to pass by luck (you won't)--the only way
to succeed here is to master the material.
You should also read the Instructions for Grading
before taking the test, so you will know for sure what is expected. |
About 2.0
CK-12 Foundation introduces its version 2.0 which provides the component missing in version 1.0 – a focus around learning. At CK-12, we believe that learning is an individual activity requiring many things – multiple modalities, interactions with other human beings (such as teachers, peers, and parents) as well as collaborations. Hence, in this version of the system we combine student-centric learning with teacher-centric tools and materials to create a dynamic system that can be used by anyone. Our belief is that this will help in reducing "gaps" and provide the ability to fill these gaps.
Users will continue to find high quality, national and international standards aligned content in K-12 Science and Math subjects. As before, that content can be used to create customized books or courses. New to the system are concepts, smaller chunks of content that can be used to learn or review specific topics. The concepts are supported with many associated modalities as well as interactive and automated exercises and assessments allowing for students to see where they are and how they are progressing. Interactive learning objects as well as simulations from entities such as Wolfram will support these concepts. In addition, we will be providing a guiding system allowing students to learn at their own pace with purpose. This navigational system at the same time, will allow for teachers to mentor their students.
Version 2 of CK-12′s system is the next step toward the foundation's mission to increase the access of high quality educational materials for all. Important features include:
High quality, standards-aligned content for science and math presented at the book and now concept levels. (Concepts can be combined to form chapters and books.) The previous format of book and chapter will still be available.
A "Concept Map" to show the interrelation of concepts, providing a guided path of learning for those who are interested.
As always, the ability to edit and customize, both at the concept and book level. |
Related Links
Mathematics
Mathematics faculty at Oakton motivate and inspire students in an environment that nurtures self-esteem, promotes the curiosity to question, and fosters the ability to learn. Offering something for everyone, Oakton's mathematics program includes:
College-level courses that provide the foundation for degrees in business, the life sciences, natural sciences, and engineering;
Applied mathematics courses that support occupational and technology programs;
Developmental classes for students who lack adequate preparation for college-level work.
Many courses also support Oakton's general education requirements.
Check out the mathematics course descriptions and the course dependency graph to learn more about the possible sequences of mathematics courses related to various areas of study.
Initial placement in the mathematical sequence of courses is determined by the results of the Mathematics Assessment Test (COMPASS) and/or by transcripts of successfully completed (C or better) college-level mathematics courses |
EPSB078
Foundation Mathematics
Callaghan and Ourimbah campuses
This course is designed to refresh your memory of mathematics and requires a basic level of numeracy and algebraic skills. It is suited to students enrolling in Intermediate Mathematics or Extension Mathematics in the Open Foundation and/or Yapug programs, or Advanced Mathematics in the Newstep program.
Note: The course is not suitable for students enrolling in Introductory Mathematics. |
Course Content and Outcome Guide for ALC 61
Date:
02-OCT-2012
Posted by:
Heiko Spoddeck
Course Number:
ALC 61
Course Title:
Basic Math Skills Lab
Credit Hours:
1
Lecture hours:
0
Lecture/Lab hours:
0
Lab hours:
30
Special Fee:
$12
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 30 hours in the lab. Completion of this course does not meet prerequisite requirements for other math courses.
Intended Outcomes for the course
Upon successful completion of this course students will be able to:
1. Choose and perform accurate computations in a variety of situations with and without a calculator.
2. Creatively and confidently apply mathematical problem solving strategies.
3. Be prepared for future coursework that requires an understanding of the mathematical concepts covered in the course.
Outcome Assessment Strategies
Assessment shall include at least two of the following measures:
Tests
Attendance
Portfolios
Individual student conference
Course Content (Themes, Concepts, Issues and Skills)
Basic Math
THEMES:
1. Mathematical vocabulary
2. Number sense
3. Computational proficiency
4. Critical thinking
5. Appropriate use of technology
6. Team work
SKILLS:
1.0 ORDER OF OPERATIONS
1.1 Vocabulary (Define and use)
1.1.1 Grouping symbols
1.1.2 Exponents
1.1.3 Square roots (perfect squares)
2.0 SIGNED NUMBERS
2.1 Vocabulary (Define and use)
2.1.1 Absolute value
2.1.2 Opposite vs. negative vs. minus (subtract)
2.2 Number sense
2.2.1 Compare signed numbers using inequality and equality notations
2.2.2 Place signed numbers on a number line
2.3 Computation
2.3.1 Add, subtract, multiply, and divide signed numbers
2.3.2 Simplify signed numbers to exponents
2.4 Order of operations with signed numbers
2.5 Applications with signed numbers
3.0 FRACTIONS
3.1 Vocabulary (Define and use)
3.1.1 Proper fractions, improper fractions, mixed numbers
3.1.2 Reciprocal
3.1.3 Prime number
3.1.4 Composite number
3.1.5 Divisibility Rules 2, 3, 5, 9, and 10
3.2 Number Sense
3.2.1 Compare fractions using inequality and equality notations
3.2.2 Place signed fractions on a number line
3.3 Computation
3.3.1 Add, subtract, multiply, and divide signed fractions
3.4 Order of operations with fractions
3.5 Applications involving fractions
3.5.1 Write answers to application problems as complete sentences and using proper units
3.5.2 Ratios and rates
4.0 DECIMALS
4.1 Vocabulary (Define and use)
4.1.1 Place values
4.1.2 Powers of ten
4.1.3 Terminating, repeating and non-terminating
4.2 Number sense
4.2.1 Compare decimals using inequality and equality notations
4.2.2 Place signed decimals on a number line
4.2.3 Rounding decimals
4.3 Computation
4.3.1 Add, subtract, multiply, and divide signed decimals
4.3.2 Convert between fractions and decimals
4.4 Order of operations with decimals
4.4.1 Round at the end of the calculation
4.5 Applications
4.5.1 Write answers to application problems as complete sentences and using proper units
4.5.2 Rates and ratios
4.5.3 Unit rate and unit price
5.0 PROPORTION AND PERCENT
5.1 Vocabulary
5.1.1 Proportion
5.1.2 Percent
5.2 Number sense
5.2.1 Convert between fractions, decimals, and percents
5.3 Computation
5.3.1 Solve proportion problems for missing value
5.3.2 Solve percent problems
5.4 Applications
5.4.1 Write answers to application problems as complete sentences and using proper units
5.4.2 Identify and solve problems that involve reasoning about proportions
5.4.3 Solving percent increase and percent decrease problems
5.5 Technology
6.0 GRAPHS
6.1 Introduce, read and interpret graphs
7.0 FORMULAS AND CONVERSIONS
7.1 Perimeter and area of rectangles, squares and triangles
7.2 Computing mean, median, and mode
7.3 Introduce unit conversions within each measurement system
7.4 Money, $0.35 vs. 35¢ (students often write 0.35¢)
Introductory Algebra I
THEMES:
Algebra skills
Graphical understanding
Problem solving
Effective communication
Critical thinking
Applications, formulas, and modeling
Functions
SKILLS:
1.0REAL NUMBERS
1.1Review prerequisite skills – signed number and fraction arithmetic
1.2Simplify arithmetic expressions using the order of operations
1.3Evaluate powers with whole number exponents; emphasize order of operations with negative bases
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 |
Technology in Education
Monday, April 5, 2010
Cabri 3D is one of dynamic geometry software. This software helps students with the visualization of 3D figures their properties. The purpose of this software is to help students to better understand three-dimensional space, since three-dimensional space is difficult to visualize. Cabri 3D allows students and teachers to construct and manipulate solid geometry objects in three dimensions. It provides a tool for teachers and students to explore properties of 3D geometric constructions
Even though it is Cabri 3D, two dimensions objects can still be created. The software is suitable with many two dimensions concepts such as length, sectors of circles, lateral area, surface area. Cabri 3D will help students to learn analyzing characteristics and properties of two- and three-dimensional geometric shapes and develop arguments of mathematics about geometrical relationships. Students also can learn to use visualization, spatial reasoning, and geometric modeling to solve problems
Cabri 3D is appropriate for secondary school students. Even though the software is not very user friendly, the students can be successful with the program if they learn through the manual. Teachers who want to use it in their classes have to be advanced in using it. Even though the software is not user friendly, it still offers a lot of great features that help student to get success in learning mathematics especially in geometry class.
Monday, March 15, 2010
I reviewed a Mathematics WebQuest. Its title is Vector WebQuest. There are some weaknesses and strengths of this WebQuest. The weaknesses are it is not complex, does not have analytical question and does not has sufficient explanation on the process. On the other hand, the strengths of the WebQuest are an interested introduction and a range of web sites been accessed.
The most weakness of the WebQuest is it is not complex. It has only three parts. They are introduction, task and process. The WebQuest does not have evaluation, conclusion, and teacher page. Based on the criteria of a WebQuest, these elements are very important. Without Evaluation and conclusion, a WebQuest will be less useful. Another weakness is there is no any analytical question. Analytical questions are very important, since one of the purposes of a Webquest is to support learner thinking at the level of analysis. On this WebQuest, The level of questions is comprehension. Overall, the questions are not able to encourage students to think at high level thinking. The last weakness is it does not have sufficient explanation that is provided to students in order to accomplish the task. The WebQuest does not have full potential of web such as sound and video.
One of strength of the WebQuest is its introduction provides information that engages students to explore further. It is started with interesting issues. This issue will grab students' attention. Another strength is its link to supported documents such as vector form. Moreover, it also provides various web sites such as .com, .edu and .gov. Some of the links take students directly to pages they need to go.
Even though the web quest has an interested introduction and various web sites been accessed, it is still inappropriate to be used by students because it does not fulfill the basic criteria of a WebQuest.
Friday, February 19, 2010
I am curious to learn and assess computer technology for learning mathematics and science. Even though there are many issues surround the using of computer technology in learning mathematics and science, computer technology offers new ways to learn. It helps students to learn based on problem solving. Another advantage is by using computer technology teachers can create inquiry-based mathematics and science classroom. Of course, besides those things, There are many other advantages of using computer technology in learning mathematics and science.
One of software that I am interested to learn is TinkerPlots. TinkerPlots is software for students in grades 4 through 8. The use of software is to build fluency with data representation and exploration. Animation, color, and dynamic manipulation support students in moving from simple representations to increasingly complex and analytic graphs. Another aim is to get students excited about what they can learn from data. TinkerPlots also helps teachers to create inquiry-based mathematics classrooms
TinkerPlots is friendly and intuitive interface that allows the user to play with the data plotted in an infinite variety of formats.
Tuesday, February 9, 2010
Speech Recognition. Windows 7 has a feature that allows people to use their voice to operate a computer and compose text. It is Speech Recognition. We can find this feature on Ease of Access. Before we get started using Speech Recognition, we will need to connect a microphone to our computer. There are some issues that we have to think about before using Speech Recognition: (1) Speech Recognition needs a good microphone. (2) Training the computer to identify the speaker sounds and pronunciation. (3) Speak clearly and pronounce words carefully, not too fast and or too slow. To open Speech Recognition: (1)Start the Speech Recognition by clicking the Start button , clicking All Programs, clicking Accessories, clicking Ease of Access, and then clicking Windows Speech Recognitions. (2)Click microphone button to start the listening mode
By using Speech Recognition we can do the following things: (1) We can use our voice to control our computer. (2) We can say commands that the computer will respond (3) We can dictate text to the computer.
