First, you can't go back to your twenties and you shouldn't try. If you're bright, motivated and take ownership of your own learning, the faculty will love interacting with you. Physics, in comparison, is relatively constrained. Being in your thirties has little to do with learning. Like you, I am working in business software development, and I simply cannot attend a brick and mortar university because I do not have the time, or would have to accept the severe cut-back in income resulting from a reduction of my work hours. Sometimes, I need some of the groundwork to be laid down for me - at least, when it comes to things like maths and scientific ideas. Personally I struggle to learning things. 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. For more than that, you will have to start to specialize. So if there is any distance education option that suits your needs, it might greatly augment your self-directed learning. 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. Physics: Halliday and Resnik[4] is one of my favorites. The third pass is the first couple years of graduate school, and goes through the same subjects again in more depth. It’s at much too advanced a point of view to help you solve nuts and bolts physics exercises, which is what you must do. Technology is everywhere around us, and you need mathematics to master it! No labs this time. Quantum field theory for those going that direction. I've taken courses on Algebraic Number Theory, Lie Groups and Lie Algebras, and Measure Theory. Take refresher classes at community college. You might also look at books like God Created the Integers by Hawking, The Calculus Gallery by William Dunham that curate interesting and historically important results, where original works are often reproduced. Take a look at The older ones are FILLED with information with graphics here and there but it's mostly text. Montessori math is full of hands-on learning, by using concrete materials to learn mathematical concepts. My car repo is here: but a much easier project is Studies [1] have shown that warm temperatures severely diminish our performance on complex mental tasks. Anticipate having to read three or four different treatments of the same thing in order to get a real understanding. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10], [11], [12], [13], [14], [15] 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. 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. I almost never went to class in university (Waterloo Engineering) and this is how I did it. I use the Skim PDF reader so that it autorefreshes on file save, and set up a Makefile and make it so the PDF is recompiled on every file save. When you return in a few days/weeks, things will almost certainly be clearer. When I was a teenager, I had great recall for things I've learned only once or twice. Your "users" inevitably catch a lot of them at "runtime". I would like to get into a field that requires a stronger grasp of mathematics but also has a need for programming and computation (maybe machine learning or computational biology). Linear algebra, done at least twice and more likely several times. Halliday & Resnick (or one of its later updates from Crane) is a better bet in this regard. A side quest is available if you want to get into fluid dynamics. 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. If you find yourself thinking hours about seemingly simple problems, do not despair! Get some good advice on how to hold the violin and the bow; look at pictures of Heifetz, etc. Anticipate pressing on anyway. If you're writing proofs, why not do it formally? Lucky for me, I come from the German-speaking realm, where there is a distance learning university that offers a solid BSc programme in mathematics at roughly one eighth of what someone would pay for tuition in the UK. 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. Youtube, EDX , and Khan academy are all good resources. I had a similar epiphany as yours in my early thirties and this is what I did and it helped me greatly. 30+ Montessori Math Activities for Preschool and Kindergarten., Jokes aside, try or Plus, you can get really, REALLY good deals on used college textbooks (some of which are still in pristine - as in never even been opened - condition). A problem you can solve easily and quickly yields zero knowledge. One of the students has an introduction into what you can expect. (Along with whomever you show it to -- I did a lot of college homework using LaTeX. As for learning a 'trade' in your 30s, I don't know, especially if you're not handy. While true, a skill that is not emphasized enough is learning (by heart) and understanding definitions. Often times what happens is that highly technical topics such as those you mentioned look attractive from the outside but get painfully dry, boring and difficult once you pick up a text book and start studying from it. Next with a constrained optimization you will see the reformulation of an objective function and constraints into one functional by using new variables (Lagrange "multipliers") so that when the gradient of this new functional is zero, not only are you somewhere in the intersection of the constraints and the objective, but you also meet the first order conditions necessary for an extremum to be found. Graph theory and discrete math I did with MIT EdX courses. For me it was graphics at first... and today it's formal proofs and type theory. For best results you need to make a nice LaTeX set up. I designed it with adults revisiting mathematics and wanting to move on to higher mathematics in mind. But there is a certain extent to which they like to work by building things on a frictionless ice world, and get uncomfortable if asked to build something on the rough ground of the real world. They knew why they were there, knew that the material was worth learning, and asked lots of questions. You will be amazed at how fast they will learn to memorize and be able to recall the answers quickly. -- J.J. Sakurai, (Incidentally, I tried reading Sakurai's Modern Quantum Mechanics on my own once and was immediately curb stomped. It's easier to offer suggestions from there. Disregard my email if it was meant only for the OP. If it's a 3d game, you'll have to do your matrices, dot products, trigonometry, etc. My advice would be find a cheap university nearby and start enrolling in courses. Warning. I would dearly, dearly love to find a tool that can assess what I know, tell me what to learn next, test me on the topic BUT continues to do so as I progress, making use of spaced repetition and interleaving. Even if it's simply a love of mathematics itself. That's how it worked for me. 