Combinatorics: A Guided TourDavid R. Mazur
409 pp., hardcover, 2010. Series: MAA Textbooks
ISBN: 978-0-88385-762-5
November 18, 2009
Combinatorics: A Guided Tour
David R. Mazur
409 pp., hardcover, 2010. Series: MAA Textbooks
ISBN: 978-0-88385-762-5
Combinatorics is the mathematics of counting. More specifically, combinatorics is the area of mathematics that encompasses issues of enumeration, existence, and construction.
The book's material is presented via the artifice of a "guided tour": 350 questions offer checkpoints to make sure readers grasp the mathematics. These questions, moreover, prepare readers for more than 450 mathematical exercises spread throughout the eight chapters and numerous sections. Anecdotes, summaries, bibliographical information, and suggestions for further reading round out the tour.
Readers of the book should be familiar with single-variable calculus, sets and set notation, proof techniques, and basic modular arithmetic in order to be fully engaged in the topics and subject matter. Aside from self-study and use in a course in combinatorics, this book is recommended for second courses in discrete mathematics and for introductory graduate courses in applied mathematics.
Sample (p. 150)
A university has 120 incoming freshman that still have to be assigned to on-campus housing. The only remaining dorm holds 105 students and contains 42 doubles (rooms housing two students) and seven triples (three students). In how many ways can the university select 105 students to house in this dorm and then arrange those students into roommate pairs and triples, without yet assigning them to rooms?
In the previous exercise, suppose the university gets approval to house temporarily the remaining 15 students among the dorm's three lounges. Each lounge will house five students. How many ways are there for the university to assign all 120 students to rooms?
Contents:
Preface. Before You Go. 1. Principles of Combinatorics. 2.Distributions and Combinatorial Proofs. 3. Algebraic Tools. 4. Famous Number Families. 5. Counting Under Equivalence. 6. Combinatorics on Graphs. 7. Designs and Codes. 8. Partially Ordered Sets. Bibliography. Hints and Answers to Selected Exercises. List of Notation. Index
About the Author:
David R. Mazur (Western New England College, in Springfield, Mass.), who received his Ph.D. in mathematics from Johns Hopkins University in 1999, was a 2000-2001 Project NExT fellow. Mazur (dmazur@wnec.edu) now serves the MAA as a consultant to Project NExT and as a member of its Membership Committee. This is Mazur's first book. He will be doing his first book signing at the Joint Mathematics Meetings in San Francisco in January 2010.
Order Combinatorics: A Guided Tour from the MAA Bookstore or call 1.800.331.1622.
List: $64.95
MAA Member Price: $51.95