Ask HN: Learning mathematics after college

Fields and subfields are just one categorization, I wouldn't put too much weight on that. It is all connected, you can attack it from many angles.

With maths I personally need to really immerse myself and block out all distractions. Then I focus until my head is "full" for the day. Then the best course of action for me is to go for physical exercise (I run, bike, or swim.) I feel like this helps me digest what I've learned.

Great learning resources can be old-fashioned books ;-) Preferably written by someone really authoritative in the field, and not just written to make a buck or for a course. For example, I really enjoyed Davenport's The Higher Arithmetic [1]. Original research papers, even if ~100 years old, can be really enjoyable too.

What is your aim? To reach enlightenment? ;-) Or to solve/understand a particular problem?

[1] https://www.goodreads.com/book/show/1874246.The_Higher_Arith...

Finding your direction is hard, usually at University you have broad range of topics at the start, then towards the end of the course you have an idea of where to go next.

I would suggest looking at MathOverflow, http://mathoverflow.net/, the level is high, don't expect to understand much of it, but you will see a wide range of topics of current interest and that may give you some ideas on direction.

I studied literature in college and am a completely self taught mathematician. You're right about quality textbooks and topics not geared to beginners, but at the same time since I got through learning all the basics (analysis, linear algebra, probability theory, etc.) , I've just followed my interests i.e. messed with my own formulas/proofs/etc. in whatever topic I'm interested in (recently sieve methods) and looked at others results in that area.

Anyway, Springer brings out a lot of good books on specific math topics so I'd say look there for learning material.

In terms of topics, it helps if you have problems to solve that require maths knowledge i.e. you need to write a compression algorithm so you dig deeper into information theory.

Also as a side tip, I allot about an hour daily to just doing math stuffs, like many might with exercise or watching tv. I have to say this has made a huge difference in terms of my ability and math knowledge over time - and its my most favorite part of the day :)

Best of luck getting back into maths!

I think the difficulty with self education often boils down to nobody telling me, "here is what you will learn over the next three months on Tuesdays and Thursdays at 10."

It seems to me that those difficulties are more psychological than structural in that learning on one's own is a bit scary, but Tuesdays and Thursdays at 10 probably aren't going to work well for me because, like life, you know.

But it turns out that not having a timetable for completing the work and taking the test means I am free to take on learning mathematics or Lisp or Linux as long-term projects like learning architecture and the further in the rearview mirror college becomes the less all those years of habits in response to academic calendars seem like the natural order of the way things are learned. I'm by no means the smartest person to suggest this. [1]

Not knowing what to learn next has two issues, one is that outside of academia knowledge is not an iterable. There is no 'next' or rather there are infinitely many and photography is a next of Python and Linear Algebra is a next of FIFA 17 and all four can be learned concurrently. The second is that 'you will probably never use that after you get out of school' applies to things that are learned after getting out of school too.

My explicit advice: when you find the right thing to learn next you will look at high school and college and post-doc level resources with the similarly high levels of enthusiasm because you cannot get enough of the subject. You will also discard and skim resources at all those levels when the learning becomes smally incremental and later, perhaps several years, some you will circle around to because you did not understand them the first time or because you understand them differently now that you have learned more.

Good luck.

[1]: http://norvig.com/21-days.html

Harvey Mudd has a great college course https://www.math.hmc.edu/~su/math131/ on Real Analysis and they use Rudin's Principles of Mathematical Analysis which is a wonderful, all be it challenging text. Professor Su does a great job of explaining it all. I put a lot of math video/lecture information on my web site that I developed to try and give 'hackrrspace' members access to an engineering/physics degree without attending college--or supplementing a non-technical or associates degree. https://hackereducation.wordpress.com/hacker-education-conte...

I've found that the internet is fantastic for compiling information or checking a concept or two, but isn't very useful for learning swathes of material. I learn mostly from used textbooks, which can often be found on sites like abebooks.com or http://gen.lib.rus.ec/

Pick a book that seems interesting and work through it. You don't have to be religious about following their topics or order though.