Speech Recognition makes a classroom or lesson more Universally Designed. Speech recognition allows students to use their voice to operate a computer and compose text. This feature is useful to students with a wide range of disabilities including those with visual, mobility and language impairments. This feature will be very useful in a classroom which the numbers of students with disabilities integrated into it. Today, nearly every class and schoolwork are related to computer. For example statistics class, students will analyze graphical displays of data, including dot plots, stem plots, and histograms, to identify and describe patterns and departures from patterns. In this class they will use computer to create graphical displays. By using Speech recognition and Microsoft excel, students with mobility impairment are still able to participate well in the class. They can input data and command to create a graphic.
Speech Recognition helps students with mobility and visual impairment. Students with mobility impairments might be unable to use (or be without) arms or fingers to interact with their computers using a standard keyboard or mouse. Using their voice is a way to interact with their computer. By using speech recognition they can operate their computer and compose text. Another is visual impairment, blindness, for example. Students who are blind interact with their computers through keyboards, Braille devices, and audio/voice rather than a traditional monitor and mouse. If they don't have these special devices, they are still able to operate their computer by using Speech Recognition.
Conclusion A more accessible technology is good for everyone, including students with disabilities and students without disability. All students benefit from technology in which it is easier to function. Providing accessible technology in the classroom to students with disabilities enables all students to have the same opportunities in education. Speech Recognition gives an easy way to interact with computer not only for students with a disability but also those without a disability. It also helps us to make an inclusive classroom with equal access for all students.
Monday, January 25, 2010
Mathematics is my subject domain, during I taught mathematics I used some dynamic geometry software, such as Cabry, Geometer's Sketchpad, GeoGebra and Autograph. These are typically used in the classroom or the computer lab and they are very helpful in teaching the difficult concept.
It is little bit difficult to find an appropriate technology device in everyday life for teaching and learning the difficult concept of mathematics. Since mathematics concept is completely different from other concepts such as social science, English, etc.Based on my teaching experience in primary school, when I teach a difficult concept, I had to prove the concept and visualized it. these things can be done by using a software for teaching mathematics that requires a certain specification of a computer.
However, Nowadays, there is a technology in education known as mobile learning. Mobile Learning is a learning model adopted cellular technology development and mobile phones where this technology can be used as a learning medium. To use this technology, we can download the applications and install them on a mobile phone or use them online by using mobile phone.
Mobile learning technology can be used to teach mathematics. One of web sites that provides mobile learning applications for teaching and learning mathematics is So far, Mobile Learning is very helpful as a supplement material for teaching mathematics. It is easy for students to bring mobile phones wherever they go, this technology will help them to learn mathematics wherever and whenever. |
Assessment Rules
CMod description
This module covers basic algebra and functions,
leading to the practice and application of differentiation. Topics covered
include equations and inequalities, dependent and independent variables; graphs
and curve sketching; polynomial functions, inverse functions, and functions of
functions; trigonometric and exponential functions. Derivatives of functions,
methods of differentiation, products and chain rule. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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Parent Resource
Welcome to the Core-Plus
Mathematics Parent Resource Web sites.
The Core-Plus Mathematics
Project (CPMP), with funding from the National Science Foundation,
has developed a four-year integrated mathematics program for high schools.
The problem-based curriculum is designed to prepare students for success
in college, in careers, and in daily contemporary society.
These sites are intended
for parents and tutors who want to learn more about Core-Plus Mathematics and assist students in learning mathematics. Check the copyright date
your student's textbook and choose the appropriate site below. |
Mathematics All Around, CourseSmart eTextbook, 5th Edition
Description
Students who enter a liberal arts math course often come with a fear of math, or they may struggle with topics during the course. Pirnot's Mathematics All Around offers the supportive and clear writing style that students need to develop their math skills. By helping to reduce students' math anxiety, Pirnot helps students to understand the use of math in the world around them. Students appreciate that the author's approach is like the help they would receive during their own instructors' office hours.
The Fifth Edition increases the text's emphasis on developing problem-solving skills with additional support in the text and new problem-solving questions in MyMathLab. Quantitative reasoning is brought to the forefront with new Between the Numbers features and related exercises. Since practice is the key to success in this course, exercise sets are updated and expanded. MyMathLab offers additional exercise coverage plus new question types for problem-solving, vocabulary, reading comprehension, and more.
Table of Contents
1. Problem Solving
1.1 Problem Solving
1.2 Inductive and Deductive Reasoning
1.3 Estimation
2. Set Theory
2.1 The Language of Sets
2.2 Comparing Sets
2.3 Set Operations
2.4 Survey Problems
2.5 Looking Deeper - Infinite Sets
3. Logic
3.1 Statements, Connectives, and Quantifiers
3.2 Truth Tables
3.3 The Conditional and Biconditional
3.4 Verifying Arguments
3.5 Using Euler Diagrams to Verify Syllogisms
3.6 Looking Deeper - Fuzzy Logic
4. Graph Theory (Networks)
4.1 Graphs, Puzzles, and Map Coloring
4.2 The Traveling Salesperson Problem
4.3 Directed Graphs
5. Numeration Systems
5.1 The Evolution of Numeration Systems
5.2 Place Value Systems
5.3 Calculating in Other Bases
5.4 Looking Deeper - Modular Systems
6. Number Theory and the Real Number System
6.1 Number Theory
6.2 The Integers
6.3 The Rational Numbers
6.4 The Real Number System
6.5 Exponents and Scientific Notation
6.6 Looking Deeper - Sequences
7. Algebraic Models and Linear Systems
7.1 Linear Equations
7.2 Modeling with Linear Equations
7.3 Modeling with Quadratic Equations
7.4 Exponential Equations and Growth
7.5 Proportions and Variations
7.6 Modeling with Systems of Linear Equations and Inequalities
7.7 Looking Deeper - Dynamical Systems
8. Consumer Mathematics
8.1 Percents, Taxes, and Inflation
8.2 Interest
8.3 Consumer Loans
8.4 Annuities
8.5 Amortization
8.6 Looking Deeper - Annual Percentage Rate
9. Geometry
9.1 Lines, Angles, and Circles
9.2 Polygons
9.3 Perimeter and Area
9.4 Volume and Surface Area
9.5 The Metric System and Dimensional Analysis
9.6 Geometric Symmetry and Tessellations
9.7 Looking Deeper - Fractals
10. Apportionment
10.1 Understanding Apportionment
10.2 The Huntington-Hill Apportionment Principle
10.3 Other Paradoxes and Apportionment Methods
10.4 Looking Deeper - Fair Division
11. Voting
11.1 Voting Methods
11.2 Defects in Voting Methods
11.3 Weighted Voting Systems
11.4 Looking Deeper - The Shapley-Shubik Index
12. Counting
12.1 Introduction to Counting Methods
12.2 The Fundamental Counting Principle
12.3 Permutations and Combinations
12.4 Looking Deeper - Counting and Gambling
13. Probability
13.1 The Basics of Probability Theory
13.2 Complements and Unions of Events
13.3 Conditional Probability and Intersections of Events
13.4 Expected Value
13.5 Looking Deeper - Binomial Experiments
14. Descriptive Statistics
14.1 Organizing and Visualizing Data
14.2 Measures of Central Tendency
14.3 Measures of Dispersion
14.4 The Normal Distribution
14.5 Looking Deeper - Linear Correlation
Appendix A. Basic Mathematics Review |
MAT 110: College Algebra
Introduction
If you decide to take college algebra online, you will be signing on for an adventure that will require a great deal of work and dedication on your part. Your reward is being able to complete this course in your own setting and at your personally selected best times of day. Your instructors will be here to help you every step of the way, serving as guides, facilitators, and a cheering section to encourage you as you proceed. They hope and expect to hear from you often.
In this course students will be expected to study commentaries and the text, complete homework assignments, enter into online discussions and take proctored paper and pencil exams.
Description
The successful completion of the equivalent of one course in geometry is a prerequisite for all credit mathematics courses.
Successful completion of this course will meet the Mathematics Core Requirement of the UW Colleges Associate of Arts and Science (AAS) degree. If a student has already met this core requirement through the successful completion of Math 108, a passing grade in this course will earn three Mathematical Science (MS) credits toward the Math and Natural Sciences breadth requirement of the AAS degree.
Prerequisites: A grade of C or better in MAT 105 or placement based on placement test score.
This college algebra course assumes that you have completed Math 105 (Introduction to College Algebra) with a grade of C or better or that you have completed two years of high school algebra or the equivalent.
Proficiencies
Institutional proficiencies assigned to this course
Successful completion of this course will enhance the student's ability to:
Interpret and synthesize information and ideas
Select and apply scientific and other appropriate methodologies
Solve quantitative and mathematical problems
Interpret graphs, tables, and diagrams
Department-specific proficiencies assigned to this course
By completing this course, students will learn to:
Graph a variety of basic equations using intercepts and symmetry where appropriate
Complete the square for graphing circles and parabolas
Graph polynomial and rational functions
Use function transformations
Use function arithmetic and composition
Understand functions and inverse function evaluation
Use the Factor Theorem for polynomials and the Fundamental Theorem of Algebra
Apply the properties of logarithms
Solve logarithmic and exponential equations
Solve systems of linear equations
Solve applied problems
Requirements
Textbook Reading Assignments
The reading assignments in this course are vitally important for your success. It is important that you learn how to read a math book, how to work through worked examples, and how to complete exercises from the problem sets in the book independently. This requires discipline, which is absolutely essential for your success in online courses.
Online Access
The required materials for this course include a MathXL online access package.
Required Online Access:
Technology
In addition to the MathXL homework assignments, there will be written homework assignments that you will submit to the Dropbox. These assignments will need to be scanned to digital format to show the work you did as part of the assignment. Alternatively, you may show your work using Microsoft Word Equation Editor or MathType.
Software
The most current edition of Microsoft Office (containing Microsoft Word (plus an equation editor) and other valuable programs) is available to University of Wisconsin students at discounted prices through the Wisconsin Integrated Software Catalog.
The most current edition of Microsoft Office (containing Microsoft Word and other valuable programs) is available to University of Wisconsin students at discounted prices through the Wisconsin Integrated Software Catalog.
Shockwave/Flash
RealPlayer
QuickTime
MathXL Player and Test Gen plug-ins
Adobe Reader
Hardware
A graphing calculator can be a useful tool in this course. You can use the specific calculator or online graphing program of your choice, but you will not need a calculator with any greater functionality than a TI-86. Also, please ensure you have a manual for your calculator, as the instructor is not responsible for any technical or operational support for your calculator. When using your calculator to work problems that will be submitted for grading, please be aware that all work for problems must be shown; full credit will not be given for answers that fail to demonstrate how the solution was determined.
