My situation: Haven't taken a math class in 10+ years. Highest level I've taken was statistics (which I didn't receive good grades in). Capable programmer.
Don't really have a goal of doing anything with math, just want to orient myself more towards math and see if that changes how I think about things.
I do have two kids in school, though, and my daughter just finished some higher level calculus courses. In my attempts to help her, I've found that we have endless and fantastic resources available online. Every type of problem has a YouTube video explaining, step by step, how to solve them.
In my opinion, there's never been a better time in history to learn advanced (or even basic!) mathematics than right now.
Ask HN: How to Study Mathematics? [1] Ask HN: How to self-study mathematics from the undergrad through graduate level? [2] Ask HN: Are there books for mathematics like Feynman's lectures on physics? [3] Ask HN: Best resources to gain math intuition? [4] Mathematics for the Adventurous Self-Learner [5]
[1]https://news.ycombinator.com/item?id=23074249 [2]https://news.ycombinator.com/item?id=18939913 [3]https://news.ycombinator.com/item?id=21346272 [4]https://news.ycombinator.com/item?id=20804582 [5]https://news.ycombinator.com/item?id=22400375
- Khan Academy is great because it covers a lot of material at school and some at college level so when you find that you have a gap you can always drop back a little and learn about stuff from school that you've forgotten. The explanations are very accessible and it's a great resource for re-learning stuff.
- MIT Opencourseware has courses for university-level mathematics. This is if you want to learn things more rigorously and the material is a bit more advanced obviously. Watch the lectures, read the textbooks, do the exercises. It's free world-class education. And once you have a foundation, you can always grab a textbook on a topic you want to go even deeper in.
- Youtube math channels like 3blue1brown are wonderful. I don't think they're for learning really but for exposing you to new ideas, giving you a different perspective on things or just allowing you to enjoy a nice explanation. It's infotainment.
The core should be working through textbooks, understanding the material as best as you can, and doing exercises. Start with something on the easier side to get things going. Search through online sources or alternative books whenever you get stuck, for more explanations and assistance.
In parallel, try to start forming a "bird's eye" view of the landscape, since there are a lot of areas you might want to focus more on later, by exposing yourself to more advanced, diverse topics and terms without any rigor. Things like watching a video, reading a non-technical book about math, checking out some random Wikipedia article you stumbled on that is way above your head etc.
I think this traditional, safe way is how you should start, and after a while you will know for yourself what to do next. There are a lot of excellent online sources, videos, blog posts etc. but there are also a lot of crappy, superficial ones, and you will need some experience to be able to judge that.
- "Problems in Mathematical Analysis", Demidovich.
- "Differential and Integral Calculus", Piskunov.
That's what our courses in university followed (first and second year), but also high-school teachers were inspired by as they studied these in university themselves. Smirnov takes you from the "concept of number" into the deep. Piskunov is cool and full of examples, including operational calculus and probability theory. Demidovich is a problems book to exercise your hand.
They are concise and to the point. Smirnov's has five volumes across seven books, though, but they're concise (density of information is high).
These books have examples from physics as well. For instance, I didn't understand enthalpy from my physics course until I read about continuity in Smirnov's book as he masterfully gave an example of discontinuity using enthalpy (phases of water).
What I would really like is something like a study group. It’s kind of difficult when you don’t understand something and there’s no one to turn to