Participants in warm rooms performed significantly worse than those in cool rooms, failing to identify almost half of the spelling and grammatical errors (those in cool rooms, on the hand, only missed a quarter of the mistakes). I made a rule to complete one chapter every evening including exercises and sticked to it. My car repo is here: https://github.com/otaviogood/carputer but a much easier project is donkeycar.com. If you can't prove it, you don't understand it. Mathematics is also useful in everyday life: Mathematics also improves our mental ability as it teaches us logical ways of thinking. Orthogonality. Here ends the undergraduate curriculum. Persistance and routine are key here. Are you really just solely interested in a solid background? 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. I learned the more advanced maths I use daily in my thirties. 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. The older ones are FILLED with information with graphics here and there but it's mostly text. Then switch to a different text on the same subject. How do I get started? Spend time on math websites (like this one! Look at images of violinists and see what rests they are using. In fact most top-paying jobs need good math skills: And Mathematics is not just numbers, it is about patterns, too! It is never too late to learn math and physics! All these people talk about some neat concepts that will help you gain more interest and think about things to pursue. The recent ones are less "textbook." Is it taught in the Coursera course you mentioned? First, define “advanced mathematics”: calculus? The time in your life for grinding on textbook knowledge is over. You need to do enough problems on a topic that you are no longer struggling, then do 4-6 more. write down the gap in your abilities you'd like to fill so you can track your progress. Pick a book, pick a pace to work through it, and spend a few months going through it. It was a tough textbook to learn from but I feel like I learned a ton. Here is a link to an extended PDF previews of the books: https://minireference.com/static/excerpts/noBSguide_v5_previ... and https://minireference.com/static/excerpts/noBSguide2LA_previ... My favorite undergraduate students when I was TA'ing were all students who had returned to school after spending time in the world. Get Ivan Galamian's book on violin. 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/. Anyway, I've digressed... First of all, you have to realize that you are learning these stuff only for the sake of learning, as an intellectual challenge, rather than making a career out of it. Even if it's simply a love of mathematics itself. I went back to school in my late 20s for this. Use Zoom for online teaching and learning. How to Improve Math Skills. Susskind's first book comes in here. https://gumroad.com/l/noBSLA. Come Up With Your Own Ways. - 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! And the great part - they're all online, excellently organized, and free: Was a physics student. Technology is everywhere around us, and you need mathematics to master it! Beyond that, you can also read books such as The Evolution of Physics by Einstein himself, Thirty Years that Shook Physics by George Gamow to get a historical perspective on the development of advanced physics. Grab three.js, and then once you've followed some tutorial somewhere to get a triangle on the screen, start doing things, but do them manually, including implementing matrix multiplication yourself. 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. It took about 3 years of exactly ops method. People are different I guess. Copying out solved problems from textbooks is also a good technique. This inspired me to get some more textbooks and try to go through them. Includes chapters on sets, graphs, calculus, linear algebra, and more! I'm in a similar situation to you. Fast forward a few years and now I'm learning both physics and mathematics. 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. in high school and undergrad which unfortunately I didn't get a taste of. ... Powered by Create your own unique website with customizable templates. - Your learning ability is not actually much lower in your 30s than it was in your 20s. Every time I tutor someone in math, I tell them to use up at least a sheet of paper for every interesting question. So don't think "I read 2 pages today", instead think "I understand graphs better now". > 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. 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. 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. Further, you wouldn't even need textbooks. I often find myself recommending Introduction to Graph Theory [0]. 3. Anticipate questions taking you six hours to solve, leaving your table and floor strewn with the history of your consciousness. +1 to Khan Academy. (7) Often, just writing things down helps a lot with making things stick. Sounds like the perfect thing for me right now. The first half deals with all the necessary maths from elementary to advanced and the second half covers physics. > If the textbook is in its 4th printing or so, the answers are correct. 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. 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. (from https://github.com/sindresorhus/awesome). This is a standard rookie mistake, and the reason why so many American kids are weaker at math compared to their Asian counterparts. I second this. ... it has a new chance at life in your 30s. Your "users" inevitably catch a lot of them at "runtime". Deep diving into math and physics just for the sake of learning etc seems to be cargo-culting. E.g. I have been really enjoying the 3blue1brown videos on Youtube. https://www.amazon.com/Renormalization-Methods-William-David... https://www.youtube.com/watch?v=foRPKAKZWx8. The quote you mentioned here " Mathematics is young man's game". (8) Counterintuitive: If you get completely stuck, move on! Graph theory and discrete math I did with MIT EdX courses. Very similar in some ways. My professor for dynamics and mechanics of materials required homework to include diagrams of the problem, neatly drawn, on unlined paper. They are thinking about the surface, not the function of the surface in rectangular coordinates. There's a lot to be said for using computer tools. A real loss for humanity. 