Looking for a Detailed and Rigorous Combinatorics Textbook

[Thinkaholic]

Hello! I’m teaching myself mathematics and physics, and I’m looking for a clear, rigorous book on combinatorics. The reason being is that past books I’ve read that included some combinatorics were difficult to understand (for example, my first encounter with the subject was in a precalculus textbook in which the binomial expansion was presented without any context really, and that was confusing). I know combinatorics is an incredibly interesting branch of mathematics, and I want to learn it badly. I’ve pretty much mastered differential and integral calculus, so a book on combinatorics that uses a bit of calculus would be good (if combinatorics uses calculus; I don’t know very many details yet). I’m also reading Enderton’s ‘Elements of Set Theory’ so I can handle a book that requires set theory.

 

[jedishrfu]

Have you looked at the Schaum's Outlines on Combinatorics?

https://www.amazon.com/gp/product/007003575X/?tag=pfamazon01-20

I found this website with many book references:

http://www.combinatorics.net/Books/Default.aspx

 

[mr.tea]

We studied discrete math using Grimaldi's book (https://www.amazon.com/dp/0201726343/?tag=pfamazon01-20) and it was great. Contains also a lot of historical notes.

 

[QuantumQuest]

Assuming an undergraduate level text I would recommend Introductory Combinatorics by Richard Brualdi. An also great book, indispensable for CS, is Concrete Mathematics by Graham, Knuth, Patashnik. It is also a good idea to have a copy of Schaum's Outline of Theory and Problems of Combinatorics including concepts of Graph Theory for a good ideal of exercises and problems, as already mentioned by jedishrfu.