Becoming an amateur mathematician?

[dpm]

I'm a third year CS/AI student. I love computer science but I also love mathematics and I sometimes wish that I studied maths outright or at least did a CS/maths joint degree.

As part of my degree, I've had to study two years of maths, as well as be able to pick further "theoretical courses" in third year (algorithmics, computational complexity and intractability theory (P=NP) etc). My degree maths education consisted of linear algebra, statistics, number theory, calculus, combinatorics, geometry and various bits of discrete mathematics (graph theory, logic etc.) as well as being pretty strong on proof (computer scientists seem to love proofs).

I like geometry, computational complexity, algebra, number theory and computational complexity. I've tried getting books from the university library and reading up on these subjects, yet quickly find myself overwhelmed - pages and pages of theorems aren't easy to digest. What I would like is to have a list of areas that build on the basics in the subjects that I like and have some structure to my learning as opposed to the aimless meandering that quickly kills my attention.

Can anyone suggest such a resource?

Thanks,
Dominic Mulligan.

 

[0rthodontist]

Your background looks similar to mine. A book I have found generally useful is Ralph P. Grimaldi's Discrete and Combinatorial Mathematics. The book contains a broad sampling of topics and a lot of good problems. Also, the table of contents is available online.
https://www.amazon.com/gp/product/0201199122/?tag=pfamazon01-20
I have the fifth edition, but the fourth edition at that link looks very cheap.

 

[neurocomp2003]

are you looking for an algorithmic type book or a functional analysis or Algebra book? Your probably looking to do some practical stuff.

Cryptography and Number Theory: Neal Koblitz

Computational Geometry: O'Rourke

I'm surprised you haven't taken a numericals methods class:
"Numerical Recipes in C" or fortran if you want to learn a new programming language

Rendering & 3D engines have tons of math:
"3D Engines" by Eberly or
"3D mathematics for gaming" Lengyel(very basic)

If your into stats and you like the AI your learning to
There are a couple of statisical Mathematics (can't remember the author of the one i used)

 

[dpm]

0rthodontist, thank you for the recommendation, I'll look it up.

neurocomp2003, I'm not particularly looking to do practical stuff, I'm interested in learning maths. I mentioned my computer science background to show what foundation I have to work from.

I'll highlight a particular problem I have with a lot of mathematics books. When I was studying mathematics at A-level, we came across hyperbolic functions. These were introduced, some of their properties were introduced and everything was fine. Then, we were shown how to use these functions and their identities in order to integrate other functions that could not be integrated before. This is the sort of thing that I like - not only a new area, but a reason as to why this area is worthwhile to read about. If there are any books like this, that would be great (perhaps I've been looking at the wrong books )

 

[dpm]

0rthodontist, I just placed my order for the book that you suggested ($3!). Thanks for the advice.