Description

Features

• Comprehensive, accessible coverage of main topics in combinatorics:
• Provides students with accessible coverage of basic concepts and principles.
• Covers a wide range of topics:
• Dilworth's Theorem
• Partitions of integers
• Counting sequences and generating functions
• Extensive graph theory coverage

• A clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles.
• An excellent treatment of Polya's Counting Theorem that does not assume students have studied group theory.
• Many worked examples illustrate methods used.

New To This Edition

• A wealth of new exercises has been added to the this edition.
• Use of the term “combination” as it applies to a set has been de-emphasized; the author now uses the essentially equivalent term of “subset” for clarity. (In the case of multisets, the text continues to use “combination” versus the more cumbersome term “submultiset.”)
• A new section (Section 1.6) on mutually overlapping circles has been moved from Chapter 7 to illustrate some of the counting techniques covered in later chapters.
• Coverage of the pigeonhole principle and permutations and combinations has been reversed; Chapter 2 now covers permutations and combinations, with Chapter 3 covering the pigeonhole principle.
• Chapter 2 now contains a short section (Section 3.6) on finite probability.
• Chapter 3 now contains a proof of Ramsey’s theorem in the case of pairs as well as Pascal’s formula.
• An extensively revised Chapter 7 moves up generating functions and exponential generating functions to Sections 7.2 and 7.3, giving them a more central treatment.
• Section 8.3 on partition numbers has been expanded.
• Significant revisions to Chapter 9 (matchings in bipartite graphs) make it an interlude chapter on SDRs (the marriage and stable marriage problems), with the discussion on bipartite graphs removed.
• As a result, the introductory chapter on graph theory (Chapter 11) no longer assumes that bipartite graphs have been previously discussed.
• Coverage of more topics of graph theory and digraphs and networks has been reversed; Chapter 12 now covers more topics of graph theory and Chapter 13 now covers digraphs and networks.
• A new section on the matching number of a graph (Section 12.5) has been added where the basic SDR result in Chapter 9 is applied to bipartite graphs.
• Chapter 13 contains a new section revisiting matchings in bipartite graphs, some of which appears in Chapter 9 of the previous edition.

Table of Contents

1. What is Combinatorics?

1.1 Example: Perfect Covers of Chessboards

1.2 Example: Magic Squares

1.3 Example: The Four-Color Problem

1.4 Example: The Problem of the 36 Officers

1.5 Example: Shortest-Route Problem

1.6 Example: Mutually Overlapping Circles

1.7 Example: The Game of Nim

2. The Pigeonhole Principle

2.1 Pigeonhole Principle: Simple Form

2.2 Pigeonhole Principle: Strong Form

2.3 A Theorem of Ramsay

3. Permutations and Combinations

3.1 Four Basic Counting Principles

3.2 Permutations of Sets

3.3 Combinations of Sets

3.4 Permutations of Multisets

3.5 Combinations of Multisets

3.6 Finite Probability

4. Generating Permutations and Combinations

4.1 Generating Permutations

4.2 Inversions in Permutations

4.3 Generating Combinations

4.4 Generating r-Combinations

4.5 Partial Orders and Equivalence Relations

5. The Binomial Coefficients

5.1 Pascal's Formula

5.2 The Binomial Theorem

5.3 Unimodality of Binomial Coefficients

5.4 The Multinomial Theorem

5.5 Newton's Binomial Theorem

5.6 More on Partially Ordered Sets

6. The Inclusion-Exclusion Principle and Applications

6.1 The Inclusion-Exclusion Principle

6.2 Combinations with Repetition

6.3 Derangements

6.4 Permutations with Forbidden Positions

6.5 Another Forbidden Position Problem

6.6 Möbius Inversion

7. Recurrence Relations and Generating Functions

7.1 Some Number Sequences

7.2 Generating Functions

7.3 Exponential Generating Functions

7.4 Solving Linear Homogeneous Recurrence Relations

7.5 Nonhomogeneous Recurrence Relations

7.6 A Geometry Example

8. Special Counting Sequences

8.1 Catalan Numbers

8.2 Difference Sequences and Stirling Numbers

8.3 Partition Numbers

8.4 A Geometric Problem

8.5 Lattice Paths and Schröder Numbers

9. Systems of Distinct Representatives

9.1 General Problem Formulation

9.2 Existence of SDRs

9.3 Stable Marriages

10. Combinatorial Designs

10.1 Modular Arithmetic

10.2 Block Designs

10.3 Steiner Triple Systems

10.4 Latin Squares

11. Introduction to Graph Theory

11.1 Basic Properties

11.2 Eulerian Trails

11.3 Hamilton Paths and Cycles

11.4 Bipartite Multigraphs

11.5 Trees

11.6 The Shannon Switching Game

11.7 More on Trees

12. More on Graph Theory

12.1 Chromatic Number

12.2 Plane and Planar Graphs

12.3 A 5-color Theorem

12.4 Independence Number and Clique Number

12.5 Matching Number

12.6 Connectivity

13. Digraphs and Networks

13.1 Digraphs

13.2 Networks

13.3 Matching in Bipartite Graphs Revisited

14. Pólya Counting

14.1 Permutation and Symmetry Groups

14.2 Burnside's Theorem

Courses

Combinatorics  (Mathematics)