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. I finished most of Apostol before starting it I am not sure about OP's reasoning, but I personally find it a bit 'motivating' to study in a slightly not-so-comfortable environment. not lined) paper. Maybe you could find a buddy to work with, like people do with the gym or whatever to shame each other into staying on task. For physics, I don't know what your background is. People who try to understand math by reading alone (or by watching videos) tend to fail in real life -- they tend to be able to recite definitions but their ability to execute on their knowledge is weak. What’s more, the headlines about the massive sums millennials will need to amass to retire — $1.8 million to $2.5 million, according to one USA Today article 1 — might seem so daunting that you don’t see the point in trying. It is a way of developing 'muscle memory'. Should you go back to college in your 20s or 30s if you’re not satisfied with your life? And anyway, it is just plain fun: what other subject is about solving puzzles? This is a skill. 21- … Even get a calculator to avoid this. 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. With Zoom you can meet online and organize meetings where students and teachers meet face to face! You want personal sessions with a mathematics professor to help plan your curriculum and direct your learning! I've met very few PhD mathematicians who are even as close to as good at applying appropriate mathematics to problems then someone with a PhD in physics who consider themselves >50% theorist. When you can throw away all the books (the knowledges are all online anyway), you are learned. These videos are frankly better explanation of college-level math concepts than most college classes. Start in the key of A major and then branch out to E major and D major. My learning actually accelerated in my 30s because knowledge pays compound interest -- the more knowledge you have, the faster it is to acquire new knowledge. Then all you can think about is the heat, and you are so lost it cannot be returned. (5) Be prepared that the timescales in physics are long. 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. You sit down in a warm or hot room, and solve them. It is never too late to learn math and physics! write down the gap in your abilities you'd like to fill so you can track your progress. Then when you are struggling working through a problem you get so frustrated. write a blog post about it) to someone else. Bounce between them to un-stick. Download the Zoom app and create a profile. 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. And it can be hard to save money when you’re just starting your career since an entry-level salary plus student loan debt mean your cash flow is limited. Start with simple books to warm up those grey cells. By Pamela Druckerman. Some offer discrete math, not many offer graph theory, and you probably won't get much astro (but you can get astronomy) or string theory from them. Seems odd to discourage someone from expanding their understanding of the world. You need to do exercises. But this is the lower college level (3 courses: Classical, E&M, Rel/quant). ), teaching webpages could be a helpful guide. Rather thought provoking. Here are five reasons you should learn to code regardless of your age: It’s Like Reading. However, you will not. This is easy to do and inexpensive if you pick up some Dover math books, but I've been making heavy use of the local academic library. As for books, I like Stewart's Calculus, Lay's Linear Algebra, and Hammack's Book of Proof. For this purpose, well regarded popular science books should be your first choice. The math books you want to read are not in high demand at the library! For discrete maths, books like The Algorithm Design by Skiena and Algorithm Design by Kleinberg and Tardos should serve you well. Commonly given to physics students as their source on Hilbert space for quantum mechanics. You have to know if this is the case. Going at your own pace, you're not going to go through as much stuff as quickly, but you will actually _really_ learn it. .... read this inspirational article! What works for me is purchasing and reading textbooks (look for online college syllabuses for good ones). I picked up various books and different learning strategies along the years but couldn't move forward cause I could not see any practical use for what I was trying to learn. Course Outline. Get Ivan Galamian's book on violin. Lesson planning. I feel like I'm getting tired of being a software engineer (defense contractor) at a small company and looking for something higher level. The first order necessary condition for an extreme point is that the derivative of the function be zero. There are people everywhere who will be much better than you at this stuff, and in some ways it's extremely motivating if you feel like with some hard work you can surpass some of your teachers, and it's extremely motivating when the best teachers recognize you as having more potential than the average student. 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. Reading, Massachusetts, but outside of a fulltime education context it requires organization and sacrifice. I'm hoping to go back to uni next year when I'll be 29. 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