About the Instructors
Rotraut Cahill Professor, Mathematics/Computer Science BA, Rutgers State University MA, University of Rochester PhD, University of Illinois at Urbana
Textbook Information for this Course
The textbook for this course should be purchased through
MBS Direct; it will not be available through UW Colleges
campus bookstores. Please note: UW Colleges Online cannot assist
with any problems that may arise when textbooks are purchased through
another vendor. |
Book Description: Your guide to a higher score in Algebra IIWhy CliffsNotes?Go with the name you know and trustGet the information you need-fast!About the Contents:PretestHelps you pinpoint where you need the most help and directs you to the corresponding sections of the book Topic Area ReviewsMath basicsFactoring and solving equationsFunction operations and transformationsPolynomialsExponential and logarithmic functionsGraphingOther equationsConic sectionsSystems of equations and inequalitiesSystems of linear equations with three or more variablesCustomized Full-Length ExamCovers all subject areas |
resource, published by Schofield & Sims, is the sixth fifth fourth Alpha Mathematics series of text books which were developed for use by more able Alpha Mathematics series of text books which were developed for use by more able students of junior and middle school age. It continues the theme of book one and allows students to review and extend their knowledge of specific topics.
Contents include:
Number…
This unit from the Continuing Mathematics Project is designed to enable students to cope confidently with expressions of the type A/B= C/D, where A, B, C and D, may be integers or algebraic products like mv2 or functions like log x, or sin y.
So equipped, students will be able to solve simple equations, change the subject of a…
This unit from the Continuing Mathematics Project goes into detail on how logarithms can be used to determine the laws which connect two variables on which experimental data has been collected. The unit follows naturally from the unit entitled The Theory of Logarithms.
The objectives of the unit are that students:
(i) understand…
Transformation of Formulae from the Continuing Mathematics Project builds on the work covered in the unit entitled Working with Ratios.
The objectives of this unit are to enable students to acquire the skills necessary to transform formulae which involve algebraical fractions, brackets, and roots, as well as formulae in which…
This unit from the Continuing Mathematics Project is concerned with the calculation of the sides and angles of triangles and how this is used by the surveyor, the navigator, and the cartographer. The development of the television, the light and the road have all relied on trigonometry.
The objectives of the unit are that students…
This is the second part of the unit on The Theory of Logarithms from the Continuing Mathematics Project. It assumes that the user has completed the first part of the unit.
The objectives of the unit are to enable students to:
(i) acquire the concept of a logarithm as an extension of the concepts of a 'power' and of…
These two units from the Continuing Mathematics Project assumes that the word 'logarithm' will be familiar to students using it, and that they will have used tables of logarithms to reduce the labour of working out expressions by arithmetic methods.
The units assume that students are interested in knowing why logarithms…
This resource from the Continuing Mathematics Project has three units covering probability.
Introducing Probability is the first unit and its objectives are that students will learn that a probability can be from intuitive considerations or actual experimental results; the meaning of 'outcomes', 'sample space',…
This unit from the Continuing Mathematics Project assumes that students have met and used directed numbers, but that their use has become rusty. The unit briefly justifies the rules by which the four operations (+, -, x and ÷) can be accurately carried out. In this sense the unit could be said to form an introduction to the…The objectives of the unit are;
(i) to introduce students…
This unit from the Continuing Mathematics Project is about linear programming - a procedure which is used widely in industry to solve management problems. The work here is an introduction to the subject.
There are no really new mathematical techniques in the unit. It is rather an amalgamation of things students have probably learnt…
This unit from the Continuing Mathematics Project has been planned to help students learn how to handle inequalities, and how to represent them graphically. Students should be familiar with manipulating positive and negative numbers, representing equations of the form y + 3x = 6 as a graph and finding the solution of equations like…
This unit from the Continuing Mathematics Project has been planned to help students remember and understand what indices indicate and the rules they obey. As with all the units in this collection the text is designed to test as it teaches and is in sections.
The content of the booklet starts with a diagnostic test then covers:…
This resource from the Continuing Mathematics project is made up of three units covering hypothesis testing.
The first unit covers the Wilcoxon Rank Sum Test and aims to teach the use of a non-parametric test for assessing the significance of the difference between two independent samples. In this context, the objectives for…
This unit from the Continuing Mathematics Project on flowcharts and Algorithms employs, three basic conventions:
(i) the use of a flowchart and the appropriate symbols
(ii) the use of computer statements, such as 'c = c + I1
(iii) the use of the inequality signs >, <, ≤ and ≥
Three very short programmes at the…
Descriptive Statistics is the name the continuing Mathematic Project has given to a sequence of four units which deal with distributions, histograms, bar charts, frequency tables and measures of central tendency and dispersion.
The first unit, Presenting Statistics, aims to teach some basic statistical techniques that are useful…
This unit from the Continuing Mathematics Project is the first of two units on Critical Path Analysis (CPA). The broad objective of this unit is for students to become familiar with the diagrammatic conventions and with some of the terminology used in CPA.
The first half of the unit is devoted to exposition and illustration of…
This unit from the Continuing Mathematics Project is about the relationship between two quantities (correlation). If the two quantities are height of father and height of son, then we often want to know the extent to which 'tall fathers have tall sons'. Two quantities may be correlated quite strongly while another two quantities…
This HMSO resource from her Majesty's Inspectors was one of a series intended to stimulate discussion and debate within the teaching profession. Published in 1979 following a two year survey, it was seen that mathematics was given a high profile by teachers but Inspectors felt disappointment that, despite this and the efforts…
This resource from Leapfrogs is part of the Link series of books which are anthologies of pictures and diagrams which have a theme running through them. Some pages more obviously than others invite mathematical activity - some pose problems, others illustrate ideas or provoke reflection.
Leads - mathematical patterns are explored… |
These resources have been developed as part of the Mathematics Enhancement Program as part of the Centre for Innovation in Mathematics Teaching (University of Exeter). They were funded principally by the Garfield Weston Charitable Foundation.
Instructor providing notes for Algebra, Calculus I II III Linear Algebra and Differential Equations. Review of Algebra/Trig for Calculus Students, a Complex Number primer, a set of Common Math Errors, and some tips on How to Study Math.
Review of topics from arithmetic to differential equations. There are no interactive materials within the notes, but there are links to "Cyberexams". The explanations are quite complete and would supplement a course nicely
The goal of the Teachers´ Lab is to provide teachers and educators with a deeper understanding of commonly taught math and science concepts...Each lab will combine online activities with background information, interactive polls or worksheets |
Bringing a new vitality to college mathematics
Let's talk variables. Do we want students to develop an understanding of variable concepts (whether in a developmental math course or not)? Is accurate use of variable notation enough? If students can model applications and accurately determine solutions … is that enough? Is there a role for linguistic literacy in mathematics?
One of the issues we face in college is dealing (or not) with prior learning. Without intervention, prior learning (even when inaccurate) survives — often surviving in the face of conflicting information in the current learning environment. Visualize the prior learning as being as a stable mass of 'knowledge' (even though it has gaps and errors); as students go through a class as adults, information that connects positively with the old reinforces the old. When new information does not connect or conflicts with the old, the low-energy (natural) response is to build new storage … resulting in that solid core being supplemented by weak veneers of new knowledge. This, of course, is an incomplete visualization for the actual processes in the human brain. The suggestion is that students approach a math class with an attitude that supports old information and minimizes cognitive effort for dealing with new or incompatible information.
In my beginning algebra class this week, we did the test on exponents and polynomials. Although the test includes some artificially difficult problems with negative exponents, most of the items deal with important ideas. One of the most basic items on the test was this:
Evaluate a² + (3b)² for a = -3 and b = 2
Several students made this mistake with the first term:
-3² = -9
A smaller group of students made this mistake with the second term:
(32)²
Now, this is a good class — all students are actually doing homework and attending class almost every day. We had dealt with the first situation at the start of the semester. How could these errors survive to this point?
Both errors are based on variable as a symbol to be replaced by a number, which is not complete. They might represent a visual approach, not verbal. Variables represent quantities involved in sums and products, where products with variables are implied … and more than this. Simplifying expressions might — or might not — uncover the incomplete understanding. What can I do to help students with this?
I am planning on incorporating some linguistic activities around variables in the first week of the semester. Some of the ideas are from a old book called "English Skills for Algebra" from the Center for Applied Linguistics (Joann Crandall, et al); I believe this book is out of print. The authors wrote this book from the viewpoint of helping students with 'limited English proficiency', which might just apply to many of our developmental students. Some of their activities involve listening to somebody read mathematical statements and the student writing them down. I think I will mostly activities that deal with written statements — identifying translations and paraphrasing (both to algebra and from algebra).
I do know that just saying "that was wrong … this is right" will not help these students develop a more complete understanding. I need to create situations where they get uncomfortable and really dig into the concepts related to variables. Some energy needs to be created so that we don't just place a veneer on top of that mass of prior knowledge; parts of that prior knowledge need to be broken up and put back together. Without that process, many of these students will be limited in their mathematics and blocked from many occupations.
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5 Comments
(1) The concept of "variable" is a means towards an end. It should thus not be surprising that to "teach an understanding of variable" does not work. It cannot.
In a developmental context, the obvious end is the discussion of function: we need a paper representation for what we input.
Thus, my attempt in could not work because, as I eventually realized and mentioned in , I should have had—and will have real soon now—a "Chapter 3 – Functions".
(2) The usual definition of powers does not work very well in the remedial situation. For something that works, see freemathtexts.org
Thus, 5(3b)^2 should be read as "5 multiplied by 2 copies of 3b", i.e. 5•3b•3b, and the default rule "when there is no coefficient, it goes without saying that it is 1″ lets us read (3b)^2 as "1 multiplied by 2 copies of 3b", i.e. 1•3b•3b.
(3) Re "linguistic activities", what is very likely to work is having the mathematics text used as the reading material in a remedial English reading course. Of course, the text cannot be the usual prescriptive stuff (that takes students for idiots) but one that has faith in the ability of the students to be receptive to arguments.
Granted, writing this kind of text is not easy.
In order to see what I mean, one might want to look up my own attempts which can be found at freemathtexts.org and freemathtexts.org |
Mr. W Schapiro Math Concepts MA 60
MA 60 Math concepts is a skills class designed to support the student in being successful in their Algebra class (MA 28). The emphasis of this class is to reinforce basic skills along with the newly learned concepts in algebra. Having the extra class period gives students more time for guided practice. |
Geometry of Quantum Theory. Varadarajan, V.S. This is a book about the mathematical foundations of quantum theory. Its aim is to develop the conceptual basis of modern quantum theory from general principles using the resources and techniques of modern mathematics. |
Description
For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus.
