Books for combinatorial thinking

Solution 1:

You might want to check these out (there are a coupe of others, but I am not home and the titles are escaping me).

• Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions)

• Principles and Techniques in Combinatori, Chen Chuan-Chong, Koh Khee-Meng

• Applied Combinatorics, Alan Tucker

• You might want to look at Donald E. Knuth - The Art of Computer Programming - Volume 4, Combinatorial Algorithms - Volume 4A, Combinatorial Algorithms: Part 1

I'd also recommend books on problem solving, for example:

• 102 Combinatorial Problems, Titu Andreescu, Zuming Feng

• Combinatorial Problems in Mathematical Competitions (Mathematical Olympiad), Yao Zhang

• Combinatorial Problems and Exercises, Laszlo Lovasz

Regards

Solution 2:

Concrete Mathematics has a feast of lip-smacking mathematics in it.

Solution 3:

I'd take a look at Proofs that really count

Solution 4:

H.J.Ryser, Combinatorial Mathematics

M.Hall, Combinatorial Theory

Solution 5:

I am working on James A Anderson's book called Discrete Mathematics with combinatorics and I'm pretty happy with it. I like the combinatorial part of mathematics the most and this book does try to look at things from that point of view on many cases. Although you should really pick it up at a library and look for yourself.

It is not however very problem oriented. You can try concrete mathematics by Knuth, Graham and Patashnik. Also, I find the problems on Van Lint and R.M WIlson's book really good (those are just in combinatorics though).