9780321305152

Discrete Mathematics

by ; ; ;
  • ISBN13:

    9780321305152

  • ISBN10:

    0321305159

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 11/18/2005
  • Publisher: Pearson
  • View Upgraded Edition

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $59!
    Your order must be $59 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • We Buy This Book Back!
    In-Store Credit: $42.00
    Check/Direct Deposit: $40.00
List Price: $193.80 Save up to $125.97
  • Rent Book $67.83
    Add to Cart Free Shipping

    TERM
    PRICE
    DUE

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
  • The Used and Rental copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

The strong algorithmic emphasis ofDiscrete Mathematicsis independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students.Algorithms are presented in English, eliminating the need for knowledge of a particular programming language. Computational and algorithmic exercise sets follow each chapter section and supplementary exercises and computer projects are included in the end-of-chapter material. This Fifth Edition features a new Chapter 3 covering matrix codes, error correcting codes, congruence, Euclidean algorithm and Diophantine equations, and the RSA algorithm.MARKET: Intended for use in a one-semester introductory course in discrete mathematics.

Table of Contents

Preface xi
To the Student xvii
An Introduction to Combinatorial Problems and Techniques
1(40)
The Time to Complete a Project
2(8)
A Matching Problem
10(6)
A Knapsack Problem
16(7)
Algorithms and Their Efficiency
23(18)
Historical Notes
35(2)
Supplementary Exercises
37(2)
Computer Projects
39(1)
Suggested Readings
40(1)
Sets, Relations, and Functions
41(58)
Set Operations
41(6)
Equivalence Relations
47(7)
Partial Ordering Relations
54(11)
Functions
65(11)
Mathematical Induction
76(8)
Applications
84(15)
Historical Notes
93(2)
Supplementary Exercises
95(3)
Computer Projects
98(1)
Suggested Readings
98(1)
Coding Theory
99(55)
Congruence
100(6)
The Euclidean Algorithm
106(7)
The RSA Method
113(9)
Error-Detecting and Error-Correcting Codes
122(10)
Matrix Codes
132(8)
Matrix Codes that Correct All Single-Digit Errors
140(14)
Historical Notes
147(2)
Supplementary Exercises
149(3)
Computer Projects
152(1)
Suggested Readings
153(1)
Graphs
154(74)
Graphs and Their Representations
154(10)
Paths and Circuits
164(17)
Shortest Paths and Distance
181(12)
Coloring a Graph
193(9)
Directed Graphs and Multigraphs
202(26)
Historical Notes
219(1)
Supplementary Exercises
220(6)
Computer Projects
226(1)
Suggested Readings
227(1)
Trees
228(85)
Properties of Trees
228(10)
Spanning Trees
238(15)
Depth-First Search
253(13)
Rooted Trees
266(8)
Binary Trees and Traversals
274(13)
Optimal Binary Trees and Binary Search Trees
287(26)
Historical Notes
306(2)
Supplementary Exercises
308(3)
Computer Projects
311(1)
Suggested Readings
312(1)
Matching
313(45)
Systems of Distinct Representatives
313(6)
Matchings in Graphs
319(8)
A Matching Algorithm
327(10)
Applications of the Algorithm
337(9)
The Hungarian Method
346(12)
Historical Notes
354(1)
Supplementary Exercises
355(2)
Computer Projects
357(1)
Suggested Readings
357(1)
Network Flows
358(44)
Flows and Cuts
358(11)
A Flow Augmentation Algorithm
369(13)
The Max-Flow Min-Cut Theorem
382(7)
Flows and Matchings
389(13)
Historical Notes
397(1)
Supplementary Exercises
397(3)
Computer Projects
400(1)
Suggested Readings
401(1)
Counting Techniques
402(56)
Pascal's Triangle and the Binomial Theorem
402(4)
Three Fundamental Principles
406(10)
Permutations and Combinations
416(5)
Arrangements and Selections with Repetitions
421(7)
Probability
428(6)
The Principle of Inclusion-Exclusion
434(11)
Generating Permutations and r-Combinations
445(13)
Historical Notes
452(1)
Supplementary Exercises
453(3)
Computer Projects
456(1)
Suggested Readings
457(1)
Recurrence Relations and Generating Functions
458(71)
Recurrence Relations
458(12)
The Method of Iteration
470(12)
Linear Difference Equations with Constant Coefficients
482(12)
Analyzing the Efficiency of Algorithms with Recurrence Relations
494(12)
Counting with Generating Functions
506(7)
The Algebra of Generating Functions
513(16)
Historical Notes
523(1)
Supplementary Exercises
524(3)
Computer Projects
527(1)
Suggested Readings
528(1)
Combinatorial Circuits and Finite State Machines
529(45)
Logical Gates
529(9)
Creating Combinatorial Circuits
538(8)
Karnaugh Maps
546(14)
Finite State Machines
560(14)
Historical Notes
569(1)
Supplementary Exercises
570(3)
Computer Projects
573(1)
Suggested Readings
573(1)
A. AN INTRODUCTION TO LOGIC AND PROOF
574(23)
A.1 Statements and Connectives
574(9)
A.2 Logical Equivalence
583(4)
A.3 Methods of Proof
587(10)
Historical Notes
593(1)
Supplementary Exercises
594(2)
Suggested Readings
596(1)
B. MATRICES
597(10)
Historical Notes
604(3)
C. THE ALGORITHMS IN THIS BOOK
607(6)
Bibliography 613(5)
Answers to Odd-Numbered Exercises 618(40)
Photo Credits 658(1)
Index 659

Rewards Program

Write a Review