
Ask HN: Learning mathematics after college - alvarosevilla95
I studied Mathematics and Computer Science at college, although I focused on the Computer Science part for most of my electives. I&#x27;ve been trying to get back into learning maths, but I&#x27;ve come across to problems:<p>- With so many fields and subfields, it&#x27;s hard to identify what I want to learn next<p>- I can&#x27;t find great learning resources, specifically resources which aren&#x27;t directed at high schoolers &#x2F; first year undergrads and are not actual university courses (for c.s. for example there&#x27;s almost an infinite number of resources easy to find ranging every area and level)<p>I&#x27;m sure a lot of readers here have self-taught maths, and I would love to hear about your experiecnes and recommendations. Thank you!
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jfaucett
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!

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jjgreen
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/](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.

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osivertsson
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...](https://www.goodreads.com/book/show/1874246.The_Higher_Arithmetic)

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brudgers
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](http://norvig.com/21-days.html)

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mimo777
Harvey Mudd has a great college course
[https://www.math.hmc.edu/~su/math131/](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...](https://hackereducation.wordpress.com/hacker-education-
content)

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Phithagoras
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/](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.

