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Discrete Mathematics with Applications

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ISBN-10: 0495391328

ISBN-13: 9780495391326

Edition: 4th 2011

Authors: Susanna S. Epp

List price: $355.95
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Book details

List price: $355.95
Edition: 4th
Copyright year: 2011
Publisher: Brooks/Cole
Publication date: 8/4/2010
Binding: Hardcover
Pages: 984
Size: 8.00" wide x 10.00" long x 1.55" tall
Weight: 4.466
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.

Speaking Mathematically
Variables
The Language of Sets
The Language of Relations and Functions
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
Predicates and Quantified Statements I
Predicatesand Quantified Statements II
Statements with 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
Indirect Argument: Two Classical Theorems
Application: Algorithms
Sequences, Mathematical Induction, and Recursion
Sequences
Mathematical Induction I
MathematicalInduction II
Strong Mathematical Induction and the Well-Ordering Principle
Application: Correctness of Algorithms
Defining Sequences Recursively
Solving Recurrence Relations by Iteration
Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
General Recursive Definitions and Structural Induction
Set Theory
Set Theory: Definitions and the Element Method of Proof
Set Identities
Disproofs and Algebraic Proofs
Boolean Algebras, Russell's Paradox, and the Halting Problem
Properties of Functions
Functions Defined on General Sets
One-to-one, Onto, Inverse Functions
Composition of Functions
Cardinality, Sizes of Infinity, and Applications to Computability
Properties of Relations
Relations on Sets (add material about relational databases)
Reflexivity, Symmetry, and Transitivity
Equivalence Relations
Modular Arithmetic with Applications to Cryptography
Partial Order Relations
Counting
Counting and Probability
The Multiplication Rule
Counting Elements of Disjoint Sets: The Addition Rule
The Pigeonhole Principle
Counting Subsets of a Set: Combinations. r-Combinations with Repetition Allowed
Pascal's Formula and the Binomial Theorem
Probability Axioms and Expected Value
Conditional Probability, Bayes' Formula, and Independent Events
Graphs and Trees
Graphs: An Introduction
Trails, Paths, and Circuits
Matrix Representations of Graphs
Isomorphisms of Graphs
Trees: Examples and Basic Properties
Rooted Trees
Spanning Trees and a Shortest Path Algorithm
Analyzing Algorithm Efficiency
Real-Valued Functions of a Real Variable and Their Graphs
O-, ?-, and ?-Notations
Application: Efficiency of Algorithms I. Exponential and Logarithmic Functions: Graphs and Orders
Application: Efficiency of Algorithms II
Regular Expressions and Finite State Automata
Formal Languages and Regular Expressions
Finite-State Automata
Simplifying Finite-State Automata