Hello, can anyone recommend good combinatorics textbooks for undergraduates? I will be teaching a 10-week course on the subject at Stanford, and I assume that the students will be strong and motivated but will not necessarily have background in subjects like abstract algebra or advanced calculus.
I intend to focus on the enumerative side of the subject and do permutations and combinations, generating functions, recurrence relations, Stirling and Catalan numbers, and related topics. However, this hasn't been set in stone and I also welcome advice for what topics to include.
I would be grateful if people would not only suggest names of books but also say a little bit about their merits. Thank you!
Best Answer
Two obvious answers are van Lint & Wilson "A Course in Combinatorics" and Peter Cameron "Combinatorics". Which is best really depends on the fine details of your course, and what content you want. Cameron's book has a lot of nice exercises, there are not as many in van Lint & Wilson (and they have a tendency to go of the deep end). As you would expect both books are very well written and have an excellent selection of topics. Cameron's book is possibly more approachable.
Grahm, Knuth and Patashnik is a fine book, but is much more focussed on classical combinatorial sequences and less on combinatorics in general.