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. Then you will pass the exams.
Ask HN: How do I learn math/physics in my thirties?
11–20 of 160 posts
Re: Ask HN: How do I learn math/physics in my thirties?
#12Re: Ask HN: How do I learn math/physics in my thirties?
#13What works for me is purchasing and reading textbooks (look for online college syllabuses for good ones). Probably the best way to read maths texts is to work the problems, but what I do is read it through once or twice. Then switch to a different text on the same subject. Things will slowly start to click, although of course you don't understand something until you can explain it (i.e. write a blog post about it) to someone else.
Re: Ask HN: How do I learn math/physics in my thirties?
#14For motivation, if there is a nearby university, start attending the relevant departments' colloquia. They are generally open to all, and will start to get you up to date on what's new across all of math/physics.
My favorite undergraduate students when I was TA'ing were all students who had returned to school after spending time in the world. They knew why they were there, knew that the material was worth learning, and asked lots of questions.
Go get it -- start small, don't stop.
Re: Ask HN: How do I learn math/physics in my thirties?
#15Take a look at brilliant.org. They teach mathematics in small chunks with practice.
https://brilliant.org/courses/#math-advanced
https://brilliant.org/courses/calculus-done-right/
https://brilliant.org/courses/linear-algebra/
Re: Ask HN: How do I learn math/physics in my thirties?
#16Being in your thirties has little to do with learning. How you learn is much more important than your age. If you learn best in a classroom, you may have a local college that teaches math in the evenings. (I got my Master's in Statistics that way.) If you learn best in small chunks, Khan Academy has differential and integral calculus and linear algebra, to start you out. If you learn best from books... there are hund…
Very true.
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. Assuming one has continued to pursue learning, someone in their 30s would have built up a significant enough semantic tree to pin new knowledge to.
Most people find it hard to learn in their 30s because they lack the energy, environment (+kids, +spouse, etc.) or internal drive that provides them the impetus. 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). But their actual abilities (even memory) haven't actually degraded all that much.
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). You have to know if this is the case. Most of the time it is not.
I would start by building up a good foundation. Learn the basics well but don't get hung up on understanding every little detail.
Chunk your learning and use your little victories to drive you (brain hack: humans are a sucker for little victories). Use the Feynman method (learn by teaching).
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). It's a process of cognitive dissonance where you actively wrestle with problems rather than passively work through them.
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.
This is a standard rookie mistake, and the reason why so many American kids are weaker at math compared to their Asian counterparts. Drilling--even if mindless at frst--really does help, especially when you're starting out on a new subject. It helps you develop muscle memory which in turn gives you confidence to move to the next level.
Re: Ask HN: How do I learn math/physics in my thirties?
#17Watch the 3Blue1Brown YouTube channel: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
These videos are frankly better explanation of college-level math concepts than most college classes.
Also, now you probably care much more about the intuitions of mathematics over the raw mechanics of it. Once again, this channel perfectly exemplifies this concept.
Re: Ask HN: How do I learn math/physics in my thirties?
#18Get 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. Then you will pass the exams.
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.
Re: Ask HN: How do I learn math/physics in my thirties?
#19I'm in a similar situation to you. I have been really enjoying the 3blue1brown videos on Youtube. He has a sequence on calculus and linear algebra and both of them are worth watching and thinking about before going through a book. I also recently started watching some of Dr. Norman Wildberger's math lectures. He's a finitist crank, but most of his class lectures are great despite this. This inspired me to get some more textbooks and try to go through them. I'm pleased if I can make it through a chapter at all on any time scale, and I think having low expectations is probably healthy.
One thing a friend of mine said, which I think has been very good advice, is to get several books on a single topic. Eventually every author will lose you and you'll get stuck; having alternate discussions will help you get through 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. The math books you want to read are not in high demand at the library! 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 find that for many topics there is a really good text. Calculus by Spivak is a great example, it straddles the line between calculus-in-college and analysis. Every topic seems to have a few really good books like this one, and there are often books that will take a totally different approach, like H Jerome Keisler's nonstandard calculus book using infinitesimals.
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. Going at your own pace, you're not going to go through as much stuff as quickly, but you will actually _really_ learn it. 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.
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. I have heard great things about the book Gravitation, but I'm totally afraid of it, not ready to go there yet. 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.
Re: Ask HN: How do I learn math/physics in my thirties?
#20I'm in a similar situation myself. My plan is to buy a high school textbook and work my way through it, chapter by chapter. 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.