An Invitation to Combinatorics

A conversational introduction to combinatorics for upper undergraduates, emphasizing problem solving and active student participation.

Shahriar Shahriari (Author)

9781108476546, Cambridge University Press

Hardback, published 22 July 2021

628 pages
25.3 x 19.4 x 3.1 cm, 1.51 kg

'One of the major attractions of this textbook is the writing style - it is designed to be very readable, as though the author were having a conversation with the reader. The result is a text which feels engaging - a quality which is sure to be of great benefit to undergraduate students.' Audie Warren, zbMATH

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

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.

Subject Areas: Maths for computer scientists [UYAM], Combinatorics & graph theory [PBV], Discrete mathematics [PBD]