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Re:How to Learn Advanced Mathematics Without Heading to Univ... by namelezz on Friday March 11, 2016 @11:50AM (#11267710)
What are the best ways for a non-genius, normal person to learn advanced mathematics?
Re:How to Learn Advanced Mathematics Without Heading to Univ... by kafkaesq on Friday March 11, 2016 @12:42PM (#11268131)
First off, "genius" talent is by no means required.

Second, it should be something you really, really like doing. Like music is to a musician (or an audiophile), cooking (and watching people get off on your creations) is to a chef, sports training is to an athlete, etc.

And third, like anything else of true value in this life -- it will take a significant amount of time; in particular devoted to practice (and very importantly, play), especially solving (often obscure-seeming) problems on your own, just to scratch an itch, or to know that you can.

Easily a few thousand hours to attain what's called "mathematical maturity"[1], and probably somewhere on the order of the fabled 10,000 to obtain what might be called true expertise in the field. Which should (by itself) be no obstacle, if it's something you're really, really, really into.

Just like any other field, basically.

[1] https://en.wikipedia.org/wiki/Mathematical_maturity

Re:How to Learn Advanced Mathematics Without Heading to Univ... by pakled_engineer on Friday March 11, 2016 @02:44PM (#11268985)
I did books recommended from here, and lots of math stackexchange searching/questions.

I started with Basic Mathematics by Lang, Eccles book on Mathematical Reasoning, A Course of Pure Mathematics by Hardy combined with the lecture notes of MITs honors single variable calc and Polya's How To Solve It, currently doing Advanced Calculus by Loomis & Shlomo.

I would imagine if you're interested in advanced math you would go to free university seminars from visiting professors and network with whoever is there as a self learner.

I get up 3hrs before work everyday and read a chapter then do as many exercises as I can. Repeat until done, or I get stumped and skip that exercise then come back to it later.

Re:How to Learn Advanced Mathematics Without Heading to Univ... by shogunmike on Friday March 11, 2016 @11:54AM (#11267731)
That depends primarily on your favoured learning style. MOOCs are certainly changing the available resources and lecturers are publishing freely available notes for particular courses on their home pages.

Unfortunately some textbooks can be expensive, but some are more reasonably priced. Unfortunately, the more "niche" the mathematical area becomes, the harder it becomes to find freely available sources.

I personally prefer a mix of video lectures and textbooks. Being able to watch video lectures, with the ability to pause and rewind, is a very useful feature that is not available in live lectures!

Re:How to Learn Advanced Mathematics Without Heading to Univ... by bmer on Friday March 11, 2016 @11:59AM (#11267774)
It is very easy to get most mathematics textbooks online, through slightly unsavoury means. It is far more difficult to figure out which textbooks are worth reading---this is a process that requires trial and error, and browsing through recommendations (math.stackexchange and mathoverflow.net have many good textbook recommendation questions, with many excellent answers).

Also, it is very easy to audit courses at universities! Get out there, ask the professor if you can audit the courses (make friends with them too!), and enjoy yourself a stress-free, and money-free, quality education.

Re:How to Learn Advanced Mathematics Without Heading to Univ... by kafkaesq on Friday March 11, 2016 @12:43PM (#11268146)
"Unsavoury", as in?
Re:How to Learn Advanced Mathematics Without Heading to Univ... by forgetsusername on Friday March 11, 2016 @01:32PM (#11268546)
Piracy.

Though, between price fixing and booksellers going under and not being able to guarantee that you will retain access to the books you bought, I'd say that this form of piracy is morally ambiguous.

Re:How to Learn Advanced Mathematics Without Heading to Univ... by octatoan on Friday March 11, 2016 @12:09PM (#11267855)
I wrote this answer to a similar question in /r/math last year. You might enjoy it:

https://www.reddit.com/r/math/comments/3ixyw3/how_can_i_begi...

Re:How to Learn Advanced Mathematics Without Heading to Univ... by pmalynin on Friday March 11, 2016 @12:36PM (#11268088)
Notes from the intro math course at my University are pretty good.

https://www.math.ualberta.ca/~xinweiyu/117-118.14-15/Math117...