The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Preface
1 First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations
1.7 Population Models
1.8 Acceleration-Velocity Models
2 Linear Equations of Higher Order
2.1 Introduction: Second-Order Linear Equations
2.2 General Solutions of Linear Equations
2.3 Homogeneous Equations with Constant Coefficients
2.4 Mechanical Vibrations
2.5 Nonhomogeneous Equations and Undetermined Coefficients
2.6 Forced Oscillations and Resonance
2.7 Electrical Circuits
2.8 Endpoint Problems and Eigenvalues
3 Power Series Methods
3.1 Introduction and Review of Power Series
3.2 Series Solutions Near Ordinary Points
3.3 Regular Singular Points
3.4 Method of Frobenius: The Exceptional Cases
3.5 Bessel's Equation
3.6 Applications of Bessel Functions
4 Laplace Transform Methods
4.1 Laplace Transforms and Inverse Transforms
4.2 Transformation of Initial Value Problems
4.3 Translation and Partial Fractions
4.4 Derivatives, Integrals, and Products of Transforms
4.5 Periodic and Piecewise Continuous Input Functions
4.6 Impulses and Delta Functions
5 Linear Systems of Differential Equations
5.1 First-Order Systems and Applications
5.2 The Method of Elimination
5.3 Matrices and Linear Systems
5.4 The Eigenvalue Method for Homogeneous Systems
5.5 Second-Order Systems and Mechanical Applications
5.6 Multiple Eigenvalue Solutions
5.7 Matrix Exponentials and Linear Systems
5.8 Nonhomogeneous Linear Systems
6 Numerical Methods
6.1 Numerical Approximation: Euler's Method
6.2 A Closer Look at the Euler Method
6.3 The Runge-Kutta Method
6.4 Numerical Methods for Systems
7 Nonlinear Systems and Phenomena
7.1 Equilibrium Solutions and Stability
7.2 Stability and the Phase Plane
7.3 Linear and Almost Linear Systems
7.4 Ecological Models: Predators and Competitors
7.5 Nonlinear Mechanical Systems
7.6 Chaos in Dynamical Systems
8 Fourier Series Methods
8.1 Periodic Functions and Trigonometric Series
8.2 General Fourier Series and Convergence
8.3 Fourier Sine and Cosine Series
8.4 Applications of Fourier Series
8.5 Heat Conduction and Separation of Variables
8.6 Vibrating Strings and the One-Dimensional Wave Equation
8.7 Steady-State Temperature and Laplace's Equation
9 Eigenvalues and Boundary Value Problems
9.1 Sturm-Liouville Problems and Eigenfunction Expansions
9.2 Applications of Eigenfunction Series
9.3 Steady Periodic Solutions and Natural Frequencies
9.4 Cylindrical Coordinate Problems
9.5 Higher-Dimensional Phenomena
References for Further Study
Appendix: Existence and Uniqueness of Solutions
Answers to Selected Problems |
Powers and Roots of Complex Numbers and de Moivre's Formula
In this lesson our instructor talks about powers and roots of complex numbers. He talks about de Moivre's formula and theorem. He does 2 examples of de Moivre's formula. He talks about roots of complex numbers and the origin of the fundamental theorem of algebra. He discusses the n-th root and does an example. Four extra example videos round up this lesson.
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Powers and Roots of Complex Numbers and de Moivre's Formula
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
WHAT DOES A MATHEMATICS MAJOR STUDY?
Mathematics is one of the fundamental areas of human knowledge. It has held an established position among the humanities for over two thousand years, and in recent centuries it has played a vital role in the sciences. The body of mathematical knowledge is growing today faster than ever before, with old questions being answered and new ones asked at an unprecedented rate.
In the paragraphs below, we sketch some of the courses and topics which mathematics majors study at Wright State University. In each case, the illustrations of what students learn are only small samples of the full curriculum.
Mathematics majors typically begin their college mathematics studies with three semesters of Calculus. Calculus is both the cornerstone of "analysis," one of the major branches of pure mathematics, and an indispensable tool for most of the sciences and engineering. Students learn to discover for themselves familiar formulas from high school geometry -- e.g., area of circle = πr2, volume of sphere = (4/3) πr3 -- and they learn how to investigate similar issues in more complex settings, as illustrated to the right. Students study mathematics describing such diverse phenomena as conservation of energy laws from physics, and continuously compounded interest from banking.
All mathematics majors also take one semester of Linear Algebra, usually by the beginning of the junior year. This basic topic resides within another major branch of pure mathematics, "algebra" and is also of critical importance in an extensive range of applications of mathematics, from management to structural engineering to telecommunications. In linear algebra, the study of linear equations, like those in beginning high school algebra -- but with the possibility of thousands of equations in thousands of unknowns -- leads to abstract mathematical spaces.
The Department of Mathematics and Statistics offers a variety of more advanced courses. Students decide which of these to take according to their interests and the particular degree which they seek.
For example, students apply multivariable calculus in probability and the mathematical foundations of statistical inference in Theory of Statistics. Related choices include Statistical Methods and Introduction to Experimental Designs, in which one learns how to collect and analyze data, for instance in scientific and industrial experiments.
Similarly, students can choose mathematics courses with special significance in computer science. A prime example is Applied Graph Theory, featuring mathematical models and algorithms applicable to such problems as traffic systems, activity scheduling, and design layout. Others are Cryptography (how to encrypt data securely) and Coding Theory (how to send messages that self-correct transmission errors).
Other courses in applied mathematics emphasize mathematical theory and problem solving methods directed toward the physical sciences and engineering. An illustrative example at the junior level is Partial Differential Equations involving several variables (e.g., both space and time). They describe such phenomena as the propagation of electromagnetic waves through space, and the flow of heat in solids.
Courses in pure mathematics concentrate upon the theoretical foundations of algebra, calculus, and other elementary courses, and at the same time point the way toward more advanced topics in modern mathematics. To illustrate, students in Real Variables (or theoretical advanced calculus) learn why the facts and computational methods learned in ordinary calculus are correct; in Modern Algebra, students study various abstract systems which include the familiar objects of school mathematics as special cases (whole numbers, rational numbers, real numbers, etc.)
In addition to taking many courses in the major field of study, every undergraduate at Wright State University is required to take a comprehensive program of General Education studies, including courses in history, English, economics, the sciences, and several other disciplines. Moreover, some degree programs allow students to take "free electives," or courses chosen by students from essentially any area. Wright State's degree programs in mathematics have a generous allotment of these free electives. |
DescriptionFeatures
Fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas.
Focus on visualization of concepts throughout the book helps readers grasp the concepts.
Icons in the margins to flag topics for which expanded or enhanced material is available on the textbook's companion Website..
A modern view of matrix multiplication is presented, with definitions and proofs focusing on the columns of a matrix rather than on the matrix entries.
Numerical Notes give a realistic flavor to the text. Students are reminded frequently of issues that arise in the real-life use of linear algebra.
Each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea.
[M] exercises appear in every section. To be solved with the aid of a [M]atrix program such as MATLAB™, Maple®, Mathematica®, MathCad®, Derive® or programmable calculators with matrix capabilities, such as the TI-83 Plus®, TI-86®, TI-89®, and HP-48G®. Data for these exercises are provided on the Web.
Author |
Success at Statistics : A Worktext with Humor - 96 edition
Summary: This comprehensive text covers all the traditional topics in a first-semester course.
Divided into 54 short sections, this book makes the topics easy to digest. Students regularly get positive reinforcement as they check their mastery with exercises at the end of each section.
Each exercise is based on a humorous riddle. If the answer to a riddle makes sense, students know all their answers for that exercise are correct. If not, they know they nee...show mored to check their answers.
Short sections make it easy to customize your course by assigning only those sections needed to fulfill your objectives.
A comprehensive basic math review at the end of this book may be used to help students whose math skills are rusty.
Thoroughly field tested for student interest and comprehension. The short sections and humor-based, self-checking riddles are greatly appreciated by students.
If you're looking for a statistics textbook that your students will enjoy, this is it |
Overview - LIFE SKILLS MATH STUDENT WORKBOOK
Life Skills Math makes math relevant for students in transition from school to independent living. This practical program provides comprehensive instruction that students and adults need for being self-sufficient. The full-color text focuses on using math skills in real-life situations for those who have basic computational skills but need practice in applying these skills. |
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MATH301: Business Mathematics
Course Credits:
3
Course Hours Per Week:
12
Course Overview
This course provides a variety of applications-based math tools and concepts for the business professional. Teaching an effective foundation on topics that include product pricing, inventory valuation, depreciation methods, payroll, investments, costs of borrowing money, and accounting basics, the basics needed for initial analysis of financial situations in business are covered.
In the course project, Financial Plan: Using Business Math to Analyze the Financial Conditions of a Company, students apply the mathematical concepts that have been practiced throughout the course. A final report is submitted outlining different analyses, strategies for investments and borrowing, return on investments (ROI), and goals and action plans for the company.
Course Learning Objectives
Apply mathematical formulas to solve business-related math problems.
Use business-related tools to make effective financial decisions.
Analyze outcomes of spreadsheet results.
Special Requirements
Packaged with the textbook, Practical Business Math Procedures, students will receive a users guide and access code for a math practice program called ALEKS for Business Math. This web-based program requires Internet access, and it will be used in each module of this course. Please note that if you purchase the textbook from a source other than the JIU Bookstore, it may not include the access code you need to complete work in this course. Therefore, WE RECOMMEND THAT YOU PURCHASE THIS ITEM ONLY FROM THE JIU BOOKSTORE. |
realgebra, by definition is the transition from arithmetic to algebra. Miller/O'Neill/Hyde Prealgebra will introduce algebraic concepts early and repeat them as student would work through a Basic College Mathematics (or arithmetic) table of contents. Prealegbra is the ground work that's needed for developmental students to take the next step into a traditional algebra course.According to our market Julie and Molly's greatest strength is the ability to conceptualize algebraic concepts. The goal of this textbook will be to help student conceptua... MORElize the mathematics and it's relevancy in everything from their daily errands to the workplace.Prealgebra can be considered a derivative ofBasic College Mathematics.One new chapter introducing the variable and equations is needed. Each subsequent chapter is basic mathematics/arithmetic content with additional sections containing algebra incorporated throughout. |
Algebra can be like a foreign language, but ELEMENTARY AND INTERMEDIATE ALGEBRA, 5E, gives you the t ... more »ools and practice you need to fully understand the language of algebra and the "why" behind problem solving. Using Strategy and Why explanations in worked examples and a six-step problem solving strategy, ELEMENTARY AND INTERMEDIATE ALGEBRA, 5E, will guide you through an integrated learning process that will expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Feel confident about your skills through additional practice in the text and Enhanced WebAssign. With ELEMENTARY AND INTERMEDIATE ALGEBRA, 5E, algebra will make sense because it is not just about the x...it's also about the WHY. « less
"Usually ships in 1 2 business days. Used book in good condition. Some cover wear, may contain marks such as highlighting or writing inside. This is an older printing. 100% satisfaction guaranteed. " -- ucaedu70 @ Wisconsin, United States |
Matrices are very powerful mathematical tools
applicable in a wide range of real world problems.
Intuitively, the main advantage in using matrices is that
they allow the logical manipulation of very large sets of
numbers at once. More rigorously, they allow the manipulation
(and solution) of linear equation systems which
in turn reppresent real world problems.
Just as example, the voltages and currents
in an electronic board with 1000 components can be described
by a very huge system of linear equations. 1000 components
imply 1000 unknown voltages and 1000 unknown currents. Attempting
to find such a large number of unknown variables without a method
is substantially a suicide. With the use of matrices such a system
can be solved in a very elegant way.
Today, matrices are used not simply for solving systems of simultaneous linear equations,
but also for describing the quantum mechanics of atomic structure, designing computer
game graphics, analyzing relationships, and even plotting complicated dance steps :)
In this article we try to develop our mathematical tool step by step.
Definition
A matrix is an ordered, bidimensional collection
of mathematical expressions usually rapresented as a rectangular table.
