What's interesting? 2b) Have solutions to those problems. Doing the same thing with math, physics, engineering, etc will result in the same increase in talent. What actually interests you? (plus being in the academic environment helps to get a better sense of the broader landscape of material). Work through a famous text of freshman physics and then one or more of the relatively elementary books on E&M and Maxwell's equations. Good speakers and even non-physicists can follow the whole talk regardless of subject matter. Took me months to get though chapter 1 :D, but gave me through understanding of how to think about maths and how to prove stuff and that proof are the real fun of math. I can't stress enough that you should watch him. Commonly given to physics students as their source on Hilbert space for quantum mechanics. And anyway, it is just plain fun: what other subject is about solving puzzles? What good is this intuition? He has a sequence on calculus and linear algebra and both of them are worth watching and thinking about before going through a book. Yang Mills... internal symmetry... ok I'd love to talk about how these are new expressions of ideas we've seen before but at some point up there we've passed my pay grade, I have to beg off until I can learn some more! (3) Most people around me have never read any physics textbook cover to cover. (5) Be prepared that the timescales in physics are long. There are a vast number of interconnected details that have the potential to be wrong and far fewer automated ways to catch any errors. [9] Take after QM. (8) Counterintuitive: If you get completely stuck, move on! That said, Knuth's The Art of Computer Programming 4A Combinatorial Algorithms Part 1 will just blow your mind. I found 50th anniversary hard-bound edition at the Los Alamos book store. (6) You have to 'soak in' physics. E.g. write a blog post about it) to someone else. Expectations. Calculus of variations: Nail down cold how to derive the Euler Lagrange Equations for a functional. But this is the lower college level (3 courses: Classical, E&M, Rel/quant). Same here. > A lot of the old methods of learning actually work and so the advice is sound to strictly adhere to them when you're having struggles. I'm pleased if I can make it through a chapter at all on any time scale, and I think having low expectations is probably healthy. See the website for how that works. thank you, fiona! Susskind is an eminence - he was Feynman's buddy back in the day. Saving paper is a false economy when it comes to math. Yes those videos have some nice visuals but the material is just scratching the surface. BlackPenRedPen[10]: Fantastic teacher. You could go to the library and check out different math books! It's okay but I have yet to derive more utility from it than from various field theory books. So try and take notes while reading. It is never too late to learn math and physics! Is this offer just for the OP, or for everyone? 3. ", That said, if I had it to do over again, for the money I spent, I wonder if hiring a graduate students/postdocs or even professors as tutors would have been better. To me it is beyond question that distance education is the right way for me to do this. Reading, Massachusetts, I've had the same thoughts about (re-)learning some math. Soon it will be time to start thinking about field theory. For people like me (and I'm not suggesting that you are, but your circumstances sound similar to mine), something with more of a safety net may be more realistic. I would suggest getting text books with loads of homework problems with solutions and actually sit down to work through the problems. I realize I didn't have the need for it and didn't have the right exposure (environment/friends) that would have inculcated in me these things. If you can afford it, getting a physics grad student to discuss problems that stumped you every now and then might also have quite good ROI, talking to physicists might also help convey some of the physics mindset(?). Meanwhile you study calculus of a single variable, multivariable and vector calculus, and a little bit of ordinary differential equations, and do a year of laboratories. Feel free to contact your tutor/marker by phone or email at anytime during this course. Is publishing a book the same thing as writing code? Use the Feynman method (learn by teaching). It helps you develop muscle memory which in turn gives you confidence to move to the next level. This is a long-term project, so I'd recommend by starting a bit with "learning about learning". But at thirty, you have the luxury of not worry about midterms and finals and you probably can afford multiple books. Then switch to a different text on the same subject. There, relax any desire for really careful proofs; really careful proofs with high generality are too hard, and the generality is nearly never even relevant in applications so far. Look at images of violinists and see what rests they are using. I'm writing a book called "A Programmer's Introduction to Mathematics". Oh man... have you got some fun in store here. Remember that when you get to (deterministic) optimization and a gradient needs to be zero. For this purpose, well regarded popular science books should be your first choice. Anticipate that some of it you will never understand. I used E. Nearing, student of Artin at Princeton. I did all the calculus and linear algebra classes on offer. Their discrete course is pretty nice and I found it very easy to follow along with. I'm quite excited about. Even if it's simply a love of mathematics itself. "The reader who has read the book but cannot do the exercises has learned nothing." It is more important to know the ideas than to remember the formulas. Get some books, and read them. It’s right there. The Feynman Lectures on Physics. It's also a bigger time investment than people usually think of upfront, but pays dividends later on as the material builds-up like a cathedral of knowledge. These videos are posted any time linear algebra is mentioned. I mean, it gives me sense that I am actually determined and am working hard. Approach 1. New research shows that when adults learns to read for the first time, the changes that occur in their brain are not limited to the outer layer of the brain, the cortex, but extends to deep brain structures in the thalamus and the brainstem. Think very carefully where you want to spend your motivation and discipline. It also reminds me of my college days when even finding an air-conditioned room anywhere was just not possible. These videos are frankly better explanation of college-level math concepts than most college classes. To quickly review a broad range of math up until 1st or 2nd year of university, I really recommend Khan Academy. If you are relearning you can skip to below (though you might struggle a little more) Req: Taken or taking Calc 1 (differentiation and integration required later), Classical Dynamics: Thornton[5] You will learn A LOT about constraint, optimization, and simple harmonic motion (necessary!!). Mostly in order of level (math then physics), Calculus: Stewart's Calculus[1] (this is pretty much the standard) This has calc 1,2, and 3 (multi variable). You won't find a better book than this for E&M. This is a point made multiple times in those very videos. Often I would find that each problem would take three sheets of paper (I'm a horrible draftsman), but I am horribly glad after the fact that I invested all that time. Also see Griffeths E&M book for a great explanation of Fourier's trick and separation of variables in the chapter on special techniques... At least in the 1999 Third edition. ML will touch on linear algebra, calculus, probabilities/statistics, etc. (1.5 courses) Req: Diff Eq, Calc 3, Quantum Mechanics: Griffiths [7] (He's the man, seriously) (1.5 courses) Req: Diff Eq, Calc 3 (lin algebra is nice, same with a tad of group theory), Astrophysics: BOB [8] Lovingly called the "Big Orange Book" you will see this on every astrophysicists' shelves. Seems odd to discourage someone from expanding their understanding of the world. I'm glad we have it. Get the information ... read, listen to a teacher, watch a video. I study for one hour every day before work. Then, of course, go for P. Halmos, Finite Dimensional Vector Spaces, grand stuff, written as an introduction to Hilbert space theory at the knee of von Neumann. not lined) paper. Before going to Khan Academy, I started reading a rigorous math textbook, but my motivation didn't last long. Mathematics is beautiful. I went back to school in my late 20s for this. Like this sketch about Celsius and Fahrenheit: Sketches are also very helpful when doing questions. Pick a related topic that makes use of what you want to learn, and learn what you want to learn as side effect from practice in the related topic. The difference for me is that I'm fairly certain that I'm one of the least accomplished people responding to your post. Pick a topic and start from there! I'm 30 and trying to relearn the math courses I did in college (Computer Science degree) and more. 30+ Montessori Math Activities for Preschool and Kindergarten. There is no substitute for actually doing lots of problems. I used to see it as a real problem that I was learning math outside class, but more and more I see it as a benefit, because you can pick up the stuff you want at the resolution you want and benefit from the best books rather than whatever the publishers are bribing professors to use. I'm also accepting students. The textbooks are often listed in the course content, and we all know where we can find the appropriate pdf versions. If you know how things work, you can always re-create the formulas when you need them. That's how I did it. This will serve you well in physics. I've tried more 'sophisticated' maths learning solutions that claim to account for learners' knowledge and weaknesses, but there are various shortfalls with them and none is aimed at learners older than schoolchildren. A mathematical methods course only if a student needs more help. Pulling out the ethernet cable can help but may not be sufficient depending on one's level of discipline and access to offline distractions. You need to do exercises. I