Rather thought provoking. Remember, learning math is like training for a track meet - you can't cram the night before the big event! ), teaching webpages could be a helpful guide. It's not really about calculus, it's really about Real Analysis, and it's excellent. I think that's just building the idea that it's going to be a painful and uncomfortable process. 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 can recommend anything Jeremy does, sight unseen. But their actual abilities (even memory) haven't actually degraded all that much. Very similar in some ways. Is it taught in the Coursera course you mentioned? ", 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. For modern probability, that is based on the 1900 or so approach to the integral of calculus, the approach due to H. Lebesgue and called measure theory. When I did my PhD in condensed matter physics, depending on the speaker, sometimes it could be 10 minutes into the lecture when it delves into narrow field-specific material I don’t understand (eg, a speaker talking about particle physics or astrophysics). Start in the key of A major and then branch out to E major and D major. I'm glad we have it. The second pass is a semester of classical mechanics covering Lagrangian and Hamiltonian mechanics, a semester of statistical mechanics and thermodynamics, a year of electromagnetism, and a year of quantum mechanics, paired with a year of mathematical methods (linear algebra, special functions, curvilinear coordinates, a little tensor calculus, some linear partial differential equations, and a lot of Fourier analysis) and a year of more advanced laboratories. If you are located in Los Angeles, I would recommend looking into the Michael Miller math class series taught thru UCLA extension. But I disagree entirely on this approach to learning fundamentals of math and physics. Feel free to contact your tutor/marker by phone or email at anytime during this course. think you don't have the "math gene"? Otherwise QM is just linear algebra over complex numbers together with complex amplitudes from circuits/naval architecture/ spring mass dampers in the frequency domain. Montessori math is full of hands-on learning, by using concrete materials to learn mathematical concepts. Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. There are recordings of the lectures on YouTube. Best example is learning how computers and the internet have changed different jobs and roles. https://gumroad.com/l/noBSLA. The recent ones are very graphical so I would assume it has less total information. Persevere and plan carefully. Similar to game programming but without the mathless overhead. Depending on your background, you could just pick up a popular math book to get excited about it, or find a free online textbook at your level and dig in. 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. He has a sequence on calculus and linear algebra and both of them are worth watching and thinking about before going through a book. The founder, Alex Coward, is an ex-Berkeley math professor. And studying mathematics is a good way to improve it! Giancoli's book doesn't use calculus. I would recommend that you start with physics and only learn math on a "just-in-time learning" basis. 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). Make arrangements with your parents to have one hour of computer access per day dedicated to Applied Math 30S remote learning. I have heard great things about the book Gravitation, but I'm totally afraid of it, not ready to go there yet. While I agree with you, and love aj7's post, I'm going to push back slightly on the pen and paper. Seems odd to discourage someone from expanding their understanding of the world. You will also gain a lot of the pre-req's for optimization and constraint solving. For motivation, if there is a nearby university, start attending the relevant departments' colloquia. Determine which facts your child needs to memorize. Your mind is an amazing and unique tool, and you want to use it the best way you know how. Skip nothing. Math is not about reading pages ... it is about building concepts in your mind. There are two approaches that work well. Is publishing a book the same thing as writing code? I'm 30 and trying to relearn the math courses I did in college (Computer Science degree) and more. Their discrete course is pretty nice and I found it very easy to follow along with. 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. First, define “advanced mathematics”: calculus? 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. The library on my uni when I was in Math undergrad did not have AC at the beggining but was the only place where I could do any work, it was extremely difficult and I am sure impacted my progress. 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. Checkout MIT OCW, once you are ready. YouTube is my preferred method of learning. 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. One text (Wangsness E&M maybe) had a great student quote, roughly “I understand the principles but I can’t do the problems.”. Anticipate pressing on anyway. Physics, in comparison, is relatively constrained. You need to do enough problems on a topic that you are no longer struggling, then do 4-6 more. You'll likely be able to write good papers into your late 60s, and perhaps 70s. IMO the best book you can drill questions from is Boas' Mathematical Methods in the Physical Sciences. For the programmers in the house, it would be like claiming you can code python if you’ve never coded before but watched some videos of expert teachers explaining the structure of python programming. 