Allied Health Study Card, 2/E
Forshier
©2006  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321394747  |  ISBN-13: 9780321394743
Suggested retail price:  $4.00    Buy from myPearsonStoreNet price: $3.00  (What's this?)More Info

Basic Math Review Card, 2/E
Addison-Wesley
©2006  |  Pearson  |  Study Card; 6 pp  |  Instock
ISBN-10: 0321394763  |  ISBN-13: 9780321394767
Suggested retail price:  $4.00    Buy from myPearsonStoreNet price: $3.00  (What's this?)More Info

Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000  |  Pearson  |  Unknown / Other  |  Instock
ISBN-10: 0201716275  |  ISBN-13: 9780201716276
Suggested retail price:  $0.00Net price: $0.00  (What's this?)More Info

Concept Videos: Algebra
Addison-Wesley
©2008  |  Pearson  |  Multiple Media Package  |  Instock
ISBN-10: 0321517199  |  ISBN-13: 9780321517197
Suggested retail price:  $36.67Net price: $27.50  (What's this?)More Info

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008  |  Pearson  |  Multiple Media Package  |  Instock
ISBN-10: 032151758X  |  ISBN-13: 9780321517586
Suggested retail price:  $36.67Net price: $27.50  (What's this?)More Info

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997  |  Pearson  |  Paper; 195 pp  |  Instock
ISBN-10: 0136492037  |  ISBN-13: 9780136492030
Suggested retail price:  $47.80    Buy from myPearsonStoreNet price: $35.85  (What's this?)More Info

Graphing Calculator Tutorial CD
Addison-Wesley
©2006  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321357744  |  ISBN-13: 9780321357748
Suggested retail price:  $13.33    Buy from myPearsonStoreNet price: $10.00  (What's this?)More Info

Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000  |  Pearson  |  Paper  |  Instock
ISBN-10: 0321069188  |  ISBN-13: 9780321069184
Suggested retail price:  $36.67    Buy from myPearsonStoreNet price: $27.50  (What's this?)More Info

Prealgebra Review Workbook
Wheel
©2006  |  Pearson  |  Paper; 300 pp  |  Instock
ISBN-10: 0321473329  |  ISBN-13: 9780321473325
Suggested retail price:  $36.67    Buy from myPearsonStoreNet price: $27.50  (What's this?)More Info

Review of Algebra, A
Howard
©2002  |  Pearson  |  Paper; 224 pp  |  Instock
ISBN-10: 0201773473  |  ISBN-13: 9780201773477
Suggested retail price:  $36.67    Buy from myPearsonStoreNet price: $27.50  (What's this?)More Info

Spanish Basic Math Study Card
Leonarte
©2007  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321438582  |  ISBN-13: 9780321438584
Suggested retail price:  $4.00    Buy from myPearsonStoreNet price: $3.00  (What's this?)More Info

TestGen All-in-One 2005 Package
Addison-Wesley
©2005  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321334469  |  ISBN-13: 9780321334466
Suggested retail price:  $0.00Net price: $0.00  (What's this?)More Info

Back to top

Back to top

Give your students a choice! PearsonChoices products are designed to give your students more value and flexibility by letting them choose from a variety of text and media formats to best match their learning style and their budget.

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students, see the Packages Tab.

• Introductory Combinatorics, Coursesmart eTextbook
  Brualdi
  ©2010  |  Pearson  |  Electronic Book; 648 pp  |  Available
  ISBN-10: 0321640764  |  ISBN-13: 9780321640765
  Online purchase price: $55.99Brief Description  | 

  

  CourseSmart Textbooks Online is an exciting new choice for students looking to save money. As an alternative to purchasing the print textbook, students can subscribe to the same content online and save up to 50% off the suggested list price of the print text. With a CourseSmart etextbook, students can search the text, make notes online, print out reading assignments that incorporate lecture notes, and bookmark important passages for later review. For more information, or to subscribe to the CourseSmart eTextbook, visit www.coursesmart.com.

  More Info  |  Students, buy access
  

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students contact your Pearson Higher Education representative.