9780130652478

Discrete Mathematics

by ;
  • ISBN13:

    9780130652478

  • ISBN10:

    0130652474

  • Edition: 5th
  • Format: Paperback
  • Copyright: 8/21/2002
  • Publisher: Pearson

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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 Rental copy of this book is 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

Key Benefit:This book presents a sound mathematical treatment that increases smoothly in sophistication.Key Topics:The book presents utility-grade discrete math tools so that any reader can understand them, use them, and move on to more advanced mathematical topics.Market:A handy reference for computer scientists.

Table of Contents

Preface to the Fifth Edition xi
To the Student Especially xv
Sets, Sequences, and Functions
1(49)
Some Warm-up Questions
1(6)
Factors and Multiples
7(9)
Office Hours
15(1)
Some Special Sets
16(6)
Set Operations
22(6)
Functions
28(6)
Sequences
34(5)
Properties of Functions
39(11)
Office Hours
46(2)
Supplementary Exercises
48(2)
Elementary Logic
50(45)
Informal Introduction
50(8)
Propositional Calculus
58(8)
Getting Started with Proofs
66(5)
Methods of Proof
71(6)
Office Hours
76(1)
Logic in Proofs
77(9)
Analysis of Arguments
86(9)
Supplementary Exercises
94(1)
Relations
95(33)
Relations
95(5)
Digraphs and Graphs
100(6)
Matrices
106(6)
Equivalence Relations and Partitions
112(7)
The Division Algorithm and Integers Mod p
119(9)
Supplementary Exercises
127(1)
Induction and Recursion
128(53)
Loop Invariants
128(9)
Mathematical Induction
137(8)
Office Hours
144(1)
Big-Oh Notation
145(8)
Recursive Definitions
153(7)
Recurrence Relations
160(7)
More Induction
167(4)
The Euclidean Algorithm
171(10)
Supplementary Exercises
179(2)
Counting
181(44)
Basic Counting Techniques
181(8)
Elementary Probability
189(8)
Inclusion-Exclusion and Binomial Methods
197(7)
Counting and Partitions
204(9)
Office Hours
212(1)
Pigeon-Hole Principle
213(12)
Supplementary Exercises
220(5)
Introduction to Graphs and Trees
225(44)
Graphs
225(7)
Edge Traversal Problems
232(7)
Trees
239(5)
Rooted Trees
244(7)
Vertex Traversal Problems
251(6)
Minimum Spanning Trees
257(12)
Supplementary Exercises
266(3)
Recursion, Trees, and Algorithms
269(49)
General Recursion
269(8)
Recursive Algorithms
277(9)
Depth-First Search Algorithms
286(12)
Polish Notation
298(6)
Weighted Trees
304(14)
Supplementary Exercises
315(3)
Digraphs
318(31)
Digraphs Revisited
318(7)
Weighted Digraphs and Scheduling Networks
325(8)
Office Hours
333(1)
Digraph Algorithms
333(16)
Supplementary Exercises
347(2)
Discrete Probability
349(40)
Independence in Probability
349(10)
Random Variables
359(7)
Expectation and Standard Deviation
366(8)
Probability Distributions
374(15)
Supplementary Exercises
387(2)
Boolean Algebra
389(35)
Boolean Algebras
389(9)
Boolean Expressions
398(7)
Logic Networks
405(7)
Karnaugh Maps
412(5)
Isomorphisms of Boolean Algebras
417(7)
Supplementary Exercises
422(2)
More on Relations
424(38)
Partially Ordered Sets
424(9)
Special Orderings
433(6)
Multiplication of Matrices
439(7)
Properties of General Relations
446(6)
Closures of Relations
452(10)
Supplementary Exercises
459(3)
Algebraic Structures
462(53)
Groups Acting on Sets
462(8)
Fixed Points and Subgroups
470(6)
Counting Orbits
476(11)
Group Homomorphisms
487(8)
Semigroups
495(6)
Other Algebraic Systems
501(14)
Supplementary Exercises
512(3)
Predicate Calculus and Infinite Sets
515(21)
Quantifiers and Predicates
515(7)
Elementary Predicate Calculus
522(5)
Infinite Sets
527(9)
Supplementary Exercises
534(2)
Dictionary 536(2)
Answers and Hints 538(69)
Index 607

Excerpts

In writing this book we have had in mind both computer science students and mathematics majors. We have aimed to make our account simple enough that these students can learn it and complete enough that they won't have to learn it again. The most visible changes in this edition are the 274 new supplementary exercises and the new chapters on probability and on algebraic structures. The supplementary exercises, which have complete answers in the back of the book, ask more than 700 separate questions. Together with the many end-of-section exercises and the examples throughout the text, these exercises let students practice using the material they are studying. One of our main goals is the development of mathematical maturity. Our presentation starts with an intuitive approach that becomes more and more rigorous as the students' appreciation for proofs and their skill at building them increase. Our account is careful but informal. As we go along, we illustrate the way mathematicians attack problems, and we show the power of an abstract approach. We and our colleagues at Oregon have used this material successfully for many years to teach students who have a standard precalculus background, and we have found that by the end of two quarters they are ready for upperclass work in both computer science and mathematics. The math majors have been introduced to the mathematics culture, and the computer science students have been equipped to look at their subject from both mathematical and operational perspectives. Every effort has been made to avoid duplicating the content of mainstream computer science courses, but we are aware that most of our readers will be coming in contact with some of the same material in their other classes, and we have tried to provide them with a clear,mathematicalview of it. An example of our approach can be seen first in Chapter 4, where we give a careful account of while loops. We base our discussion of mathematical induction on these loops, and also, in Chapter 4 and subsequently, show how to use them to design and verify a number of algorithms. We have deliberately stopped short of looking at implementation details for our algorithms, but we have provided most of them with time complexity analyses. We hope in this way to develop in the reader the habit of automatically considering the running time of any algorithm. In, addition, our analyses illustrate the use of some of the basic tools we have been developing for estimating efficiency. The overall outline of the book is essentially that of the fourth edition, with the addition of two new chapters and a large number of supplementary exercises. The first four chapters contain what we regard as the core material of any serious discrete mathematics course. These topics can readily be covered in a quarter. A semester course can add combinatorics and some probability or can pick up graphs, trees, and recursive algorithms. We have retained some of the special features of previous editions, such as the development of mathematical induction from a study of while loop invariants, but we have also looked for opportunities to improve the presentation, sometimes by changing notation. We have gone through the book section by section looking for ways to provide more motivation, with the result that many sections now begin where they used to end, in the sense that the punch lines now appear first as questions or goals that get resolved by the end of the section. We have added another "Office Hours" section at the end of Chapter 1, this one emphasizing the importance of learning definitions and notation. These sections, which we introduced in the fourth edition, allow us to step back a bit from our role as text authors to address the kinds of questions that our own students have Asked. They give us a chance to suggest how to study the material and focus on what's important. You may want to reinforce our words, or you may wa

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