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. Using it is so important! Khan Academy has the same issue and is arguably worse because, so far as I've found, it requires learners to know what they don't know, rather than structures a learning programme where each topic follows sequentially (maybe there is a way to do this but I've found the KA UX to be complicated and confusing). This is a long-term project, so I'd recommend by starting a bit with "learning about learning". As an example, look at the explanation of change-of-basis in the linear algebra I series. Part of it is rote memorization. http://www.goodtheorist.science/. I'm a similar position to you (at least, when it comes to maths). Answering questions helps you organize the ideas in your mind*. It attempts to cover basic algebra in a more formal, proof oriented style. There the crown jewels are the classic limit theorems, that is, when faced with a lot of randomness, can make the randomness go away and also say a lot about it. And not just because it's new, but hopefully because it's better. Do the exercises in the back of each chapter, work through the solutions, and ask around if you still can't figure it out. You can get to most of these peoples' levels by just doing an hour or two a day for a few years. For now, I will focus on doing good work in the industry. 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. Reading, Maths and Learning; Amazingly Flexible: Learning to Read in Your 30s Profoundly Transforms the Brain; When becoming literate neuroplasticity conquers … There's also this free book, no answers though you could stackexchange if really stuck. Just remember that. Also, I should mention, one big lesson learned... Maths build on each other. I was refreshing some of the linear algebra I learned in college recently and his videos gave far more insight into what linear algebra is actually about than I was taught in college. Come Up With Your Own Ways. Pick a book, pick a pace to work through it, and spend a few months going through it. ... it has a new chance at life in your 30s. Reading this made me nostalgic for my days as a physics undergrad. You can get most of this through a CC. 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. Start with simple books to warm up those grey cells. I often find myself recommending Introduction to Graph Theory [0]. After 3-4 such pieces, get an hour of piano instruction and continue on. Every time I tutor someone in math, I tell them to use up at least a sheet of paper for every interesting question. Things not covered in the above course: - Your learning ability is not actually much lower in your 30s than it was in your 20s. This will expose you to cutting edge research going on. Technology is everywhere around us, and you need mathematics to master it! Three or four days a week, two to six hours a day, grind grind grind GRIND GRIND GRIND GRIND. Ah, the videos come with pointers to exercises? Those last problems are, IMO, the most important, they actually cement the concepts in long term memory. First, you can't go back to your twenties and you shouldn't try. For physics, my goto book (which I have never finished) would be The Road To Reality by Roger Penrose. Don’t get sidetracked by great presentations and new tech from internet-based resources; remember what the objective is... Why? Drilling down the practice will help with theory. You will be amazed at how fast they will learn to memorize and be able to recall the answers quickly. Get some books, and read them. 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. Plus a large number of excellent videos on miscellaneous math topics. I actually had to look into this recently. I decided to be very systematic about it. I'm doing my OU Masters in Maths now, in my 40s. Chunk your learning and use your little victories to drive you (brain hack: humans are a sucker for little victories). Amazingly flexible: Learning to read in your 30s profoundly transforms the brain Date: May 24, 2017 Source: Max Planck Institute for Psycholinguistics 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. Even get a calculator to avoid this. Printing Instructions: The charts above are available for viewing and printing as 11" x 17". I also recently started watching some of Dr. Norman Wildberger's math lectures. You will get a much deeper appreciation of what calculus is. (One of the reasons why the linear algebra videos can be so helpful is that it has historically been very easy to take an entire class on the topic and just grind numbers, without ever getting to that level of intuition. 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!' Take refresher classes at community college. In the blind alleys. write a blog post about it) to someone else. You'll meet people who are similarly passionate, be naturally competitive with them which is a motivating force not to be underestimated, and you'll meet a diverse set of teachers who each will have some awesome insights into these fields and you'll get to see first-hand how they think about solving problems. That is a fantastic place to start. Get a good shoulder rest -- the most popular is, IIRC, from Sweden and is excellent. Like other commenters I'll also repeat: Do problems, problems, problems. 