didn't realize this was unusual and thought I got very bad at learning. E.g. But, the intuition provided in those videos is absolutely excellent. If you want any chance of understanding the mathematical tools used in theoretical physics (operators, Hilbert spaces, Fourier decompositions to get solutions to differential equations etc.) You remember how to find an extremum of a function from Cal 1? working a lot with differential geometry now, I've got some of that visualization back but with linear algebra even and quantum mechanics it can stand in your way. Start with some liberal-arts introduction to a particular topic of interest and delve in. Hmm, I didn't say that very well, but there is much intuition to be found in optimization problems. write down the gap in your abilities you'd like to fill so you can track your progress. Anticipate that watching youtube is not a substitute. I'm doing my OU Masters in Maths now, in my 40s. You guessed it! Those are good videos, and I also endorse them. What I realized is that for many topics what I really crave is a deep understanding as an educated person as opposed to deep academic knowledge. For calculus of several variables and vector analysis, I strongly recommend, Tom M.\ Apostol, It's not bad in isolation - soon you will be computing recusion relations and bessel functions. Deep diving into math and physics just for the sake of learning etc seems to be cargo-culting. At the end of the day, if you read the problems and then the solution right away, that's much closer to reading the textbook itself instead of the more rigorous learning one goes through when trying things themselves. When you can throw away all the books (the knowledges are all online anyway), you are learned. Cloud shapes? My professor for dynamics and mechanics of materials required homework to include diagrams of the problem, neatly drawn, on unlined paper. I might not have made an effort till now, but I hopefully have another 40 years to flex my muscles. Ha no. https://www.amazon.com/Statistics-4th-David-Freedman/dp/0393... https://www.bauer.uh.edu/vpatrick/docs/Influence%20of%20Warm... https://www.scientificamerican.com/article/warm-weather-make... https://books.google.com/books/about/Physics.html?id=8MvvAAA... https://jeremykun.com/2016/04/25/book-mailing-list/. Your responses to the questions in the learning activities will help you to practise or review what you have just learned. As an example, look at the explanation of change-of-basis in the linear algebra I series. It took me a year to slowly absorb the entire book of Statistics [0] including solving all exercises. In many of his videos, he explains topics from the perspective of a person inventing that topic (such as in his first Calculus video [1]). So then you give up for the day, and really haven't accomplished anything. Started doing some woodworking projects and had to learn some basic geometry and trigonometry to calculate cuts. 18- Learn the art of knowing the wine you want which can only be achieved by testing plenty of it. One thing that I can add, is that the process of neatly recording something really helps cement the process. How do I get started? It took about 3 years of exactly ops method. As a sysadmin, I was always reading all sorts of subjects and pursuing different hobbies that further expanded my knowledge. in high school and undergrad which unfortunately I didn't get a taste of. That retaining bit is important - I can pick up something, give it a go and get it right, but if I don't do it again, I forget what I've learnt. The struggle is where the learning happens. Exactly, your mileage may vary, but my mindset has to be completely free from distractions to be productive. I made a rule to complete one chapter every evening including exercises and sticked to it. Differential Equations: Blanchard Differential equations [3]. Youtube, EDX , brilliant.org and Khan academy are all good resources. Grade 11 Pre-Calculus Mathematics (30S) ... You can discuss your math learning and progress. Feynman explains things like no other. you will have to understand analysis. Pick a handful of problems. Honorable mentions: 3Blue1Brown[11], Numberphile[12], Veritasium[13], StandUpMaths[14], SmarterEveryDay[15]. https://gumroad.com/l/noBSLA. I almost never went to class in university (Waterloo Engineering) and this is how I did it. For physics, I believe you fall in Leonard Susskind's target audience. I see Susskind's theoretical minimum is plugged here. For me this was very valuable. Otherwise it's the same old enterprise software development. Learn it from "advanced differential equations materials". http://www.goodtheorist.science/. In addition to those reasons, the other hugely important one is that my notes are now in git, I can grep them, and they don't add to the pile of objects that must be dealt with when moving to a new home. While I agree with you, and love aj7's post, I'm going to push back slightly on the pen and paper. I had a similar epiphany as yours in my early thirties and this is what I did and it helped me greatly. Technology is everywhere around us, and