Very broad and open question.
My personal opinion is that a good programmer should have skills in problem-solving and language. By language I don't mean programming language but instead the skill of expressing thoughts and ideas, both in writing and verbally. Once you have this skill, you can easily learn new programming languages and express yourself in that language. I use C, PHP, Xojo Basic, shell and JavaScript on a daily basis for work and I'm not preferring any over the other - they are good at different things.
I've been mentor for students in college where they teach a specific language (almost exclusively Java but also some JavaScript and (sigh) HTML). Learning a language but not learning problem-solving gives excellent programmers that are useless at solving an actual problem and if you have learned to do OOP specifically in Java but haven't grasped the OOP concept you are likely to fail in a real-world project.
As to math - it gives you an important aspect when it comes to problem-solving and which is good. I have been working in projects heavy on math so I had to refresh integrals and statistic analysis methods for that specific project (I attended university in late 90's for a master in Electrical Engineering so some of the details of Newton-Raphson's method were lost to me and I had to refresh).
As to literature on programming I prefer language-agnostic books describing concepts and algorithms in pseudo-code. This makes is possible for me to implement the concept in the language of my choice. Some personal favorites are:
* PHP and MySQL Web Development (Thomson and Welling) - the first edition of this book took me from programming web-systems in perl to PHP back in 2001.
* Design Patterns (Gemma, Helm, Johnson and Vlissides)
* Algorithms (Sedgewick and Wayne)
* The Art of Computer Programming (Knuth) - a must have as a programmer, but I doubt most of us have actually read it cover-to-cover...
* (More recent) - The Fizz Buzz Fix (Barnard)
Wishing you all luck in your programming career!
/Mattias
