An Invitation to Combinatorics

Shahriar Shahriari is Professor of Mathematics at Pomona College. He has over fifty publications in mathematics including two books: Approximately Calculus (AMS 2006) and Algebra in Action: A Course in Groups, Rings, and Fields (AMS 2017). His book Approximately Calculus was chosen as an American Library Association's Choice Outstanding Academic Title of 2007, and he won the Mathematical Association of America's Carl B. Allendoerfer Award for expository writing in 1998. Shahriari was awarded the Mathematical Association of America's Haimo National Teaching award in 2015, the Southern California-Nevada Section of the Mathematics Association of America's Teaching Award in 2014, and Pomona College's collegewide student-voted Wig Distinguished Teacher award five different times.

• Preface; Introduction; 1. Induction and Recurrence Relations; 2. The Pigeonhole Principle and Ramsey Theory; 3. Counting, Probability, Balls and Boxes; 4. Permutations and Combinations; 5. Binomial and Multinomial Coefficients; 6. Stirling Numbers; 7. Integer Partitions; 8. The Inclusion-Exclusion Principle; 9. Generating Functions; 10. Graph Theory; 11. Posets, Matchings, and Boolean Lattices; Appendices; Bibliography; Index.

'I would certainly accept this 'invitation.' The text covers essentially all of the basic combinatorial subjects in a both gentle and intense way. The extensive problems, examples, and 'projects,' especially the collaborative projects, exemplify current pedagogical research on effective teaching methods. I would expect it to remain as a reference on many shelves.' Bruce Rothschild, University of California, Los Angeles