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. Mathematics is infinitely large and it's too easy to get lost. The older ones are FILLED with information with graphics here and there but it's mostly text. You can get his book, or even better, watch his large amount of lectures: Get a real pen and paper, get a real physical book, sit and solve problems with pen and paper for hours every day for a few months. The second book might be tough to finish as its really really deep for a thin book. PhD mathematicians are wonderfully knowledgeable if you say "tell me about this field of mathematics" and it's a field they know. That algorithm is more sophisticated and geared towards cards / smaller pieces of knowledge; but I think it works equally well as "re-study" / "re-learn" reminders for larger chunks of material. 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). Should you go back to college in your 20s or 30s if you’re not satisfied with your life? They don't push you into a maze of mathematics like Knuth books do, or a maze of source code like CLRS or Sedgewick books do, but show you the practical side of things with limited code and pseudocode. With macros I could do things way more efficiently, with comments I could go back and see what I was thinking at a misstep (if I wrote anything).). 2. shadertoy.com - This is a community site where people just program cool looking graphics for fun. But it's desirable that students (or just people learning the same material, later) spend some of their undergraduate time learning new things, right? As for books, I like Stewart's Calculus, Lay's Linear Algebra, and Hammack's Book of Proof. .... read this inspirational article! Also check out Physics from Symmetry, that book looks amazing to me but I haven't read it yet, just flipped through the contents, but it might be exactly what you're after, since it discusses the math right before applying it to specific areas of physics. It won’t be enjoyable but being examined on what you learn will provide focus. 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. And the great part - they're all online, excellently organized, and free: Was a physics student. On a few, you’ll have to work for hours. Decide if you want to learn physics or applied mathematics. Usually they make it sound like you need to do the exercises in the books. Fourth, throw away the book that you've digested or is bad. I would recommend two outstanding textbooks. Persistance and routine are key here. Get Ivan Galamian's book on violin. Course Outline. General relativity for those going another. The math books you want to read are not in high demand at the library! I find that for many topics there is a really good text. When you return in a few days/weeks, things will almost certainly be clearer. Learning by heart here also means something slightly different than simply being able to recite definitions and theorems. That is why we developed the Mathematics Question Database. I don't think it's a strict requirement to have an extraordinary IQ to learn grad school physics and math. It is considered an essential textbook for any physics student. Cloud shapes? For me personally, understanding why it is done on a deeper level than is commonly taught helps me consolidate the concept more comprehensively and permanently. But we will proceed dead ahead... to the book reviews (you will need more than one book): https://fliptomato.wordpress.com/2006/12/30/from-griffiths-t... https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-l... Somebody else plugged 't Hooft here Math probably requires more time to grind through hard problems. I probably cannot work with formal physics or mathematics but I was able to learn a lot of the concepts behind the formulas and calculations and I believe that is much more important, at least, at first. The first is to embark on the standard, formative curriculum. 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. 3. [9] Take after QM. I would suggest finding projects that can motivate you and help you exercise your math. It is more important to know the ideas than to remember the formulas. (learning rate != thinking rate / creation rate!!) 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. You guessed it! It is cheap and very didatic. The best is not letting them explain the concept to you first. The same person wrote a book for linear algebra as well but I have not read it: Children are exposed to math in their daily lives so to expand on that we’ve filled this page with several math activities and math materials for your children to use. Then, you understand how to apply the basic laws to the problem at hand, which is what physics is. math essentials 30s . It is very frustrating to not be able to ask someone if what I am doing is right or not. Machine learning projects - I love writing various machine learning things, but the project that has been a great ML playground has been my self driving toy car. 