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.
- Promotes discovery, active learning and collaboration with ten mini-projects, warm-up problems in every section, thought-provoking opening chapter problems, and a conversational tone
- Allows students to work their way up to the most difficult combinatorics exercises by splitting them up into several smaller problems or addressing a single problem with many steps
- Helps students work out the 1200+ problems and familiarize themselves with well-written solutions by including 256 hints, 181 short answers and 142 complete solutions in the back of the book
- Includes 'Open Problems and Conjectures' sections that invite the students to explore cutting-edge research in the field
- Emphasizes the global origins of combinatorics with historical asides and alternative naming of some familiar mathematical objects
- Serves as a text for a one-semester upper-undergraduate course
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Reviews & endorsements
'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
'Shahriari's voice as an experienced classroom teacher shines through in this brilliantly crafted student-friendly text. Each mini-project provides a guided exploration of an interesting topic in combinatorics. These, together with the plethora of interesting exercises, help the student to build problem-solving muscle and to experience the joy of mathematical discovery.' Jamie Pommersheim, Reed College
'From well-chosen motivating problems in the introduction to deeper material near the book's conclusion, Shahriari invites students encountering combinatorics systematically for the first time to think, to build, and to play. His warm writing style and cross-cultural approach to core topics of the field are sure to engage readers from many backgrounds and levels of preparation.' Joshua Cooper, University of South Carolina
'This book is a mathematically rigorous introductory textbook on combinatorics. It contains an excellent range of problems and exercises that will help students practice and learn the material. It also lists open questions in combinatorics so students can see that the field continues to develop. The really special feature of this book is a lovely collection of mini-projects that let students explore a variety of topics and deepen their understanding.' David Auckly, Kansas State University
'I highly recommend this text. Among its most interesting, unusual, and valuable features, one finds a long list of collaborative mini-projects for students to work on in groups, together with other problems to work on individually; nice historical asides, including references to the work of non-Western mathematicians; and a very accessible conversational style. It fits well with discovery-style or problem-oriented courses on the subject.' William Monty McGovern, University of Washington
'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
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Product details
- Date Published: July 2021
- format: Hardback
- isbn: 9781108476546
- length: 628 pages
- dimensions: 253 x 194 x 31 mm
- weight: 1.51kg
- availability: In stock
Table of Contents
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.
Look Inside
Author
Shahriar Shahriari, Pomona College, California
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.