2. 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. Lesson planning. What good is this intuition? (Besides, I have been to brick and mortar before, and not being very social, I do not think I am missing out on the social aspects of it at all.) Pick a handful of problems. I think that doing just that can be boring and demotivating. There are exceptions and people who do significant work even later, but that's more unlikely. You will also learn about Hamiltonian Systems. In preparation for remote learning: 1. Anyone who tells you can "learn" math and pyhsics by just watching videos is lying to you. Start with simple books to warm up those grey cells. Hi, I calculated it basing it on the super-memo algorithm. You remember how to find an extremum of a function from Cal 1? It is important to learn about one idea at a time, make sure you understand it, and do plenty of exercises so you become expert. I study for one hour every day before work. (5) Finding someone to talk to is really useful. algebra II? This is awesomely overengineered and not-invented-here, and I mean that in the best possible way. As for learning a 'trade' in your 30s, I don't know, especially if you're not handy. It is possible to look at samples online for you to compare if you want to see the difference. Do them with pen and paper, not just in your head. 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? If the textbook is in its 4th printing or so, the answers are correct. (You can get previous versions to save money. That is a fascinating number series. ", 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. Amazingly flexible: Learning to read in your 30s profoundly transforms the brain Date: May 24, 2017 Source: Max Planck Institute for Psycholinguistics But I disagree entirely on this approach to learning fundamentals of math and physics. I elaborate on the method in my response. Explanations are super clear. 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.) 2. Anticipate that some of it you will never understand. I am not sure where you got the impression that it's essential for any physics student, but I have never used it and don't think it's mattered much in my upbringing as a physicist. What You Learn in Your 40s. Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. In that case you're in luck. Ensure you have your binder and science textbook from your locker. Violin: Much the same except need more help at the start. I decided to be very systematic about it. Pick a topic and start from there! And you may also be able to do more clever things with your ideas. Any particular reason to recommend the old editions over the latter ones? You can still learn a lot, but it's meaningfully harder. Learning new/different things is just a small step further beyond learning old things with new/different assistants. Expect to get stuck with any one of them. Good. It's geology; time and pressure. General relativity for those going another. Don’t get sidetracked by great presentations and new tech from internet-based resources; remember what the objective is... Why? Pen, graph paper, and maybe a calculator. > participants were asked to proofread an article while they were in either a warm (77°) or a cool (67°) room. This is a long-term project, so I'd recommend by starting a bit with "learning about learning". I'm a bit wary of some of the suggestions here. Outcome Chart - Manitoba - Grade 11 Essential Mathematics (30S) Half Course III Analysis of Games and Numbers 11E3. For physics, I don't know what your background is. A side quest is available if you want to get into fluid dynamics. Edit: the book gives you the fundamentals though on which you work. .... read this inspirational article! One of the students has an introduction into what you can expect. Some people are much more proficient at it, but I be you'll see that they have much more experience. Oh man... have you got some fun in store here. But it's desirable that students (or just people learning the same material, later) spend some of their undergraduate time learning new things, right? 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). When they do, their skills improve quickly. Good popsci books provide enough stimulation to your mind. There is one sure way, and it’s a test of your fortitude. There's also a mailing list: https://jeremykun.com/2016/04/25/book-mailing-list/. This will serve you well in physics. 2199 cards and counting, Math is something that needs to be learned by rigorous practice. The most important thing for learning is to be inspired and have fun with what you're learning. My plan is to buy a high school textbook and work my way through it, chapter by chapter. One interesting option that computer programmers have to understand linear algebra that most people do not is that you could go do some stuff with computer graphics. It's easier to offer suggestions from there. To me it is beyond question that distance education is the right way for me to do this. I find that for many topics there is a really good text. 1) Find a good source of information --- typically, this is either very good lectures (like on youtube), a good textbook, or good lecture notes. What's interesting? Currently a biggie is a lot in probability theory. For discrete maths, books like The Algorithm Design by Skiena and Algorithm Design by Kleinberg and Tardos should serve you well. A problem you can solve easily and quickly yields zero knowledge. The content of these is mostly the same). 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. 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