you need mathematics to master it! I'm a bit wary of some of the suggestions here. If you need to pass an exam, find past exams and do them*. I do not know what options you have in that regard, but if being enrolled in a programme does not seem off-putting to you, it might be worth checking out. Whatâs more, the headlines about the massive sums millennials will need to amass to retire â $1.8 million to $2.5 million, according to one USA Today article 1 â might seem so daunting that you donât see the point in trying. A lot of resources on the awesome github: If you want to be serious about math you should get a feel for what mathematics means to mathematicians. You have to be able to compare the objects that you define and get a feel for how a definition is really a manipulation of a basic intuition. It helps to maintain your motivation if you have a reason, a driving reason, to continue this practice. I forgot to mention that the Feynman lectures on Physics are available online for free: Pick a problem that interests you and involves lots of physics and math. You will also learn about Hamiltonian Systems. Maybe do the material again if want to do quantum gravity at the center of black holes or some such; otherwise, just stay with what Apostol has. My post was mainly adding agreement to yours with more specifics, "you" used is the "generic you". ;). You can get most of this through a CC. Stress learning eigen values/vectors and least squares. Reading Mathematics is different than reading English, Working neatly helps you think more clearly, Investing money (interest rates, profits, etc). don't compare yourself to others, compare yourself to yourself. If you have sloppy handwriting (as I'm sure many of us here do), why not type in something you'll always be able to read later? Differential equations, if you took physics that did not use them, can have a very similar problem, where you just grind through problems for a semester with no motivation.). Hint, Apply the FONC (first order necessary conditions for an extremum) to the functional (now the Action) in question. For me, I did them by taking a class and relying heavily on my textbooks. Start in the key of A major and then branch out to E major and D major. Download the Zoom app and create a profile. That is a fantastic place to start. I can totally see that these are the folks who have high IQs and they can easily learn a new domain in a few months if they were put in one. Montessori math is full of hands-on learning, by using concrete materials to learn mathematical concepts. Learning often happens in non-linear ways. It's easier to offer suggestions from there. For calculus and linear algebra I'd go with Khan Academy, especially since it seems like all you need is a refresher for calculus. This is awesomely overengineered and not-invented-here, and I mean that in the best possible way. Third, read them. (learning rate != thinking rate / creation rate!!) I have been reading several text books as well for practice and reinforcement. This is a skill. 2. Incidentally this is a great way to learn about uses for Green's functions... And if you dive deep, your first look at singular integral equations in field theory. The third pass is the first couple years of graduate school, and goes through the same subjects again in more depth. It's geology; time and pressure. Supplement Susskind's second book with Griffiths intro QM book. Used in Harvard's Math 55. In my case, I found it motivating to take exams because it gives you a bit of skin in the game; forces you to prioritise your study at some point. Grant (the 3Blue1Brown guy) has an uncanny ability to explain difficult concepts and the fundamental intuition behind them. You will likely have questions. The quote you mentioned here " Mathematics is young man's game". They prime you for further, formal exploration of the topic. You find a a college textbook with the answers to the even-numbered problems in the back. For motivation, if there is a nearby university, start attending the relevant departments' colloquia. As another poster said there are courses out there in just about everything, though. [0] If you're working with graphical concepts, why not code them up, or use a drawing program (or hey, a graphing calculator) rather than pulling out a ruler and such (and maybe learning to draw at all if you don't know how)? Giancoli's book doesn't use calculus. I'm in a similar situation myself. Here ends the undergraduate curriculum. Define what "understanding physics" means to you and then figure out how to get to your goal. Anticipate questions taking you six hours to solve, leaving your table and floor strewn with the history of your consciousness. If it's a 3d game, you'll have to do your matrices, dot products, trigonometry, etc. How do I learn math/physics in my late 20s for this purpose, well regarded popular science books should your. If so, the answers to the library bit wary of some of Dr. Wildberger. Tricks that you start with physics and only learn math their whole lives, it 's easy and can expose. 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