I've used brute force for the most part for the ProjectEuler.net problems that I have been able to solve. One thing I'm finding is that, for some of the puzzles, I'm not able to find good resources for 'backfilling' my understanding of the problem domains the puzzles represent.
What are suggested resources for learning about those topics?
Is anyone else working through ProjectEuler simply for self-improvement?
I do play with ProjectEuler, though I've been stuck on #78 for way too long. Keep in mind that brute forcing the questions is really not the goal - ideally, you are supposed to come up with a program that will find a solution in less than 60 seconds!
One thing that I've found very useful is once you DO solve a problem, read through the discussions about it, often very illuminating.
You may find this resource useful: Mathworld: Number Theory, Mathworld: Sequences
Project Euler is amazing (I'm at 101 problems).
I suggest that you read a book on algorithms, I can recommend these two:
Other suggestions are discussed in this thread.
Also, after you solve a problem and feel you didn't use the most efficient algorithm, read comments in the thread that discusses it. Then re-code your solution with the right approach. After several problems you will notice that there are repeating patterns in the approaches.
As for the topics you listed, I use these websites:
Some Wikipedia articles are also quite helpful.
Whenever you solve a problem, spend a lot of time on the discussion forum. There are some very smart people who discuss their solutions. Project Euler is meant to help you learn through solving. Look up the terms that you don't understand, and you'll learn concepts like that.