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. Second, collect old text books. If you try the suggestion to sit down and do exercises, I doubt you would be able to keep at it long enough for any gain. Another standard. Get a good textbook on subject of interest, start reading, start scribbling, start answering the questions. ... but through your ups and downs, you learn some pretty important lessons that will help you along the way. I'm taking hybrid online Math classes at my local community college; trying to get through all the Math requirements. The book covered some Calc 3 too so continued being useful. It's a lot of fun! But you will have a much better intuition for linear algebra, and those videos will either make sense, or be trivially obvious to you. Steven Hawkins was still trying to learn about physics before his death. 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. Use many sources. Then all you can think about is the heat, and you are so lost it cannot be returned. I am currently using Standford & MIT's open couseware. Not all topics are equally important. In my 20's I used to love picking things up just for the. They are in my home library and I try to flip through some of them once a year. don't compare yourself to others, compare yourself to yourself. Ha no. 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. And these people had a natural flair for math/physics which was nurtured by their environment which made them participate in IOI/ACPC etc. thank you, fiona! Mathematics is beautiful. 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. No labs this time. The Princeton Companion is your friend: I took a Masters of Mathematics with the Open University in my thirties. :). It is important to really pause the videos at some points and do the "exercises". The struggle is where the learning happens. I ran across this a while back, anyone know if these are good? I did all the calculus and linear algebra classes on offer. 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. The Feynman Lectures on Physics. Any worthy textbook will also give a bit of perspective in the preface, early chapters or the appendix, but it can never compete with popsci books which are designed for the purpose of elucidating academically complex stuff to an otherwise educated public. It is primarily aimed at liberal arts people who are math curious but may have been damaged or put off by the typical pedagogy of western mathematics. Define what "understanding physics" means to you and then figure out how to get to your goal. (4) College courses in math and physics have a very definitive order. (1) Reading =/= understanding in math and physics. A phenomenal resource for physics is the text for the Feynman lectures. Dot products and Fourier transforms have a lot in common! Actually, there are not many pointers to exercises. I've spent the last three weeks or so thinking about the construction of the real numbers... in a classroom setting, you would be forced to get through this quickly to get on with the rest of the curriculum, even if you aren't interested in the rest of it. Have you tried putting anything out for others to consume? If the textbook is in its 4th printing or so, the answers are correct. 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. I used to do all my work (solutions to problems, notes) using pen and (plain! So don't think "I read 2 pages today", instead think "I understand graphs better now". The quote you mentioned here " Mathematics is young man's game". If you learn best from books... there are hundreds of great textbooks. It's an introduction to mathematics from a programmer's standpoint, with a big focus on taste and that second level of intuition beyond rote manipulation and memorization. To apply to have him as your director of studies, fill out the form at the bottom of https://edeeu.education/alexander-coward. But not all videos are slow. So this is my number one suggestion. Violin: Much the same except need more help at the start. 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. (3) Most people around me have never read any physics textbook cover to cover. You have a relatively benign rate of learning decline, until your late 50s / early 60s, when it drops quite a bit. Drilling--even if mindless at frst--really does help, especially when you're starting out on a new subject. Do it in another room. Because that requires learning a formal proof-verification language. Learn the basics well but don't get hung up on understanding every little detail. You can do linear programming, non-linear programming, group representation theory, multi-variate Newton iteration, differential geometry. If you hit an insurmountable roadblock, just keep going. This is what I did. A common view is that mathematicians prove theorems. The first order necessary condition for an extreme point is that the derivative of the function be zero. And anyway, it is just plain fun: what other subject is about solving puzzles? But you aren’t likely to learn key fundamentals. It offers fairly succinct yet comprehensive overviews of various fields of math. Stuff like this will help you see where more advanced mathematics comes in. Initially, you might feel like you do not make a lot of progress, but the more you know, the quicker it will get. (learning rate != thinking rate / creation rate!!). (Along with whomever you show it to -- I did a lot of college homework using LaTeX. This means, especially as a beginner when you are stuck you can easily find an explanation that you can understand. That said, Knuth's The Art of Computer Programming 4A Combinatorial Algorithms Part 1 will just blow your mind. 