Discrete Mathematics with Applications

ISBN-10: 0534359450

ISBN-13: 9780534359454

Edition: 3rd 2004

Authors: Susanna S. Epp

List price: $391.95
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Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.
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Book details

List price: $391.95
Edition: 3rd
Copyright year: 2004
Publisher: Brooks/Cole
Publication date: 12/22/2003
Binding: Hardcover
Pages: 928
Size: 8.00" wide x 9.75" long x 1.25" tall
Weight: 3.124
Language: English

Susanna S. Epp received her Ph.D. in 1968 from the University of Chicago, taught briefly at Boston University and the University of Illinois at Chicago, and is currently Vincent DePaul Professor of Mathematical Sciences at DePaul University. After initial research in commutative algebra, she became interested in cognitive issues associated with teaching analytical thinking and proof and has published a number of articles and given many talks related to this topic. She has also spoken widely on discrete mathematics and has organized sessions at national meetings on discrete mathematics instruction. In addition to DISCRETE MATHEMATICS WITH APPLICATION, she is co-author of PRECALCULUS AND DISCRETE MATHEMATICS, which was developed as part of the University of Chicago School Mathematics Project. Epp co-organized an international symposium on teaching logical reasoning, sponsored by the Institute for Discrete Mathematics and Theoretical Computer Science (DIMACS), and she was an associate editor of MATHEMATICS MAGAZINE from 1991 to 2001. Long active in the Mathematical Association of America (MAA), she is a co-author of the new set of curricular guidelines for undergraduate mathematics programs: CUPM CURRICULUM GUIDE 2004.

The Logic of Compound Statements
Logical Form and Logical Equivalence
Conditional Statements
Valid and Invalid Arguments
Application: Digital Logic Circuits
Application: Number Systems and Circuits for Addition
The Logic of Quantified Statements
Introduction to Predicates and Quantified Statements I
Introduction to Predicates and Quantified Statements II
Statements Containing Multiple Quantifiers
Arguments with Quantified Statements
Elementary Number Theory and Methods of Proof
Direct Proof and Counterexample I: Introduction
Direct Proof and Counterexample II: Rational Numbers
Direct Proof and Counterexample III: Divisibility
Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem
Direct Proof and Counterexample V: Floor and Ceiling
Indirect Argument: Contradiction and Contraposition
Two Classical Theorems
Application: Algorithms
Sequences and Mathematical Induction
Mathematical Induction I
Mathematical Induction II
Strong Mathematical Induction and the Well-Ordering Principle
Application: Correctness of Algorithms
Set Theory
Basic Definitions of Set Theory
Properties of Sets
Disproofs, Algebraic Proofs, and Boolean Algebras
Russell's Paradox and the Halting Problem
Counting and Probability
Possibility Trees and the Multiplication Rule
Counting Elements of Disjoint Sets: The Addition Rule
Counting Subsets of a Set: Combinations
R-Combinations with Repetition Allowed
The Algebra of Combinations
The Binomial Theorem
Probability Axioms and Expected Value
Conditional Probability, Bayes' Formula, and Independent Events
Functions Defined on General Sets
One-to-One and Onto, Inverse Functions
Application: The Pigeonhole Principle
Composition of Functions
Cardinality with Applications to Computability
Recursively Defined Sequences
Solving Recurrence Relations by Iteration
Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
General Recursive Definitions
The Efficiency of Algorithms
Real-Valued Functions of a Real Variable and Their Graphs
O-, Omega-, and Theta-Notations
Application: Efficiency of Algorithms I
Exponential and Logarithmic Functions: Graphs and Orders
Application: Efficiency of Algorithms II
Relations on Sets
Reflexivity, Symmetry, and Transitivity
Equivalence Relations
Modular Arithmetic with Applications to Cryptography
Partial Order Relations
Graphs and Trees
Graphs: An Introduction
Paths and Circuits
Matrix Representations of Graphs
Isomorphisms of Graphs
Spanning Trees
Finite State Automata and Applications
Finite-State Automata
Application: Regular Expressions
Finite-State Automata
Simplifying Finite-State Automata
Properties of the Real Numbers
Solutions and Hints to Selected Exercises
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