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9780618415380

Discrete Mathematics

by
  • ISBN13:

    9780618415380

  • ISBN10:

    0618415386

  • Format: Hardcover
  • Copyright: 2008-02-05
  • Publisher: Cengage Learning
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List Price: $299.95

Summary

Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for students who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory.

Table of Contents

Representing Numbers
Proofs
Logic and Sets
Statement Forms and Logical Equivalences
Set Notation
Quantifiers
Set Operations and Identities
Valid Arguments
Review Problems
Basic Proof Writing
Direct Demonstration
General Demonstration (Part 1)
General Demonstration (Part 2)
Indirect Arguments
Splitting into Cases
Review Problems
Elementary Number Theory
Divisors
Consequences of Well-Ordering
Euclid's Algorithm and Lemma
Rational Numbers
Irrational Numbers
Modular Arithmetic
Review Problems
Indexed by Integers
Sequences, Indexing, and Recursion
Sigma Notation
Mathematical Induction, an Introduction
Induction and Summations
Strong Induction
The Binomial Theorem
Review Problems
Relations
General Relations
Special Relations on Sets
Basics of Functions
Special Functions
General Set Constructions
Cardinality
Review Problems
Combinatorics
Basic Counting
The Multiplication Principle
Permutations and Combinations
Addition and Subtraction
Probability
Applications of Combinations
Correcting for Overcounting
Review Problems
More Counting
Inclusion-Exclusion
Multinomial Coefficients
Generating Functions
Counting Orbits
Combinatorial Arguments
Review Problems
Basic Graph Theory
Motivation and Introduction
Matrices and Special Graphs
Isomorphisms
Invariants
Directed Graphs and Markov Chains
Review Problems
Graph Properties
Connectivity
Euler Circuits
Hamiltonian Cycles
Planar Graphs
Chromatic Number
Review Problems
Trees and Algorithms
Trees
Search Trees
Weighted Trees
Analysis of Algorithms (Part 1)
Analysis of Algorithms (Part 2)
Review Problems
Assumed Properties of Z and R
Pseudocode
Table of Contents provided by Publisher. All Rights Reserved.

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