Regardless, I'll give my two cents for textbooks anyway. Constraint solving and optimization problems aren't things I self studied, but you can find a variety of resources to help with those based on how you learn best. You can get most of this through a CC. (4) College courses in math and physics have a very definitive order. By thirty you probably get the hint that life is not about solving fake problems, and most of the knowledge you learn at school is useless and pointless. Mathematics is beautiful. For me, I did them by taking a class and relying heavily on my textbooks. 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. 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. It's okay but I have yet to derive more utility from it than from various field theory books. 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). The struggle is where the learning happens. Which WILL have, probably already does, an effect on your learning process). ), teaching webpages could be a helpful guide. You need to do enough problems on a topic that you are no longer struggling, then do 4-6 more. Saving paper is a false economy when it comes to math. See Lanczos "Calculus of Variations" (Dover Books) to sort out your initial questions and learn the smooth little trick with integration by parts. > I follow a bunch of folks on the internet and idolize them for their multifaceted personalities. Edward Purcell’s Berkeley Physics Series Second Volume on Electricity and Magnetism. Here's also Gerard 't Hooft's (Nobel laureate) list of concepts and books to master. Others find it hard to learn because of bad habits and a poor foundation (their semantic tree wasn't that well built up in their youth). Don't be embarrassed to start with a pre-calculus text/course. What You Learn in Your 40s. 12 Life Lessons You Learn In Your 30s. Do you want to be able to say read papers? Then you will pass the exams. 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. Part of it is rote memorization. The mountain peak is the polar decomposition and then singular value decomposition, etc. As a sysadmin, I was always reading all sorts of subjects and pursuing different hobbies that further expanded my knowledge. A great book to start with is Rudin's Principles of mathematical analysis. These videos are posted any time linear algebra is mentioned. In fact most top-paying jobs need good math skills: And Mathematics is not just numbers, it is about patterns, too! While I agree with everything else, I'd have to vehemently disagree with this. Is it taught in the Coursera course you mentioned? 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. This is what I did. ), and join a forum (like the Math is Fun Forum). He has a sequence on calculus and linear algebra and both of them are worth watching and thinking about before going through a book. Repeat about 2x a week for a year, and do independent study with a book on one side of the table and a notepad on the other between classes. 30+ Montessori Math Activities for Preschool and Kindergarten. Susskind is an eminence - he was Feynman's buddy back in the day. As for books, I like Stewart's Calculus, Lay's Linear Algebra, and Hammack's Book of Proof. Gotta keep the brain ticking just like you exercise the body. I still have my copy sitting at home. Started doing some woodworking projects and had to learn some basic geometry and trigonometry to calculate cuts. I believe I'm a little wiser than how I was a few years back, so I'm turning to the community for help. I have the same aims as you, also learning math/physics in my 30s, and it's been a huge boost to move from purely self-directed online learning to having sessions with a math professor and a planned curriculum. Math can be a difficult subject, particularly if you don't have the right skills in place. ), and join a forum (like the Math is Fun Forum). I'm doing my OU Masters in Maths now, in my 40s. http://www.goodtheorist.science/ I believe they may be planning to add some written materials, so maybe in the future, but not currently. When you can throw away all the books (the knowledges are all online anyway), you are learned. Try to invent the math as you go along by covering the explanatory pages with pieces of paper and reading only one line at a time. > 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. They are generally open to all, and will start to get you up to date on what's new across all of math/physics. How patient are you when doing problems? Best example is learning how computers and the internet have changed different jobs and roles. I struggled with the latter part. This is an 11 session 7-10pm math graduate level math course. The Feynman Lectures on Physics. 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. Take refresher classes at community college. It's terrifying that it takes 4 printings before the answers should be considered trustworthy... Publishing a perfect book is difficult on par with writing code. In your 40s, these no longer seem necessary. Here are five reasons you should learn to code regardless of your age: It’s Like Reading. I’ll emphasize the point by stating it’s converse. I follow a bunch of folks on the internet and idolize them for their multifaceted personalities - be it math, programming/problem solving, physics, music etc. It takes time. Drill yourself with exercises rather than trying to understand everything -- math is one of those things where it is easier to learn hands-on by working on problems BEFORE understanding the definitions fully... understanding comes later (the patterns will emerge once your semantic tree is solid). 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.). Another poster already mentioned linear algebra for simple computer graphics. Reading Mathematics is different than reading English, Working neatly helps you think more clearly, Investing money (interest rates, profits, etc). Spend time on math websites (like this one! From my music theory post, learn how to tune a violin. It helps to maintain your motivation if you have a reason, a driving reason, to continue this practice. Do it! You'll likely be able to write good papers into your late 60s, and perhaps 70s. Things will slowly start to click, although of course you don't understand something until you can explain it (i.e. Essential Math 30S Geography 20F Rugby and Dragon Boat Contact Me Formula Booklet. Time and pressure. For exterior algebra of differential forms, try hard enough to be successful ignoring that stuff unless you later insist on high end approaches to differential geometry and relativity theory. This is a standard rookie mistake, and the reason why so many American kids are weaker at math compared to their Asian counterparts. Take him up on his offer. (Along with whomever you show it to -- I did a lot of college homework using LaTeX. For more, get into numerical methods and applications. A common view is that mathematicians prove theorems. https://en.wikipedia.org/wiki/Mathematical_Methods_in_the_Ph... First of all - great idea! I enjoyed reading the No Bullshit Guide to Math and Physics: May I ask what your goal is? And studying mathematics is a good way to improve it! [1] https://smile.amazon.com/Calculus-Early-Transcendentals-Jame... [2] https://smile.amazon.com/Linear-Algebra-Its-Applications-3rd... [3] https://smile.amazon.com/Differential-Equations-Tools-Printe... [4] https://smile.amazon.com/Fundamentals-Physics-David-Halliday... [5] https://smile.amazon.com/Classical-Dynamics-Particles-System... [6] https://smile.amazon.com/Introduction-Electrodynamics-David-... [7] https://smile.amazon.com/Introduction-Quantum-Mechanics-Davi... [8] https://smile.amazon.com/Introduction-Modern-Astrophysics-Br... [9] https://smile.amazon.com/Introduction-Elementary-Particles-D... [10] https://www.youtube.com/channel/UC_SvYP0k05UKiJ_2ndB02IA, [11] https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw, [12]https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A, [13] https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA, [14] https://www.youtube.com/user/standupmaths, [15] https://www.youtube.com/channel/UC6107grRI4m0o2-emgoDnAA. 