Discrete and Combinatorial Mathematics / Edition 5

Paperback (Print)
Rent from BN.com
(Save 75%)
Est. Return Date: 07/28/2015
Buy Used
Buy Used from BN.com
(Save 37%)
Item is in good condition but packaging may have signs of shelf wear/aging or torn packaging.
Condition: Used – Good details
Used and New from Other Sellers
Used and New from Other Sellers
from $74.73
Usually ships in 1-2 business days
(Save 61%)
Other sellers (Paperback)
  • All (18) from $74.73   
  • New (8) from $145.43   
  • Used (10) from $74.73   


This fifth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.
Read More Show Less

Product Details

  • ISBN-13: 9780201726343
  • Publisher: Pearson
  • Publication date: 7/17/2003
  • Series: Featured Titles for Discrete Mathematics Series
  • Edition description: REV
  • Edition number: 5
  • Pages: 833
  • Sales rank: 767,860
  • Product dimensions: 8.30 (w) x 9.90 (h) x 1.50 (d)

Table of Contents


1. Fundamental Principles of Counting.

The Rules of Sum and Product.


Combinations: The Binomial Theorem.

Combinations with Repetition.

The Catalan Numbers (Optional).

Summary and Historical Review.

2. Fundamentals of Logic.

Basic Connectives and Truth Tables.

Logical Equivalence: The Laws of Logic.

Logical Implication: Rules of Inference.

The Use of Quantifiers.

Quantifiers, Definitions, and the Proofs of Theorems.

Summary and Historical Review.

3. Set Theory.

Sets and Subsets.

Set Operations and the Laws of Set Theory.

Counting and Venn Diagrams.

A First Word on Probability.

The Axioms of Probability (Optional).

Conditional Probability: Independence (Optional).

Discrete Random Variables (Optional).

Summary and Historical Review.

4. Properties of the Integers: Mathematical Induction.

The Well-Ordering Principle: Mathematical Induction.

Recursive Definitions.

The Division Algorithm: Prime Numbers.

The Greatest Common Divisor: The Euclidean Algorithm.

The Fundamental Theorem of Arithmetic.

Summary and Historical Review.

5. Relations and Functions.

Cartesian Products and Relations.

Functions: Plain and One-to-One.

Onto Functions: Stirling Numbers of the Second Kind.

Special Functions.

The Pigeonhole Principle.

Function Composition and Inverse Functions.

Computational Complexity.

Analysis of Algorithms.

Summary and Historical Review.

6. Languages: Finite State Machines.

Language: The Set Theory of Strings.

Finite State Machines: A First Encounter.

Finite State Machines: A Second Encounter.

Summary and Historical Review.

7. Relations: The Second Time Around.

Relations Revisited: Properties of Relations.

Computer Recognition: Zero-One Matrices and Directed Graphs.

Partial Orders: Hasse Diagrams.

Equivalence Relations and Partitions.

Finite State Machines: The Minimization Process.

Summary and Historical Review.


8. The Principle of Inclusion and Exclusion.

The Principle of Inclusion and Exclusion.

Generalizations of the Principle.

Derangements: Nothing Is in Its Right Place.

Rook Polynomials.

Arrangements with Forbidden Positions.

Summary and Historical Review.

9. Generating Functions.

Introductory Examples.

Definition and Examples: Calculational Techniques.

Partitions of Integers.

The Exponential Generating Functions.

The Summation Operator.

Summary and Historical Review.

10. Recurrence Relations.

The First-Order Linear Recurrence Relation.

The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients.

The Nonhomogeneous Recurrence Relation.

The Method of Generating Functions.

A Special Kind of Nonlinear Recurrence Relation (Optional).

Divide and Conquer Algorithms.

Summary and Historical Review.


11. An Introduction to Graph Theory.

Definitions and Examples.

Subgraphs, Complements, and Graph Isomorphism.

Vertex Degree: Euler Trails and Circuits.

Planar Graphs.

Hamilton Paths and Cycles.

Graph Coloring and Chromatic Polynomials.

Summary and Historical Review.

12. Trees.

Definitions, Properties, and Examples.

Rooted Trees.

Trees and Sorting.

Weighted Trees and Prefix Codes.

Biconnected Components and Articulation Points.

Summary and Historical Review.

13. Optimization and Matching.

Dijkstra's Shortest Path Algorithm.

Minimal Spanning Trees: The Algorithms of Kruskal and Prim.

Transport Networks: The Max-Flow Min-Cut Theorem.

Matching Theory.

Summary and Historical Review.


14. Rings and Modular Arithmetic.

The Ring Structure: Definition and Examples.

Ring Properties and Substructures.

The Integers Modulo n. Cryptology.

Ring Homomorphisms and Isomorphisms: The Chinese Remainder Theorem.

Summary and Historical Review.

15. Boolean Algebra and Switching Functions.

Switching Functions: Disjunctive and Conjunctive Normal Forms.

Gating Networks: Minimal Sums of Products: Karnaugh Maps.

Further Applications: Don't-Care Conditions.

The Structure of a Boolean Algebra (Optional).

Summary and Historical Review.

16. Groups, Coding Theory, and Polya's Theory of Enumeration.

Definition, Examples, and Elementary Properties.

Homomorphisms, Isomorphisms, and Cyclic Groups.

Cosets and Lagrange's Theorem.

The RSA Cipher (Optional).

Elements of Coding Theory.

The Hamming Metric.

The Parity-Check and Generator Matrices.

Group Codes: Decoding with Coset Leaders.

Hamming Matrices.

Counting and Equivalence: Burnside's Theorem.

The Cycle Index.

The Pattern Inventory: Polya's Method of Enumeration.

Summary and Historical Review.

17. Finite Fields and Combinatorial Designs.

Polynomial Rings.

Irreducible Polynomials: Finite Fields.

Latin Squares.

Finite Geometries and Affine Planes.

Block Designs and Projective Planes.

Summary and Historical Review.


Exponential and Logarithmic Functions.

Matrices, Matrix Operations, and Determinants.

Countable and Uncountable Sets.



Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)