The horizontal lines in a matrix are called rows and the vertical
lines are called columns. A matrix with m rows and
n columns is called an m-by-n matrix (written mxn)
and m and n are called its dimensions. The dimensions of a matrix
are always given with the number of rows first, then the number of columns.
If the number of rows of a matrix equals the number of columns (m = n) then
the matrix is said to be square otherwise it's just rectangular.
Square matrixes have several interesting properties that we'll talk about later.
The entry of a matrix A that lies in the i-th row and the j-th column is called
the i,j entry or (i,j)-th entry of A. This is written as ai,j,
aij or A[i,j]. The row is always noted first, then the column.
A special matrix with one of the dimensions set to 1 is called vector.
A 1xn matrix is called row vector
while a mx1 matrix is called column vector.
If the entries of a matrix are all real numbers then the matrix is said
to be real. If the entries are complex numbers then
the matrix is too said to be complex. If the entries
are polynomials then (guess what?) the matrix is said to be polynomial too.
The entries of a matrix usually have some associated meaning but for now
let's just say they are mathematical expressions (maybe numbers) and
concentrate on matrix manipulation.
Let's play with it
We define the matrix sum as an operation that given
two mxn matrices A,B returns a mxn matrix C with entries that are sums
of the corresponding entries in A and B. Please note that the sum
is defined only for matrices of exactly the same dimensions: we say
that such matrices are sum-compatible.
For sum-compatible matrices it's obvious that
and
We define the scalar multiplication as an operation
that given a mxn matrix A and a scalar expression K returns a mxn matrix B
with each entry made of the corresponding entry of A multiplied by K.
It's again obvious that for sum-compatible matrices A,B and any scalar expression k
and for any matrix A and any couple of scalar expressions
k1, k2
Food for thoughs: Multiplication by scalar is commutative
if the underlying ring (of expressions) is commutative. This is true when the expressions
are (real or complex) numbers or polynomials, that is most real-world cases in that matrices
are applicable. However, the matrix algebra can be applied also to non commutative rings
(for example quaternions) where the multiplication by scalar must be splitted in two
different operations: left multiplication and right multiplication.
Not that obvious
We define the matrix multiplication as an operation
that given a mxp matrix A and a pxn matrix B
returns a mxn matrix C with element i,j computed
as the scalar vector product of the i-th row of A and the j-th column
of B.
Note that the matrix multiplication is well defined only for
couples in that the left matrix has the number of columns equal to the
number of rows of the right matrix. We say such two matrices
to be multiplication-compatible.
Food for thoughs: the multiplication
of two nxn matrices processes 2 n2
entries. However there is no known algorithm with computational
cost of O(n2). Most algorithm
are O(n3) and the most clever
implementations are O(n2.8).
An O(n2.376) algorithm has been proposed
by Coppersmith and Winograd but its implicit factor hidden by the O() notation
is so big that its implementation is worthwile only if we're going to
multiply matrices with n that is out of our current computing possibilities.
It's very easy to show that (and here comes the non obvious) the matrix
multiplication is generally not commutative, that is
except for very few special cases. The (square) matrices for that
are said to commute and must satisfy strict rules
on their elements.
The non commutativity of the matrix multiplication makes
the algebraic manipulation to become non trivial and causes
infinite headcaches to engineering students.
However, we're lucky since the associative and distributive properties
still apply and it can be proven that the following equations are all true
(given that the matrices involved are multiplication-compatible and
the underlying ring is commutative).
Transpose
We define the transpose of a mxn matrix A
as a nxm matrix B obtained from A by swapping rows with columns.
The transpose of a matrix A is often written as AT
or as A'.
Note that swapping rows with means effectively swapping
the order of indices of each element. The element aij
of the matrix A becomes the element aji of
the transpose.
Food for thoughs: This property is interesting in computer
matrix processing. To apply an algorithm to the transpose of a matrix instead of the original
one we can simply swap the parameters of all the matrix element access functions...
A matrix whose transpose is equal to itself is called a symmetric matrix;
that is, A is symmetric if AT = A. Note that A must be
square to be symmetric and internally the elements must satisfy the relation
aij = aji.
It's easy to show that
for any matrix A, thus the transposition is a self-inverse operation.
Also for two matrices with the same dimensions
If the matrices A and B are multiplication-compatible then
Note that the order of multiplication is inverted.
And finally taking the transpose of a scalar (1x1 matrix) is a null operation
The identity
A particular square matrix that commutes with all other
matrices of the same size is the identity matrix.
The identity matrix has all unit elements on
its main diagonal.
It's easy to prove that
and thus the identity matrix is the "unity" element of the matrix algebra
and the multiplication by the identity matrix is an idempotent operation.
Obviously the transpose of an identity matrix is still an identity matrix.
The inverse
Given a square matrix A we define the inverse matrix of A
as the matrix that when multiplied by A gives the identity matrix as result.
The inverse matrix is usually written as A-1.
The inverse matrix does not necessairly exist. A matrix that has no inverse
is said to be non invertible or singular.
Note that A and its inverse (when it exists) do commute.
Food for thoughs: for non square matrices
we can define the left (A-1A=I) and the
right inverse (AA-1)=I. Such inverses
have few real world applications...
It can be shown that the inverse of a matrix is again invertible and that
for any invertible matrix A and that
for any invertible matrix A and any non null scalar k.
It can be also proven that
for invertible matrices A and B of the same size. Note that the order
of factors is inverted and the formula is very similar to the one
that involves transposition.
Finding the inverse of a matrix is a very common highly intensive computational task.
There are several algorithms that implement this operation and many of
them operate better on matrices with elements that satisfy certain properties
or conformations.
The above system of m linear equations in n unknown variables can be rewritten
by using matrices as follows
The rows of the A matrix on the left contain the coefficients
of the linear equations of the system. The unknown variables and
the known terms are collected in row vectors x and b.
Solving the system means finding the set of values x1,x2,...,xn
that satisfy all the equations at the same time.
In most cases (if the field of the matrix elements is
infinite) exactly one of the following statements is true:
the system is undetermined (the set of solutions is empty)
the system is overdetermined (the set of solutions contains infinitely many elements)
the system is exactly determined (the set of solutions contains contain exactly one element)
The most interesting case is obviously the one with exactly one solution.
The Rouche'-Capelli theorem states that for a system of linear equations with
n unknown variables to be exactly determined there must be at
least n linearly independent equations.
Since more equations are unnecessary then the most interesting
linear systems are described by a square coefficient matrix.
By using trivial manipulations we can now show that by inverting
the matrix of coefficients we can solve the system.
We multiply boths sides of the system equation by the inverse of A
Since by definition
so the formula above can be rewritten as
and since
then trivially
The last formula is very important since it provides the
real motivation for studying the inverse matrices. If we're
able to find the inverse of A, we can solve the system.
Determinants
The definition of the matrix determinant is quite scary.
Given a square nxn matrix A, it's determinant is defined as
where E(n) is the set of permutations
of the numbers {1,2,....n}, P is a single permutation taken out of that set and sgn(P)
is a function that returns +1 if the permutation P is
even
and -1 if the permutation P is odd.
P(i), then, is the i-th element of the permutation P.
The formula above is also known as Liebniz formula.
and is better explained with an example. Consider the following 2x2 matrix.
In this case n is 2 and thus E(n) is the set of the possible
permutations of numbers {1,2}. E(n) obviously contains only
two elements: the trivial "null" permutation {1,2} (which is even)
and the permutation {2,1} (which is odd).
The Liebniz formula expands then to a sum of two elements
dictated by the two permutations just described.
Each element of the sum is a product of n elements
of the matrix taken from distinct columns. The row of each element
is choosen by the permutation.
In the first product we move along the columns (indexed by i)
from left to right and take the first and the second row (null
permutation). This means a11 and a22.
Since the permutation used is even, then the sign of this product is positive.
In the second product we move along the columns
from left to right and take the second and then the first row
(the odd permutation). This means a21 and a12.
Since the permutation is odd, then the sign of this product is negative.
The determinant of the 2x2 matrix is then
This is rather easy to remember if you note that it's the
sum of the products of the two diagonals of the 2x2 matrix.
The product is positive if the diagonal goes "up" from left
to right while it's negative if the diagonal goes "down"
from left to right.
The formula for 3x3 matrices is more complex
and it contains 6 elements.
If you look close you can still spot the same pattern.
There are positive diagonal lines that go down from left
to right and negative diagonal lines that go up
from left to right.
The formula for 4x4 matrices becomes really complex
and is rarely written explicitly. For larger n values
the formula becomes very difficult to use because
it's hard to enumerate all the permutations of n numbers.
Other methods for finding the determinant exist
and later we'll probably spot some of them
but now let's look at some of the determinant properties.
It can be shown that for square matrices A and B, any scalar r
and the square unit matrix I the following properties are true
1.
2.
3.
4.
5.
6.
Invertible matrices and their determinants
Since for an invertible matrix A
then by property 4 of the previous paragraph
and since
then
which implies that
and that
Conversely, it can be shown that a non-zero determinant
for matrix A implies that the inverse of A exists.
The proof requires the notion of the rank of a matrix
which we haven't covered so I'm going to omit it here.
However, the two deductions lead us to the following theorem:
"A matrix is singular if and only if its determinant is zero"
or alternatively
"A matrix is invertible if and only if its determinant is non zero"
Food for thoughs:
As a rule of thumb, almost all square matrices are invertible. Over
the field of real numbers, this can be made precise as follows: the set
of singular n-by-n matrices, is a null set, i.e., has Lebesgue measure zero.
Intuitively, this means that if you pick a random square matrix over
the reals, the probability that it will be singular is zero.
In practice however, one may encounter non-invertible matrices. And in numerical
calculations, matrices which are invertible, but close to a non-invertible
matrix, can still be problematic; such matrices are said to be ill conditioned. |
Pre-Algebra
Description
This pre-algebra work-text gives a brief but complete review of all arithmetic topics, broadening many topics to include more than one approach to the correct solution. Much of the text is devoted to algebra and related topics, scientific notation, geometry, statistics, and trigonometry. Problem-solving strategies help students apply mathematical skills to word problems. Students build confidence in their mathematical potential as they successfully work in advanced topics that are presented in an understandable and interesting style |
Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra. All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts. Utilizing... more...
Everything you need to know to ace the math sections of the NEW SAT!. He's back! And this time Bob Miller is helping you tackle the math sections of the new and scarier SAT! Backed by his bestselling ''Clueless'' approach and appeal, Bob Miller's second edition of SAT Math for the Clueless once again features his renowned tips, techniques, and insider... more...
Boiled-down essentials of the top-selling Schaum's Outline seriesFlummoxed by formulas? Queasy about equations? Perturbed by pi? Now you can stop cursing over calculus and start cackling over Math, the newest volume in Bill Robertson's accurate but amusing Stop Faking It! best sellers. As Robertson sees it, too many people view mathematics as a set of rules to be followed, procedures to memorize, and theoremsBlending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach-and how both can become better learners. Dispatches as... more...
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Geometry, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: |
Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every... more... more...
Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.
The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical t more...
From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more...
500 Ways to Achieve Your Best Grades. We want you to succeed on your college algebra and trigonometry midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and getyour best grades. These questions and answers are similar to the ones you'll find on a typical... more...
Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications. more...
Don't be tripped up by trigonometry. Master this math with practice, practice, practice!
Practice Makes Perfect: Trigonometry is a comprehensive guide and workbook that covers all the basics of trigonometry that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples,... more...
Schaum's has Satisfied Students for 50 Years.
Now Schaum's Biggest Sellers are in New Editions!,... more... |
The series is an easy-to-teach mathematics course, giving simple and direct explanations for concepts. The books are replete with examples from daily life to help strengthen the student''s understanding of basic concepts. Well-thought-out illustrations have been included to aid visualization of concepts. Each book of the series comes with a companion CD which contains interesting animations and interactive exercises, making the teaching and learning of mathematics a thoroughly enjoyable experience.
Dr. RaviPrakash is Reader in mathematics in Rajdhani College, University of Delhi with more than thirty years of experience in teaching. A double gold medallist from the University of Delhi, he is also a mathematics resource person and regularly conducts mathematics workshops. He has authored five mathematics books at the higher secondary level as also published several research papers in reputed international journals of mathematics.
JayashreeLakshmanan has more than two decades of experience in teaching mathematics. She has served as a mathematics teacher in The American International School, Padma Seshadri Bala Bhavan, DAV School, Chennai and Indian School, Bahrain.
JayashriVasudevan has over 17 years of teaching experience. She has taught mathematics in Padmashri P.N. Dhawan Adarsh Vidyalaya Matriculation Higher Secondary School, Chennai.
KRameswari has over 22 years of teaching experience. She worked as a mathematics and computer science teacher in Padmashri P.N. Dhawan Adarsh Vidyalaya Matriculation Higher Secondary School, Chennai.
MonicaKochar is teaching in Pathways International School, Noida. Earlier she has taught at Mother's International School, Delhi. She has conducted numerous workshops in mathematics for different schools on creativity in mathematics classroom.
RenukaLamech has over 18 years of experience in teaching children aged 3 to 5 years. She is a graduate in Psychology and a Diploma holder in Nursery teaching from London Montessori School. She started her career as a teacher in Lady Andal Venkatasubha Rao School in 1993 and is currently running her own Montessori School in Chennai which she established in 2002.
SmitaGupta is an experienced senior mathematics teacher in Mother's International School, Delhi. She has been actively involved in conducting workshops in mathematics as well as on the implementation of CCE in schools. |
From the uses of mathematics throughout history to solve problems to representation of abstract ideas through mathematical representation, this video introduces middle school students to more advanced concepts about the general nature and uses of mathematics. |
Solving Compound Inequalities Test Recovery 16 compound inequality problems. At the top of the worksheet is 2 worked out examples that are excellent guides for students to follow.
I actually use it as a way for them to raise up their test grade. For each 2 problems they get correct, I will raise their grade 1%. After each test they have the opportunity to raise their test grade by doing extra problems. I only allow them to have one of the worksheets at a time and when they complete it I grade it and go over it with them if there is still some misunderstandings. I have found that it works great because the students that truly care about understanding the material will do these worksheets. This is helpful because a lot of the time when I try and go over a test in class, students lose focus and are uninterested. This way I don't spend time in class going over the test and I don't get frustrated with them not taking advantage of the reviews.
Word Document File
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Mathematics / Pangarau
It is generally acknowledged that everyone needs to learn and use mathematics. Most areas of employment require at least some ability in understanding and using numbers. It is also used in many areas of daily life; anyone who wants to manage a household budget, organise a holiday, decorate a room or build a fence will need mathematics.
An understanding of mathematics helps people to develop and use logical approaches to procedures and arguments. A grasp of geometrical ideas helps people to appreciate symmetry and patterns and helps them to make sensible designs.
Mathematics involves skills of calculation and estimation and the ability to reason logically. It develops the creativity and problem solving involved in technological and scientific innovation and discovery.
Skills learned and practiced in the mathematics curriculum can be applied across a wide range of occupations such as banking, accountancy, statistics, management, architecture, science, teaching, engineering, insurance, financial planning, economics, weather forecasting, trades and so on. |
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Course Communities
Lesson 23: Integer Exponents
Course Topic(s):
Developmental Math | Exponentials
To motivate the convention for negative and zero exponents, the lesson begins by observing the halving pattern found in continuously decreasing the exponent of a power of two by one. After an application looking at the formula for Body Mass Index calculation, power functions of the form (f(x) = kx^p) are introduced. Radiation Intensity application problems follow before pure algebraic manipulation of exponential expressions are presented. The lesson concludes with a review of scientific notation. |
It is true that they are more rigorous that the Edexcel textbooks, which are not very taxing for the person who is aiming for A/A* in Further Maths A Level. I'm not sure how necessary they are though. Why not loan a copy from a library before deciding on the purchase, or just purchasing the first one before committing, at least?
I used the further pure book when doing my A-level further maths on AQA. It was good for additional exercises and additional persepctive from my main course book (the Gaulter and Gaulter one) but it was pretty old, at least the edition I was using was. Someone will correct me if I'm mistaken, but I think my teacher mentioned it was the book she used in the 1980s for her A-levels so you may find it's a bit old fashioned in the approach.
It's true that these books are very old but we still use them with our students doing Maths and especially Further Maths on the CIE syllabus.
The problem is not so much old fashioned-ness in style, but that they don't match to your syllabus. The red book probably covers the A-level more or less completely, but the stuff you need is mixed up with stuff you don't, so it's a bit inconvenient. The yellow book may or may not cover all of your Further syllabus, and it will definitely have stuff you don't need (unless you're doing STEP, and even then you might not need groups), and it might be missing very important parts (e.g. in CIE we do vector spaces, and it's lacking in that area).
They have a lot of detail and a lot of good, challenging questions - they'll be a good supplementary text for higher achieving students.
(Original post by isp-)
Maths:
[ Further Maths: |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
Mathematical concepts are explained in this illustrated set, along with a fascinating historical overview of the field. It explores the uses and effects of math in daily life, and provides information on different career choices in this field. Each volume includes sidebars, bibliographies, timelines, charts, a glossary, a guide to resources on the Web, and individual and cumulative indexes.
Review:
"From 'Abacus' to 'Zero' this alphabetically arranged encyclopedia complements the hands-on approach of standard textbooks or resources...Boxed side notes, definitions of special terms, several see references, and, occasionally, small diagrams or black-and-white photos, enhance the entries...Libraries serving strong science programs will find this set particularly useful." -- School Library Journal (November 2002) |
fartherThis book is about how to solve difficult real problems by an easy method that uses the dimensions of the problem to derive an answer. Dimensions are things like inches, feet, seconds, and so on that are used to set up the answer to a problem usually described in words. How many meters in a mile? How many seconds in a year? How fast is a car going if it accelerates for ten miles per hour every second for 20 seconds? How far has it traveled? How high is an airplane if a wrench dropped from it takes 30 seconds to hit the ground? How many moles of water in 12 pounds? How much money can be saved by insulating a house?
These and practically all problems that have a dimension can be solved by the methods shown in this book.
The author strongly believes that this method should be taught in all high schools. He believes that 9th grade would be the best starting time and at the beginning of the year. He has called this method Dimensional Analysis. Students would only require two weeks to become proficient.
Mr. Kelly taught three 8th grade classes how to use Dimensional Analysis in only three days. The response by the science teacher and students was strongly positive.
It became clear however that reinforcement of the technique was needed. This book �IT�S DIMENSIONAL� is a result of that perceived need. |
Description
Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.
Recommendations:
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MATH 221: Vectors and Matrices
This is a course in the algebra of matrices and Euclidean spaces that emphasizes the concrete and geometric. Topics to be developed include solving systems of linear equations; matrix addition, scalar multiplication, and multiplication; properties of invertible matrices; determinants; elements of the theory of abstract finite dimensional real vector spaces; dimension of vector spaces; and the rank of a matrix. These ideas are used to develop basic ideas of Euclidean geometry and to illustrate the behavior of linear systems. We conclude with a discussion of eigenvalues and the diagonalization of matrices.... more »
Credits:1
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Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
Manga Guide to Linear Algebra – Review
[14 Aug 2012]
I recently received a review copy of The Manga Guide to Linear Algebra.
The "Manga Guides" have been very popular and currently the series includes such topics as Biochemistry, Calculus, Databases, Electricity, Electricity, Molecular Biology, Physics, Regression Analysis, Relativity, Statistics, and The Universe. The front of the book includes rave reviews for these earlier books in the series.
Earlier I reviewed the "Statistics" and "Databases" volumes. I said at the time the Manga Guides appeared to be a "winning formula", since the manga story motivated the reader to read on to the next chapter, and the books show empathy for the struggles students experience while learning such topics.
I'm not as enthusiastic about the Linear Algebra volume, since I think it missed several opportunities to help the novice learner.
Guide to Linear Algebra – the promise
The story involves Reiji, a skinny kid and Misa, the cute sister of a karate master.
Many students struggle with linear algebra, so I was looking forward to diving in, especially to see the discussion on practical applications.
The good
Let's face it. Most math books are not page-turners for most people. Anything a writer can do to maintain motivation is a good thing.
Keeping with the tradition of the others in the series, The Manga Guide to Linear Algebra has a cute story line. Nerdy Reiji takes on the job of tutoring the Hanamichi Hammer's little sister in the topic of Linear Algebra. In return, he can join the Hammer's karate club. In his first meeting with the big brother, Reiji is warned not to fraternize with Misa.
The manga story continues throughout the book between each slab of math. It works – you want to find out what happens next in the story and with math sandwiched between the manga, it's quite a good concept.
Included are a few nice explanations of Japanese culture, like "ossu" (a saying used by martial artists to increase concentration).
On the math side, Gaussian Elimination in Japanese is "Hakidashihou", or "Sweeping out". This is a good way to remember the concept (both for Japanese native speakers and those reading a translation).
The not-so-good
I feel that a book like this provides a great opportunity to discuss the "big picture" concepts, so readers become more aware of the "why" and "how it is used" of Linear Algebra. Leave the nitty-gritty of the micro-level math to the conventional textbooks and ensure the reader has the answers to the key what, why and how questions.
Certainly the book attempts to achieve that outcome, however, I was disappointed that some of the opportunities were lost, and some of the messages promulgated by the book are unfortunate.
Early on, (p15), Misa asks some reasonable questions that most students will ask.
Misa: But I still don't understand… What is linear algebra exactly?
Reiji: That's a tough question to answer properly.
Misa: Really? Why?
Reiji: Well, it's pretty abstract stuff.
He goes on to explain the main idea using translations of 3-D objects to 2 dimensions (like drawing a building on a piece of paper).
However, his summary would not be understood by most newbie students, I suspect:
Reiji: "Linear algebra is about translating something residing in an m-dimensional space into a corresponding shape in an n-dimensional space.
Say what? (If this was framed in a different way it may have been more convincing. Something like, "The fancy way of saying this is…, but that simply means …")
Most people want to know how they will use what they are studying. Misa asks the classic question (p17):
Misa: What exactly is it good for? Outside of academic interest, of course?