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? Oh and studying complex singular integrals in isolation is good too. 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. I would suggest getting text books with loads of homework problems with solutions and actually sit down to work through the problems. ML will touch on linear algebra, calculus, probabilities/statistics, etc. In my 20's I used to love picking things up just for the. If you long for maths; it's likely it'll conceptually take you places you won't go without it. The overall idea is to capture. Honestly, despite all the crap universities get, taking an undergraduate degree with a double major in physics and maths is an awesome way to do this. Graph theory and discrete math I did with MIT EdX courses. 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. I don't know why this is downvoted, but the process of writing and working problems on paper, at least for me, helps cement the knowledge. So no, you have no reason to feel you're too old. (4) You need guidance on what is important and what is not. At this point astrophysicists tend to separate off and start learning the knowledge for that domain instead of the second semesters of electromagnetism and quantum mechanics. For physics, I don't know what your background is. Linear algebra, done at least twice and more likely several times. Mathematics is also useful in everyday life: Mathematics also improves our mental ability as it teaches us logical ways of thinking. Determine which facts your child needs to memorize. This was observed in illiterate Indian women who learned how to read and write for six months. Particle Physics: That's right! Instead of ruing missed opportunities, I want to take it under my stride in my thirties to learn math/physics so as to become better at it. This inspired me to get some more textbooks and try to go through them. Learning programming in my 30s I majored in something completely unrelated to CS, but I recently have discovered a severe interest for it and really want to get into a career in programming. Are you planning to study math for your career? [5], TL;DR -- I made a poop joke and turned it into a learning opportunity, [2] https://github.com/amorphid/i_am_a_teapot_container, [3] https://github.com/amorphid/hottpotato-elixir, Leverage what you know against what you don't. Feel free to contact your tutor/marker by phone or email at anytime during this course. One thing that I can add, is that the process of neatly recording something really helps cement the process. You can get to most of these peoples' levels by just doing an hour or two a day for a few years. Exactly, your mileage may vary, but my mindset has to be completely free from distractions to be productive. It offers fairly succinct yet comprehensive overviews of various fields of math. Drilling down the practice will help with theory. BlackPenRedPen[10]: Fantastic teacher. However I realized a couple of years ago that becoming fluent in LaTeX was a better option for me. It's not bad in isolation - soon you will be computing recusion relations and bessel functions. However, it seems clear that he/she has already answered that question, and now they are trying to figure out the "how". But it's desirable that students (or just people learning the same material, later) spend some of their undergraduate time learning new things, right? E.g. I do x2 speed. I would recommend two outstanding textbooks. Then when you are struggling working through a problem you get so frustrated. (6) You have to 'soak in' physics. I've taken courses on Algebraic Number Theory, Lie Groups and Lie Algebras, and Measure Theory. [1] The problem with maths in academia is that it's massively biased toward proofs of mathematics and not use of mathematics. Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. I'll second this idea having survived a Physics BS doing just this. Get Started. So I have sort of always been in the midst of mid level maths and physics, but, as it happens, I lost it all except for some fundamental concepts. Think very carefully where you want to spend your motivation and discipline. PhD mathematicians are wonderfully knowledgeable if you say "tell me about this field of mathematics" and it's a field they know. I am about to defend my PhD in Physics at MIT. Cultivating some relationship that allows you to ask questions is invaluable. You guessed it! Not what sounds fascinating or what seems prestigious. Then switch to a different text on the same subject. 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. I'm looking to (re)learn the following - calculus, linear algebra, constraint solving, optimization problems, graph theory, discrete math and slowly gain knowledge and expertise to appreciate theoretical physics, astrophysics, string theory etc. Supplement Susskind's second book with Griffiths intro QM book. The videos suggest pausing and trying to figure the next bit out yourself and a couple of the videos do end with a suggestion to prove something yourself. I never really studied physics, but I found the first books from the "Feynman lectures on Physics" to be very good. If you learn best from books... there are hundreds of great textbooks. If you have to, solve the conceptual ones. Sounds like they are good story-tellers along with whatever else they do. I personally went back to school because it was a way of putting pressure on myself. 20- Learn to connect deeper with your spirituality: pray, meditate, have faith. It won’t be enjoyable but being examined on what you learn will provide focus. Nearing was good but had a bit too much, and his appendix on linear programming was curious but otherwise awful -- linear programming can be made dirt simple, mostly just Gauss elimination tweaked a little. Modern graphics has moved so far up the stack nowadays that you probably shouldn't say that you "know 3D graphics" after that exercise, because you'll know 3D graphics circa 1995. Now I'm interested in mechanical machines and electrical machines. The applications range from physics to economics to machine learning and cryptography. Get some books, and read them. What purpose do you have for textbook physics? 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