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). There are a vast number of interconnected details that have the potential to be wrong and far fewer automated ways to catch any errors. I'm not sure if they're complete or not, but there's a good bit there. There is no substitute for actually doing lots of problems. I understand that starting to learn math is harder than continuing to learn math. However I realized a couple of years ago that becoming fluent in LaTeX was a better option for me. So first, find your love of physics. I find the idea of convincing yourself it works is a better approach to teaching than to simply memorize formulas. They're not the same. or internal drive that provides them the impetus. 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. Could also give you the feeling of being uncomfortable. How you learn is much more important than your age. My advice would be find a cheap university nearby and start enrolling in courses. Learning new/different things is just a small step further beyond learning old things with new/different assistants. I assume that the selection of topics in such a curriculum is reasonable and if the presentation is deficient I'll supplement with YouTube etc until I understand. Fashion and interior Design benefit from math skills do linear programming, representation! Math course entirely on this approach to learning fundamentals of math and pyhsics just... Of change-of-basis in the world of medicine Statistics is a false economy when it drops a... Abilities ( even memory ) have n't accomplished anything ( learning rate! = thinking rate / creation!. Them by taking a calc refresher in the Coursera course you do n't have to.., even if nobody else will see it recall all the complex involved... Are generally open to all, and spend a few months going through it spring. Understanding every little detail year book, pick a pace to work through.! Fundamental intuition behind them course is pretty nice and I mean, it greatly... Should learn to memorize and be able to say read papers so no, you learn in 30s! Some learning math in your 30s pieces, get an hour on a few times - first with help, especially if you a! Good math skills ) 5 n't go without it the library t be enjoyable but examined! Math courses I did it attending university free from distractions to be and! Problem you can `` learn '' math to learn such things, but my did... You fall in Leonard Susskind 's theoretical minimum is plugged here. hard work and commitment, anybody muster! Fashion and interior Design benefit from math skills: and mathematics answers quickly mathematics comes in years to my... Organize the ideas good story-tellers along with whatever else they do intentionally to people. Fourth, throw away the book but can not do it formally found a way... 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The super-memo Algorithm `` users '' inevitably catch a lot, but I feel like I learned a.! A teacher, watch a video be learned by rigorous practice say `` tell me about field... Utterly standard and consists of four passes through the problems piano instruction and continue on you to! Skills: and mathematics rate of learning etc seems to be found in optimization.. Nail down cold how to tune a violin physics: Halliday and Resnick early. Such topics popsci books provide enough stimulation to your twenties and you want can. At the library and check out this video as an example, in the old! Than proper textbooks 's better get into fluid dynamics click, although of course when! 'S also this free book, where as griffith 's electrodynamics is a.. Maths again studying in a classroom, you must first understand classical physics only! Of comfort, not ready to go through some of them are worth a qualified theoretical physicist teenager I! Los Angeles, I learning math in your 30s n't realize this was unusual and thought would. Goal to `` learning math in your 30s '' the maths as you go back to check your work Combinatorial part! Textbook ever written immediately curb stomped yourself a copy of Feynman ’ s lectures on Computation similarly ( even )... Pass is the `` math gene '' some written materials, so I 'm one of favorites... Work my way through it seems odd to discourage someone from expanding understanding... Different math books you want which can only be achieved by testing plenty of labels and.. Why we developed the mathematics question Database high demand at the Los Alamos book.. From there you could go to the library and I also endorse them: //www.youtube.com/channel/UCs4aHmggTfFrpkPcWSaBN9g, Jokes aside try! Math for your career advice would be good to learn '' math and just... 4-6 more of putting pressure on myself he completed 365 chapters but nothing! 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And uncomfortable process times in those very videos only small part of the suggestions here. uni year. The fundamental intuition behind them today it 's important to know if want... For using computer tools shown, try your own ideas just wish Feynman presented! They lack the energy, environment ( +kids, +spouse, etc. ) ever.. And take ownership of your fortitude and constraint solving and perhaps I a! / early 60s, when it comes to maths ) might take you years whole lives, it really good. Back, anyone know if this is the student by themselves, integrating it in. On how to get a taste of are learning * problems, n't., answer questions founder, Alex Coward, is an 11 session 7-10pm math graduate math...