Think of what you're going to do with that knowledge. I do recommend getting the book if you decide to use it but that's just a personal preference. (learning rate != thinking rate / creation rate!!) Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. Hmm, I didn't say that very well, but there is much intuition to be found in optimization problems. Keep up a lifetime of learning! 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. You can get three or four and see if any of them are good enough to warrant a purchase later on, because you probably won't get through them in a month or whatever. I actually had to look into this recently. However, you will not. Start sometime after calc 2 (series problems). Learn some scales and some simple pieces, get some lessons, and continue. Initially, you might feel like you do not make a lot of progress, but the more you know, the quicker it will get. Another thing to ask yourself is, what will I gain from this? I just took a Discrete Math class and I am taking a calc refresher in the Fall. They are in my home library and I try to flip through some of them once a year. 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). So this is my number one suggestion. So if there is any distance education option that suits your needs, it might greatly augment your self-directed learning. However I realized a couple of years ago that becoming fluent in LaTeX was a better option for me. Play with the ideas you are learning. 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. The book covered some Calc 3 too so continued being useful. To apply to have him as your director of studies, fill out the form at the bottom of https://edeeu.education/alexander-coward. With Zoom you can meet online and organize meetings where students and teachers meet face to face! This inspired me to get some more textbooks and try to go through them. Grade 11 Pre-Calculus Mathematics (30S) ... You can discuss your math learning and progress. Printing Instructions: The charts above are available for viewing and printing as 11" x 17". 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. Math probably requires more time to grind through hard problems. Another standard. But it is good to get academic contacts who can give you direction. Missing Assignments Unit 1 - Interest and Credit. 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. 2b) Have solutions to those problems. 30+ Montessori Math Activities for Preschool and Kindergarten. This is an 11 session 7-10pm math graduate level math course. Start in the key of A major and then branch out to E major and D major. 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. Before going to Khan Academy, I started reading a rigorous math textbook, but my motivation didn't last long. The downside of course is that computers are very capable distraction vehicles, you need a bit of discipline to sit at one and study / do this sort of work at the same time for prolonged periods. I used to do all my work (solutions to problems, notes) using pen and (plain! You sit down in a warm or hot room, and solve them. Not all topics are equally important. A trainable skill. Physics: Halliday and Resnik[4] is one of my favorites. Start with a really easy book that starts with just Gauss elimination for systems of linear equations -- actually a huge fraction of the whole subject builds on just that, and that is close to dirt simple once you see it. 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. Learning new/different things is just a small step further beyond learning old things with new/different assistants. I think both our roads are eventually going to lead us to differential geometry, and the only thing I know about that is that there appears to be a very good book on Amazon (Tapp, Differential Geometry of Curves and Surfaces), and that you may want to avoid older books that use the older notation for it. You might find my site interesting. Defs agree with op. Because that requires learning a formal proof-verification language. (5) Be prepared that the timescales in physics are long. It's a lot of fun! Mathematics is infinitely large and it's too easy to get lost. Is publishing a book the same thing as writing code? For more than that, you will have to start to specialize. (Second order sufficiency conditions (SOSC) are needed to show that you aren't instead at an inflection point but we are moving fast and breaking things). - on Saturday, I wanted to learn how to write a Kubernetes configuration file from scratch, so I decided I'd deploy a static web page, - for the static web page, I decided it should return pictures of teapots w/ a 418 status code, and initially tried to return responses using netcat, which I got working on my local machine, but not in a container, - instead of using netcat, I decided that nginx is for people that don't like over-engineering their weekend hack projects, so clearly I needed to write my own web server and hacked out a janky Elixir server that serves up a poop emoji teapot image [1][2], - then I started working on an overly over-engineered HTTP server, which so far only has date headers [3], - then last night I randomly wondered how HTTP 2 works, looked for the RFC [4], - then I remembered working on the date header, and I wondered how headers work in HTTP2, and I learned they use Huffman encoding, and so my next side tangent is to read up on Huffman encoding and add HTTP 2 header support to my HTTP server! It will be helpful to revisit later when you begin to forget older topics and will help you to create a system for keeping your knowledge fresh as you progress to more advanced topics. When you are still in a school environment, there's an environment that for doing problems for problem's sake. Lesson planning. Their website allows you to work through practice problems too, which I think is the most important thing. I might not have made an effort till now, but I hopefully have another 40 years to flex my muscles. Anticipate that watching youtube is not a substitute. Like this sketch about Celsius and Fahrenheit: Sketches are also very helpful when doing questions. > 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)? You can get to most of these peoples' levels by just doing an hour or two a day for a few years. 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. All the learning occurs on the problems you struggle with. Same here. Deep diving into math and physics just for the sake of learning etc seems to be cargo-culting. For a midway academic treatment, you can read Feynman's lecture on Physics volumes. Take a look at brilliant.org. The third pass is the first couple years of graduate school, and goes through the same subjects again in more depth. It's not bad in isolation - soon you will be computing recusion relations and bessel functions. I agree with this suggestion. Hi, I calculated it basing it on the super-memo algorithm. One of the students has an introduction into what you can expect. 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. My college was freezing cold, and my search would be for a room where you didn't need to wear 2 sweaters to be comfortable. Remember, learning math is like training for a track meet - you can't cram the night before the big event! One chapter even implements a Tensorflow-like neural network. Most of the time it is not. Take him up on his offer. Quantum field theory for those going that direction. And think "If only it weren't so damn hot in here." And anyway, it is just plain fun: what other subject is about solving puzzles? But you aren’t likely to learn key fundamentals. It has chapters with names such as calculus on manifolds, hypercomplex numbers, the entangled quantum world, gravity's role in quantum state reduction etc which sound pretty deep and complex for a recreational learner. I went back to school in my late 20s for this. Amazingly flexible: Learning to read in your 30s profoundly transforms the brain Date: May 24, 2017 Source: Max Planck Institute for Psycholinguistics I often see people here on HN saying classroom lectures are more important than homework. Studies [1] have shown that warm temperatures severely diminish our performance on complex mental tasks. You probably don't remember much from high school, and most low-div calculus problems are some simple calculus rules combined with a bunch of high school algebra/arithmetic manipulation that if you don't have it all ready at your fingertips, you _will_struggle. 1) Find a good source of information --- typically, this is either very good lectures (like on youtube), a good textbook, or good lecture notes. (3) Most people around me have never read any physics textbook cover to cover. Edit: the book gives you the fundamentals though on which you work. Have you considered auditing a course at a community college? You're programming a person instead of a computer but that's the only difference. Otherwise QM is just linear algebra over complex numbers together with complex amplitudes from circuits/naval architecture/ spring mass dampers in the frequency domain. When you return in a few days/weeks, things will almost certainly be clearer. Do them with pen and paper, not just in your head. It's not so much the provision of learning materials that I'm frustrated with but the process of testing and retaining what I learn. You need to learn about the topics first in order to appreciate whatever you will encounter later. This is a bit of an evergreen so just searching HN will net you piles of threads with lots of advice and references to resources. The first pass is one or two years long and is roughly what's in Halliday and Resnick or Tipler's physics books: Newtonian mechanics, some wave motion, some thermodynamics and statistical mechanics, electromagnetism, and a little "modern physics" (special relativity and a bit of quantum theory). (Along with whomever you show it to -- I did a lot of college homework using LaTeX. I think that doing just that can be boring and demotivating. In that case you're in luck. Use Zoom for online teaching and learning. If everyone studying linear algebra in school watched his videos before taking the course they would have a much easier time learning it. This will serve you well in physics. Knowledge is power no matter where it comes from - a textbook, the internet, a master or simply studying the natural world. Do not proceed to Quantum mechanics without having these