Softcover ISBN:  9781470472863 
Product Code:  TEXT/55.S 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781470453015 
Product Code:  TEXT/55.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Softcover ISBN:  9781470472863 
eBook: ISBN:  9781470453015 
Product Code:  TEXT/55.S.B 
List Price:  $144.00 $109.50 
MAA Member Price:  $118.35 $82.13 
AMS Member Price:  $111.45 $82.13 
Softcover ISBN:  9781470472863 
Product Code:  TEXT/55.S 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781470453015 
Product Code:  TEXT/55.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Softcover ISBN:  9781470472863 
eBook ISBN:  9781470453015 
Product Code:  TEXT/55.S.B 
List Price:  $144.00 $109.50 
MAA Member Price:  $118.35 $82.13 
AMS Member Price:  $111.45 $82.13 

Book DetailsAMS/MAA TextbooksVolume: 55; 2010; 390 pp
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are singlevariable calculus and familiarity with sets and basic proof techniques.
The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the endofsection exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.

Table of Contents

Chapters

Chapter 1. Principles of Combinatorics

Chapter 2. Distributions and Combinatorial Proofs

Chapter 3. Algebraic Tools

Chapter 4. Famous Number Families

Chapter 5. Counting Under Equivalence

Chapter 6. Combinatorics on Graphs

Chapter 7. Designs and Codes

Chapter 8. Partially Ordered Sets


Reviews

This is a wellwritten, readerfriendly, and selfcontained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about half of them come with hints.
M. Bona, Choice Magazine 
... The delineation of the topics is first rate—better than I have ever seen in any other book. ... CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book.
The UMAP Journal 
... [This book] is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. ... This book is the best candidate for a textbook in combinatorics that I have encountered.
Charles Ashbacher


RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are singlevariable calculus and familiarity with sets and basic proof techniques.
The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the endofsection exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.

Chapters

Chapter 1. Principles of Combinatorics

Chapter 2. Distributions and Combinatorial Proofs

Chapter 3. Algebraic Tools

Chapter 4. Famous Number Families

Chapter 5. Counting Under Equivalence

Chapter 6. Combinatorics on Graphs

Chapter 7. Designs and Codes

Chapter 8. Partially Ordered Sets

This is a wellwritten, readerfriendly, and selfcontained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about half of them come with hints.
M. Bona, Choice Magazine 
... The delineation of the topics is first rate—better than I have ever seen in any other book. ... CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book.
The UMAP Journal 
... [This book] is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. ... This book is the best candidate for a textbook in combinatorics that I have encountered.
Charles Ashbacher