Reiji: You just had to ask me the dreaded question, didn't you? While it is useful for a multitude of purposes indirectly, such as earthquake proofing architecture, fighting diseases, protecting marine wildlife, and generating computer graphics… it doesn't stand too well on its own, to be honest…
… Like it or not, it's just one of those things you've got to know.
I feel the book would have been much stronger if it had been built around such practical examples, rather than concentrating on the (pure) math. Readers could still learn the theoretical concepts as a result of studying such examples. I'm not sure how many university students will be convinced by "it's just one of those things you've got to know".
What came across to me in these 2 vignettes is Reiji is uncomfortable talking about the "big picture" aspects. It would have been more satisfying if he was less apologetic about why this topic is included in many undergraduate programs.
Perhaps I'm being unfair here. Maybe my angst should be directed towards colleges who make topics such as Linear Algebra compulsory because "it's good for the students". This may be fine for math majors who have signed up because they love all sorts of math and don't mind what's offered, but for students studying other majors, they really should be given a good idea why they are doing it.
And yes, I know all students should have their thinking challenged and broadened at college level, but it needs to be done meaningfully.
Calculations
Sadly, the book concentrates too much on the calculations involved. Much of this calculation can, and should be done using computers, which then frees up time for everyone to learn the key concepts and how to apply them.
In the story, Misa is not a mathematics major. She, like many real students, ends up taking abstract courses like Linear Algebra with very little idea why, or when it will be useful to her. They learn it for the exam and promptly forget it.
It's not clear why Reiji launches into an explanation of complex numbers on page 25. Misa starts to become stressed, and Reiji says:
Reiji: I think it's be better if we avoided them for now since they might make it harder to understand the really important parts.
Exactly! Why even mention complex numbers (here) if they are not going to be used throughout the rest of the book?
The cofactor method is mentioned on p88, but Reiji says:
Reiji: The calculations invovled in cofactor method can very easily become cumbersome, so ignore it as long as you're not expecting it on a test.
Sadly, the message here is "Learn for tests".
Misa: If this is on the test, I'm done for.
Reiji: Don't worry, they are usually only 2×2 or 3×3.
So why confuse the poor girl with much larger examples?
Why do we learn Gaussian Elimination? On page 88, we have:
Reiji: In addition to finding inverse matrices, Gaussian Elimination can also be used to solve linear systems.
Fair enough. But after doing an example which involved solving a system of equations, he says (p89):
Reiji: Gaussian Elimination is about trying to get this part here [pointing to the right hand side of the working] to approach the identity matrix, not about solving for variables.
This would leave many first-time students somewhat unsatisfied and confused. So why are we doing it again?
Pages 98 to 105 contain some really pointless – and complicated – calculation rules. Sarrus' Rule is particularly untidy. I say "pointless" because evaluating determinants is exactly the kind of thing we should let computers do. I say "untidy" because for non-mathematicians, there are hundreds of steps involved, many patterns to recognize and remember, and way too many places to make a mistake. And in this work, a mistake early on can bubble down through the whole problem. (Yes, students should learn to be accurate and to check their work. But matrix operations are universally disliked because they are tedious, prone to many mistakes and should be done using software in the first place.)
Here the message that comes across is "Math is about calculation".
Should have more…
Throughout the book there are interesting practical examples, but they are only briefly mentioned. I'd like to see more examples and more space devoted to examples involving:
Enlargements & rotations using matrices
Linear transformations with graphs (e.g. p 212)
Area of parallelogram (p 97) using determinants.
Volume parallelpiped using 3×3 determinant.
Who is the audience?
I enjoy the Manga Guides concept, but I wonder how many math teachers would assign this as a text? (I wouldn't, since the math is too calculation-based).
How many students would buy it?
The Preface says it's for:
University students about to take linear algebra
Those who've taken it in the past but don't understand it still
High school students who are aiming to enter a technical university
Anyone else with a sense of humor and an interest in mathematics!
I put myself in the latter category. I did enjoy the story!
Let me know if you have bought books in the Manga Guides series and are in any of the above categories. What was your experience learning from the book?
Conclusion
I feel that the Manga Guide to Linear Algebra has missed the mark somewhat. The story line and artwork are very good, but concentrating on the calculation aspects of the math at the expense of the "big picture" aspects was a disappointment.
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2 Comments on "Manga Guide to Linear Algebra – Review"
I bought this book because I have an interest in math & have a sense of humor. Or more likely a complete fear of mathematics since my encounter with differential equations! But now I'm heading to grad school, and the stuff I'm really interested in will deal with vector calculus and differential topology. So, I thought I'd at least learn what linear algebra was via comics. Seemed to work for me when the comic version of Bible came out in the 1980′s.
Was I entertained while reading about linear algebra? Sure, probably much more so than if I just bought a book about it. I did learn some things about it, but the book just didn't cover a lot of "why". So, while not the best introduction to the subject, they did cover enough of the basics that I'll remember what things are. |
Synopsis
Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results.
The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online |
Prerequisite: "C" or better in MATH 093 or minimum ACT math subscore of 20. Field and order axioms; equations, inequalities; relations and functions; exponentials; roots; logarithms; sequences. This course satisfies the required core-math reasoning for general education. |
Mathematics for Edexcel GCSE - Student Support Books The Student Support Book are an ideal companion for any main text and provide extra learning opportunities for students to enhance exam success. ...
Mathematics for Edexcel GCSE - Student Support Books The Student Support Book are an ideal companion for any main text and provide extra learning opportunities for students to enhance exam success. ... |
Intermediate Algebra (cloth) - 2nd edition
ISBN13:978-0073312682 ISBN10: 0073312681 This edition has also been released as: ISBN13: 978-0073028729 ISBN10: 007302872X
Summary: Miller/O'Neill/Hyde, built by teachers just like you, continues continues to offer an enlightened approach grounded in the fundamentals of classroom experience in the 2nd edition of Intermediate Algebra. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the textbook. Throughout the text, the authors have integr...show moreated many Study Tips and Avoiding Mistakes hints, which are reflective of the comments and instruction presented to students in the classroom. In this way, the text communicates to students, the very points their instructors are likely to make during lecture, helping to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition, Problem-Recognition exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises, is to help students overcome what is sometimes a natural inclination toward applying problem-sovling algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the first edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class, as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGraw-Hill's online homework management system, MathZone. ...show less7.00 +$3.99 s/h
Acceptable
Booksavers MD Hagerstown, MD
2006 Hardcover Fair 2008. An acceptable used copy with heavy cover wear and school markings. Book only-does not include additional resources. Booksavers receives donated books and recycles them in...show more a variety of ways. Proceeds benefit the work of Mennonite Central Committee (MCC) in the U.S. and around the world |
Search Mathematical Communication:
Mathematical Communication
Exam review
Topic Teaching Tip(s):
Courses in which students communicate about mathematics | Communication recitations
This recitation from MIT's communication-intensive offering of Real Analysis focuses on exam review and on formulating precise questions. Students come to recitation with two precise questions about an aspect of the exam material that they find confusing. Students discuss their questions in groups to help each other. In the second half of recitation, the class discusses any remaining questions. |
Fundamentals of Math DVD with Books
Fundamentals of Math for Distance Learning
Fundamentals of Math (2nd edition) focuses on problem solving and real-life uses of math with special features in each chapter while reinforcing computational skills and building a solid math foundation. Dominion through Math problems regularly illustrates how mathematics can be used to manage God's creation to His glory.
Mr. Harmon teaches this course.
Recommended Viewing Schedule: five 30-minute lessons a week; 164 |
Specification
Aims
to supply evidence that such problems are both intriguing and provocative, and require rigorous proof;
to explain the fundamental ideas of sets, numbers and functions;
to compare and contrast language and logic;
to introduce a detailed study of the integers, including prime numbers and modular arithmetic;
to show how mathematicians generalize ideas, so unique factorization of integers is shown to hold for permutations;
to introduce the ideas of algebraic structures and so show, by examples throughout the course, how the same structure can arise in many different situations.
Brief Description of the unit
This course introduces students to the concept of proof, by studying
sets, numbers and functions from a rigorous viewpoint. These topics
underlie most areas of modern mathematics, and recur regularly in years
2, 3, and 4. The logical content of the material is more sophisticated
than that of many A-level courses, and the aim of the lectures is to
enhance students' understanding and enjoyment by providing a sequence of
interesting short-term goals, and encouraging class participation.
Learning Outcomes
On completion of this unit successful students will be able to:
analyze statements using truth tables;
construct simple proofs including proofs by contradiction and proofs by induction;
prove statements about sets and functions;
prove standard results about countable sets;
apply Euclid 's Algorithm to find the greatest common divisor of pairs of integers and to solve linear Diophantine equations;
to solve simultaneous linear congruences;
multiply and factorize permutations;
prove the infinitude of prime numbers, prove Fermat's Little Theorem and use it to find modular inverses and to solve linear congruences;
construct multiplication tables for congruence classes, reduced congruence classes and sets of permutations. Have an informal understanding of isomorphisms between the groups seen in the course.
Future topics requiring this course unit
Almost all Mathematics course units, particularly those in pure mathematics.
Assessment
Arrangements
Midterm Test
The Midterm Test will be in-class and closed book, and will relate
to the first five weeks of the course ONLY. It will involve
answering questions similar to those on the relevant Problem Sheets;
students who have taken full advantage of their supervision classes
should therefore find the Test straightforward. It will be worth
15% of the final mark for the course. Answers will be marked
and returned in due course, as part of the learning process. |
Categories
Other Links
A review of basic arithmetic operations and algebraic operations. Topics covered include the arithmetic of fractions
and decimals, algebraic manipulations of polynomials, linear equations, and factoring. This course cannot be used to satisfy
General Education requirements or for credit toward a Mathematics major or minor. |
MAA Review
In a 1990 paper entitled "What Is Geometry?" Shiing-Shen Chern [3] identified six pivotal developments in the history of geometry:
Euclid's axiomatic treatment,
the introduction of coordinates (Fermat and Descartes),
the invention of the calculus (Newton and Leibniz),
the recognition of the fundamental role of transformation groups (Klein and Lie),
manifolds (Riemann), and
fiber bundles (E. Cartan and Whitney).
The geometry presently taught in American high schools includes significant parts of (1) and (2), and some students get an introduction to (3). Transformations (4) make a cameo appearance in many contemporary American high school geometry textbooks, and play a featured role in a few. (5) and (6) have not influenced the high school curriculum.
The Common Core State Standards for Mathematics, which have now been adopted as a guide for the K–12 mathematics curriculum in 44 states, put transformations in center stage. Students in Grade 8 are introduced to geometry by experimenting with rotations, reflections and translations and they are expected to understand congruence in terms of rigid motions. High-school students develop these ideas more rigorously, learning standard terminology and fundamental facts about rigid motions and dilations of the plane as a foundation for the study of Euclidean geometry. In giving such prominence to transformations, the authors of the Common Core took into account both pedagogical evidence as well as the structure of the mathematics underlying the curriculum. Nonetheless, in view of the traditional organization of the curriculum, this is one of the bolder proposals of the Common Core.