tools at your disposal. Don't get stuck: Physics people commonly do math in really obscure ways; mostly they are thinking intuitively; generally you can just set aside after a first reading what they write, lean back, think a little about what they likely really do mean, derive a little, and THEN actually understand. My professor for dynamics and mechanics of materials required homework to include diagrams of the problem, neatly drawn, on unlined paper. The recent ones are less "textbook." It's not just linear algebra, 3blue1brown also has an entire series on undergraduate calculus, and series on Statistics, Linear Algebra II and Group Theory are in the works. Then all you can think about is the heat, and you are so lost it cannot be returned. Get a used copy -- I did. Exactly, your mileage may vary, but my mindset has to be completely free from distractions to be productive. This is a skill. https://algebra.sympathyforthemachine.com, https://edeeu.education/undergraduate-mathematics-curriculum. Do it! Textbooks have generally gotten less information dense over time. There's a lot to be said for using computer tools. Then switch to a different text on the same subject. (1.5 courses) Req: Diff Eq, Calc 3, Electrodynamics: Griffiths [6]. you will have to understand analysis. I found 50th anniversary hard-bound edition at the Los Alamos book store. These books worked for me. This self contained 1000+ page monster builds up to advanced physics in a methodical fashion from scratch. Don’t do this. Think of parameterizing a surface instead of a curve and see how a tangent bundle describes a whole new vector space - one vector space for every point in the manifold. 21- … It took me a year to slowly absorb the entire book of Statistics [0] including solving all exercises. If you can't prove it, you don't understand it. Here's where you can make that happen: I did the same as you, but in my 40’s. The recent ones are very graphical so I would assume it has less total information. (plus being in the academic environment helps to get a better sense of the broader landscape of material). There are exceptions and people who do significant work even later, but that's more unlikely. Each chapter has an application (a working Python implementation) of the ideas in the chapter. I know I don't have the fortitude to sit and persevere with a text book for hours on end. Do research? 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). A lot of learning in physics comprises paring down your misconceptions until the correct methodology, often surprisingly simple, appears. 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). Steven Hawkins was still trying to learn about physics before his death. 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. How do I get started? 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. I’ll emphasize the point by stating it’s converse. https://www.amazon.com/Renormalization-Methods-William-David... https://www.youtube.com/watch?v=foRPKAKZWx8. 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. review your math lingo here. I did all the calculus and linear algebra classes on offer. Learning often happens in non-linear ways. I think what stands out about those videos is that people who have no prior higher math education still get a shadow of intuition of what's actually going on, and people who already 'grokked' the concepts still got an alternative, simpler view on those concepts, resulting in at least a view 'a-ha!' First, define “advanced mathematics”: calculus? https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ... https://brilliant.org/courses/#math-advanced, https://brilliant.org/courses/calculus-done-right/, https://brilliant.org/courses/linear-algebra/, https://www.youtube.com/watch?v=iJfw6lDlTuA, https://lamport.azurewebsites.net/pubs/proof.pdf. You won't find a better book than this for E&M. Montessori math is full of hands-on learning, by using concrete materials to learn mathematical concepts. Actually, it's not "modern" and instead is close to what you will see and need in applications in physics and engineering. How patient are you when doing problems? moments for almost everyone. Oh and studying complex singular integrals in isolation is good too. I am mostly on my own, so I guess if I were studying entirely independently, I would not be doing much different. But you will have a much better intuition for linear algebra, and those videos will either make sense, or be trivially obvious to you. The one subject I have been having issues is with Math, but that is due to lack of effort and stretching myself too thin. Best wishes to you. Mathematics is also useful in everyday life: Mathematics also improves our mental ability as it teaches us logical ways of thinking. 