[feklar]

First I would recommend Cal Newport's blog about using time wisely. http://calnewport.com/blog/2008/11/25/case-study-how-i-got-t... Plenty more great info in the archive: http://calnewport.com/blog/archive/ Obviously the best way would be to go through your school's course syllabus for whatever classes you want to take and look at the material you will be doing, but these are good for a general preparedness:

Axler - Precalculus 2nd version http://precalculus.axler.net/ He works through every odd exercise solution, in full. Also gives you a good intro to sets and series, summation notation, binomial theorem, all this will come up later in discrete math. He assumes the reader knows nothing about Trig as well.

Gilbert Strang's videos "Highlights of Calculus" https://ocw.mit.edu/resources/res-18-005-highlights-of-calcu... just to get an overview of what calculus really is since I assume your university will throw you into an applied single variable class first year. MIT Open Courseware has their calculus (18.01/18.02) course lectures up if you want to watch them too to get an idea of what you'll run into.

"Elements of Mathematics: From Euclid to Gödel" gives quite a good explanation of Mathematics as a whole, like why we learn elementary math the way we do and how it applies to more advanced concepts, explains Rings/Fields and has a really good introduction to Logic. I wish this book existed 5 years ago when I started http://press.princeton.edu/titles/10697.html

"An Introduction to Mathematical Reasoning" by Eccles is short and excellent. You can also download the lecture notes here from CMU's course on proofs http://math.cmu.edu/~svasey/concepts-summer-1-2014/ and try some of the homework if you want but you probably won't see any of this until second year judging by most university calendars and recommended program course list I've seen.

CLRS https://en.wikipedia.org/wiki/Introduction_to_Algorithms which has a great first chapter "Foundations" that compliments Knuth's 'Mathematical Preliminaries' chapter in TAOCP vol 1. Knuth's book you can really drill yourself in these concepts though with the many, many exercises writing proofs. The skills I learned doing these exercises paid in full years later when I started more advanced math and even at work.

[nekopa]

Thanks for the info. Do you think I will be able to use the Elements of Mathematics to kind of build a "Tech Tree" of math? One of the hardest things for me to find so far is what should be my order of acquisition for math. I did find this:

http://forums.xkcd.com/download/file.php?id=29015&sid=060c11...

But I have no others to go on to compare.

[sn9]

This is a common complaint with a simple solution.

Just look at the curricula for various undergrad math programs at some number of decent universities. They have a set of required courses and the course descriptions usually list the prerequisites, and sometimes this is even accompanied with a diagram of the DAG as a flowchart.

For any given course, there's usually a canonical text or set of roughly equivalent in quality texts.

You can do the same thing for basically any area of study that can be found as an undergrad major at most universities.