The challenge will be implementation. We will need K–12 textbooks that are very different from those most widely used. At least as important will be assuring that teachers are intellectually equipped. Good scholarship presented in a form accessible to teachers (or those planning to become teachers) and focused on the meaning and role of transformations in geometry is needed. One would hope to find this in textbooks for junior/senior-level college geometry courses, but unfortunately few books fill the bill. There is no standard undergraduate course in geometry, and the available textbooks have less in common than the books for courses such as abstract algebra or basic analysis that have acquired a canonical form. Geometry textbooks tend either to present some kind of axiomatic treatment and then to branch off into topics or else to be, through and through, a sampling of approaches and ideas. Transformations tend to be treated in college in the same way that they are treated in high school, namely, as an interesting branch of a great tree.
The purpose of the book of Barker and Howe is to develop the main ideas about geometric transformations of the Euclidean plane and their applications. It could play a valuable role in introducing college students, especially future teachers, to this topic. However, it does not jump immediately to its main topic. Chapter I, which takes up the first 120 pages of the 529 pages of this text, is devoted to a careful development of Euclidean plane geometry based on an axiom system similar to SMSG, which features the Ruler and Protractor Postulates. This opening chapter sets the mathematical tone. It is careful, rigorous, thorough and explicit in its attention to detail. I expect that this would not only be a good book from which learn some geometry, but also a fine introduction to the habits of logical thinking and precise exposition that a math major needs to acquire.
Transformations make their first appearance in Chapter II, which culminates on pages 157–161 by classifying the isometries of the plane according to the number of their fixed points, demonstrating that every isometry is a composite of at most three reflections, and proving that, for any pair of congruent triangles, there is an isometry that takes one to the other. Readers who are familiar with these theorems might wonder if 160 pages of preparation are needed. The main ideas in the proofs are intuitively clear, and can be conveyed vividly by well-designed paper-folding activities. But what a student will take away from an informal presentation is very different from what he or she might acquire by following the course that the book lays out. Paper-folding, whatever legitimate pedagogical purposes it may serve, does not equip learners with a useful language for reasoning about transformations. This book will provide plenty of opportunity to learn good mathematical language and practice its use.
Chapter III begins with a discussion of compositions of reflections and the kinds of plane isometries that may be produced, leading up to the classification of isometries as reflections, rotations, translations or glide reflections on page 188. Numerous fine color illustrations make the twenty pages of preparation for this theorem a delightful visual experience. This is followed by a discussion of orientation based on the proposition that the parity of an isometry is well-defined. The chapter then introduces the idea of a group of transformations and in a sequence of exercises beginning on page 203 invites readers to investigate the structure of many examples. The remainder of the chapter deals with factorization in the plane isometry group.
Chapter IV concerns similarities. This chapter is especially important for future teachers because of the prominence of similarities in high-school mathematics. The treatment here parallels the treatment of isometries in the previous chapters, building up to the structure and classification theorems.
Chapter V studies the conjugacy relation in transformation groups and the decomposition of groups into conjugacy classes. This chapter ends with an interesting but sketchy discussion of the idea of developing geometry from the group of symmetries alone by means of the correspondences between lines and reflections and between points and 180-degree rotations. As a matter of fact, this is an idea that was developed extensively in the early 20th century by German-speaking mathematicians Gerhard Hessenberg, Johannes Hjelmslev and Gerhard Thomsen; see [4]. The standard reference is Friedrich Bachmann's book [1]. Unfortunately, the works of Hessenberg, Hjelmslev and Thomsen have not been translated into English, nor has Bachmann's book. However, a good synopsis in English is contained in chapter 5 of [2].
Chapter VI describes applications of transformations to Euclidean plane geometry. Running from page 287 to 346, it includes numerous interesting results. Transformations appear sometimes as essential tools, sometimes as useful aids, sometimes as a way to interpret a construction and sometimes merely as a point of view. Section 2 describes some theorems on the concurrence of special lines in triangles.
The first theorem on the circumcenter (the point of concurrence of the perpendicular bisectors of the sides of triangle ABC) helps to illustrate my remark about the varying role of transformations. The proof is essentially as follows: Let w be the perpendicular bisector of segment AB and let u be the perpendicular bisector of segment BC. Let P be the point of intersection of w and u. Then P is equidistant from A and B because it's on w and also P is equidistant from B and C because it's on u. Therefore, P is equidistant from A and C, so P lies on the perpendicular bisector of segment AC. Transformations illuminate the argument — w and u are axes of reflections and it is these reflections that show the congruence of segments AP, BP and CP — but certainly it is not necessary to know this to follow the proof.
The incenter, centroid and orthocenter are treated in a similar fashion, using arguments in which the role of transformations is clear, illuminating but not essential. Section 3 uses dilation about the centroid by a factor of –2 to unify a discussion of the Euler line and the nine point circle. Here, the transformation does some real work. Section 5 of this chapter concerns the orthocenter (the point of concurrence of the altitudes). The discussion hinges on the analysis of the composition of the reflections whose axes are the sides of a triangle. Here, transformations are not only hard at work, but are leading the development.
Chapters VI (pages 347–375) concerns the symmetries of bounded figures in the plane, leading up to a discussion of dihedral groups. Chapter VII (pages 376–458) is a careful treatment of frieze and wallpaper groups. The last chapter concerns area, volume and scaling.
I had hoped to use this book in a one-semester course in geometry that I teach periodically, but up till now the scheduling has not worked out. The course is populated primarily by math majors who are seeking certification as secondary teachers. Most of these people take a proof-based course in real analysis as well as other junior/senior courses, including probability, abstract algebra, number theory and other advanced topics. The typical student in this group will likely struggle at first with the level of exposition in Continuous Symmetry, particularly if he or she has not previously taken the analysis course, but surely will be capable of handling it. Because the text is detailed and methodical, patience and persistence is needed. However, it clear and explicit enough that it will never leave students helpless or befuddled, provided they are serious and spend the time to read carefully.
I plan to use the text next time I teach the class. I expect to have to pick and choose carefully, especially in the first chapter. I find the level of rigor of Euclid to be a very workable goal in this class. It does not pay off to be overly concerned with facts, such as the Crossbar Theorem, that are evident from the topological properties of diagrams. I think the geometry of the number line is an essential topic, and a good opening for the course. This is consistent with the layout of the book.
My goal will be to spend only enough time in chapter I to prepare for chapters II, III and IV. These, I want to treat carefully because of the tasks these future high-school teachers will face in the classrooms where they will eventually teach. I shall need to include some material on area and volume, and Chapter IX can support this. Some discussion of coordinates, particularly linear change of coordinates, will be desirable. For this, I shall need to supplement the book. R. Hartshorne has made some observations about conventions related to the Ruler Postulate in a review of this book that appeared recently in the American Mathematical Monthly. Anyone who plans to use the book should be aware of his remarks.
Although I have mentioned them only once, the abundant, high-quality illustrations throughout the text are one of the most attractive features.
The book does not always choose the quickest or most elegant route to a result. For example, Proposition IX.2.14 on the area of a parallelogram could have been proved more elegantly by repeating Euclid's proof of Proposition 35 of Book 1 of the Elements. Nevertheless, I learned a lot by reading the book, mainly because the material is arranged in a manner that invites and inspires one to reflect about the connections among the ideas being discussed. It is thought-provoking throughout. If a textbook is meant to be a tool for learning, then the extent to which it makes one think in the manner of a mathematician is by far the most important feature — much more important than any quibbles about the slickness of a proof. I am very much looking forward to the opportunity to use this book in my classes.
Comments
A full review of Continuous Symmetry was written by Robin Hartshorne for the American Mathematical Monthly, Volume 118, Number 6, June 2011, pp. 565–568. Subscribers can see this review online by going to |
The Complete Idiot's Concise Guide To
Algebra
Edition 2
Published by Alpha Books
Just the facts (and figures) to understanding algebra. The Complete Idiot's Guide to Algebra has been updated to include easier-to-read graphs and additional practice problems. It covers variations of standard problems that will assist students with their algebra courses, along with all the basic concepts, including linear equations and inequalities, polynomials, exponents and logarithms, conic sections, discrete math, word problems |
Algebra World – An Introduction
Algebra World software will turn struggling students into successful math learners and average students into accelerated math learners!
Algebra World teaches and reinforces introductory algebra concepts and meets NCTM standards. Mathematics topics have series of lessons and real world examples that accompany them. Equations and their relationship to word problems are emphasized throughout the program.
The major topics covered in Algebra World are: Expressions, Variables, Algebra Notation, Pattern Recognition, Integers, One Variable Equations, Two Step Equations, Ratio, Proportion and Percent, and Geometry. Each topic has a series of detailed lessons designed to teach key mathematical concepts. The lessons are followed by challenges in three skill levels that assess understanding of the subject and mathematical reasoning ability.
MathRealm's research showed that students are not as responsive to long narrations in software as they are to interactive visuals and audio effects that draw them into the program as active learners, rather than passive listeners.
Hands-on virtual manipulatives with limited text reading and immediate visual feedback will capture your students' attention and help them understand concepts, as well as develop logical reasoning. |
Thinking and Quantitative Reasoning
Designed for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need ...Show synopsisDesigned for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need to learn in order to be better quantitative thinkers and decision-makers. The author team's approach emphasizes collaborative learning and critical thinking while presenting problem solving in purposeful and meaningful contexts. While this text is more concise than the author team's Mathematical Excursions ((c) 2007), it contains many of the same features and learning techniques, such as the proven Aufmann Interactive Method. An extensive technology package provides instructors and students with a comprehensive set of support toolHide synopsis80618777389-5777372Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780618777372Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780618777389-2 |
DVD Review: The Basic Math Word Problem Tutor and The Algebra 2 Tutor
Math has never been a particularly strong suit of mine. Everything started going downhill after long division, and I was well lost by the time multiplying and dividing fractions rolled around, let alone algebra. It was with some fear and trembling that I found The Algebra 2 Tutor - 6 Hour Video Course from MathTutorDVD in the mail. The Basic Math Word Problem Tutor - 8 Hour Video Course I felt confident in my ability to conquer, but the algebra — it scared me. It wasn't even Algebra 1, but an advanced level!
Thankfully instructor/owner Jason Gibson's highly visual, common sense approach to math made algebra seem within even my limited grasp. In each video course Gibson breaks down mathematical concepts by dividing and conquering. Each math topic, whether it be algebra, word problems or his other DVDs on calculus, physics, etc. divides the topic into sub-topics, each of which is worked through in an ascending level of complexity through abundant problems drawn out on a white board. Avoiding lengthy lectures, Gibson gets down to basics and explores the necessary connections while working out problems at the board. In fact, most of what you'll see is the back of his head; he turns to instruct and give detail, but most of his explanations are interwoven with real problems.
His thorough breakdown of concepts is best demonstrated by sharing the outline of the courses |
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Reviewed by a reader
a hefty price on a teacher's salary. But few books on your desk willbecome so dog-eared.
Reviewed by a reader
This book has been a Godsend for me and many other teachers who are more interested in "teaching" than in following the latest fad. Let us hope that more teachers read it.
Reviewed by [email protected] (Nathan Crow)
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Preparing for Algebra: By Building the Concepts, Preliminary Edition
Editorial review
An introductory textbook for students at any age who lack a basic understanding of numbers and elementary arithmetic. Uses hand-on materials and exercises to learn pencil-and-paper arithmetic and certain algebraic manipulation skills, but |
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