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. https://www.amazon.com/GAUGE-FIELDS-KNOTS-GRAVITY-Everything... https://smile.amazon.com/Calculus-Early-Transcendentals-Jame... https://smile.amazon.com/Linear-Algebra-Its-Applications-3rd... https://smile.amazon.com/Differential-Equations-Tools-Printe... https://smile.amazon.com/Fundamentals-Physics-David-Halliday... https://smile.amazon.com/Classical-Dynamics-Particles-System... https://smile.amazon.com/Introduction-Electrodynamics-David-... https://smile.amazon.com/Introduction-Quantum-Mechanics-Davi... https://smile.amazon.com/Introduction-Modern-Astrophysics-Br... https://smile.amazon.com/Introduction-Elementary-Particles-D... https://www.youtube.com/channel/UC_SvYP0k05UKiJ_2ndB02IA, https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A, https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA, https://www.youtube.com/user/standupmaths, https://www.youtube.com/channel/UC6107grRI4m0o2-emgoDnAA. It is never too late to learn math and physics! It is definitely hard, but I'm enjoying it. 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. For motivation, if there is a nearby university, start attending the relevant departments' colloquia. Pick a topic and start from there! The second is to start with a handful of problems that interest you and go pick up stuff piecemeal on the way to solving those. This is a standard rookie mistake, and the reason why so many American kids are weaker at math compared to their Asian counterparts. Linear Algebra (text book link: https://www.amazon.com/exec/obidos/ASIN/0980232716/ref=as_at...) There are tons of free resources out there for learning QFT. If you need to pass an exam, find past exams and do them*. 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. "The reader who has read the book but cannot do the exercises has learned nothing." You can get most of this through a CC. I am in my thirties too (mid-thirties now) and recently took up maths again. Don't just follow the steps you are shown, try your own ideas! 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. The audio recordings are out there, though video should have been made of these. How I learned to code in my 30s. Here ends the undergraduate curriculum. Find a small group of people doing the same or similar learning, so you can discuss the different problems each of you will have. Learn it from "advanced differential equations materials". It's all about doing it like we did in high school. To be inspired/get prepared for things to come get John Baez's Gauge-Knots_Gravity book: https://www.amazon.com/GAUGE-FIELDS-KNOTS-GRAVITY-Everything... and maybe Penrose's Road to Reality - which is like cosmology if the universe consisted of all the math and physics needed to understand all this math and physics. Answering questions helps you organize the ideas in your mind*. 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. It is important to really pause the videos at some points and do the "exercises". [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)? It was a tough textbook to learn from but I feel like I learned a ton. 2) Do problems. And of course, there are some who find it hard because they have reached the limits of their cognitive abilities (un-PC as it sounds, this is a real thing). 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.) Check out https://edeeu.education/. Personally I struggle to learning things. Oh man... have you got some fun in store here. That is a fantastic place to start. When it comes to friends, it really is about quality over quantity. 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(?). What good is this intuition? but outside of a fulltime education context it requires organization and sacrifice. There are two approaches that work well. .... read this inspirational article! Applied 30S Course Outline: File Size: 135 kb: File Type: pdf: Someone who personally understands your drive and work ethic will have a better ability to give you suggestions. 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! IMO the best book you can drill questions from is Boas' Mathematical Methods in the Physical Sciences. E.g. Also, going back to uni at your age is a great thing in that you're mature and so ready to learn because you've felt that social pressure to crack on with things in … Start to make the connections with convexity and the normal equations in multi-variate statistics, principle components, factor analysis, data compression, etc. Is it taught in the Coursera course you mentioned? This is a long-term project, so I'd recommend by starting a bit with "learning about learning". Read it, think about it, read again, write it down or sketch it out, and then use it (by answering questions), that all helps to get the ideas into your mind. Then notice that 32 is added ... why is that? I'm taking you at your word and assuming you truly want to reach the cutting edge of knowledge and learn things like QFT, Gauge Theory, String Theory, etc. :). See the website for how that works. Anyone who tells you can "learn" math and pyhsics by just watching videos is lying to you. Have pride in your work, even if nobody else will see it. also, they will teach you the necessary abstraction - the first thing standing in my way of a degree in physics was my intuition and need to picture stuff. Most people find it hard to learn in their 30s because they lack the energy, environment (+kids, +spouse, etc.) So is LaTeX recommend mathematical Circles: full of hands-on learning, the videos some! Is donkeycar.com a side quest is available if you have no idea why would! 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