Maybe not "made me better at math" per-se, but definitely "made me more enthusiastic about math":

The Universe Speaks in Numbers[1] by Graham Farmelo

I found this very motivating and insightful, in terms of developing even more of an appreciation for how much math underpins other branches of science. Not that that is a novel insight by any means... but the details of the incidents where breakthroughs in mathematics allowed further advances in physics, etc. and looking at the "back and forth" between the domains, that was wildly interesting to me. Reading this book definitely helped motivate me to get serious about committing more time / focus to studying mathematics.

I also enjoyed the "counterpoint" book by Sabine Hosenfelder, Lost in Math[2]. I think these two books complement each other nicely.

Then the handful of additional (no pun intended) books that jump to mind would be:

- How Mathematicians Think by William Byers[3]

- How to Think Like a Mathematician by Kevin Houston[4]

- Discrete Mathematics with Applications[5] by Susanna Epp

- How Not To Be Wrong[6] by Jordan Ellenberg

- Introduction to Mathematical Thinking[7] by Keith Devlin

- How to Measure Anything[8] by Douglas Hubbard

[1]: https://www.amazon.com/Universe-Speaks-Numbers-Reveals-Natur...

[2]: https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/15...

[3]: https://www.amazon.com/How-Mathematicians-Think-Contradictio...

[4]: https://www.amazon.com/How-Think-Like-Mathematician-Undergra...

[5]: https://www.amazon.com/Susanna-S-Epp-Mathematics-Application...

[6]: https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143...

[7]: https://www.amazon.com/Introduction-Mathematical-Thinking-Ke...

[8]: https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...

SOME ADVICE BEFORE YOU DO A DEEP DIVE INTO WHATEVER YOU END UP STUDYING MATH-WISE:

My Background: Current Undergraduate in CS and I recently added Mathematics

The most difficult part for a person who hasn't done a lot of math to become a person who does a lot of math is to read and understand rigorous proofs. You will encounter countless difficult proofs in any mathematical topic you try to study. Read a few books on mathematical thinking and proof techniques before/during/after reading any other dense math book.

Like you, I realize the value of having a mathematical mindset and want to have a deep understanding. When I added math as a major, I had a very hard time jumping from computational courses (typical math courses, geared towards any major) to theoretical and conceptual courses (proof-based courses that use all the fun and interesting math books everyone has linked here). These books helped:

https://www.amazon.com/How-Read-Proofs-Introduction-Mathemat...

https://www.amazon.com/How-Think-Like-Mathematician-Undergra...

https://press.princeton.edu/titles/669.html

<3 this is a great book, obvi since its george polya

I read this the first time posted (didn't get any comments), very poignant, especially the part about relearning trig/geometry, precalc. There's boundless resources for learning now but you don't get little endorphin/epinephrine releases like you do when your gcc/clang/VS compile succeeds, it's still mostly notebooks, whiteboards, pencils and 4-color pens (tho i've seen lots of cool JS animations, ipython notebooks, and libs in R, matlab/octave and now julia)

- a few universities have put (many/most) of lecture notes and student notes up: http://www.maths.cam.ac.uk/studentreps/res/notes.html as well as study guides: http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf

- books about how to think like a mathematician: Keith Devlin, Kolmogorov/Alexandrov et al did 2 Dover books, and Houston: http://www.amazon.com/How-Think-Like-Mathematician-Undergrad... and http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199... and Ellenberg: http://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/15942...

- Concrete Math by Patashkin, Knuth et al; Streetfighting Math by Mahajan and his newer, freely available: http://mitpress.mit.edu/books/art-insight-science-and-engine...

- this machine learning/data science list: http://www.reddit.com/r/MachineLearning/comments/1jeawf/mach...

- Cal newport blog: http://calnewport.com/blog/2012/10/26/mastering-linear-algeb...

- besides Dover, Schaum Outlines are a good cheap resource abundantly available in used bookstores(tho there are in fact some type-ridden ones also)

____________

the best advice general advice i've seen is the same as what they tell you in college: form study groups and make commitments to regular discussion. Stronger students strengthen their understanding by tutoring others at the whiteboard. There's lots of machine learning and data sciencey meetups and informal groups springing up e.g.http://machine-learning.meetup.com/

Concrete Mathematics should not be too hard to understand for someone who understands basic algebra. Most of the topics it covers use nothing more than arithmetic and simple logic.

That said it is not a good general mathematics book (it is designed as a Computer Science book).

A book that will help you - How to think like a Mathematician: http://www.amazon.ca/How-Think-Like-Mathematician-Undergradu...