Book description
Discrete Mathematics provides an introduction to some of the fundamental concepts in modern mathematics. Abundant examples help explain the principles and practices of discrete mathematics. The book intends to cover material required by readers for whom mathematics is just a tool, as well as provide a strong foundation for mathematics majors. The vital role that discrete mathematics plays in computer science is strongly emphasized as well. The book is useful for students and instructors, and also software professionals.
Table of contents
 Cover
 Title Page
 Contents
 Dedication
 Preface

Proof Methods and Induction
 Formal Proofs
 Proofs and the Real World
 Propositional Reasoning Examples
 Proofs by Contradiction
 Proofs
 False Proofs
 Inductive Proofs
 More Simple Induction
 Tiling Problem
 Geometry
 Double Induction
 Strong Induction
 Tournaments
 Induction, Strong Induction, and Wellordering
 Structural Induction
 Induction and Recursive Algorithms

1. Symbolic Logic
 1.1 Introduction to Logic
 1.2 Boolean Expressions
 1.3 Construction of Boolean Expressions
 1.4 Meaning of Boolean Expressions
 1.5 Construction of Truth Tables
 1.6 Logical Equivalence
 1.7 DeMorgan’s Law
 1.8 Why Use Logical Equivalences
 1.9 Tautologies and Contradictions
 1.10 Implication and Biconditionals
 1.11 Logical Equivalences
 1.12 Another Equivalence
 1.13 Negation of Conditionals
 1.14 Variations on a Theme
 1.15 Translations
 1.16 Arguments
 1.17 Fallacies
 1.18 Valid Argument with a False Conclusion
 1.19 Contradiction Rule
 1.20 Applications of Boolean Expressions
 1.21 Logic Gates
 1.22 How to Construct Circuits
 1.23 How to Derive a Boolean Expression
 1.24 Creating a Circuit from Truth Tables
 1.25 Adders
 1.26 Predicate Calculus
 1.27 Boolean Formulas
 1.28 Understanding Quantifiers
 1.29 Negation of Quantifiers
 1.30 Vacuously True Statements
 1.31 Normal Forms in Propositional Logic
 1.32 Normal Forms in Predicate Logic
 1.33 The Resolution Principle
 1.34 Parenthesized Infix Notation and Polish Notation
 2. Set Theory
 3. Relations
 4. Functions and Recursion
 5. Algebraic Structures
 6. Graph Theory
 7. Counting

8. Combinatorics
 8.1 The Pigeonhole Principle
 8.2 Strong Pigeonholes
 8.3 Dilworth’s Theorem
 8.4 Problems
 8.5 Sets of the Same Size: Bijections
 8.6 Finite Sets
 8.7 InclusionExclusion
 8.8 Infinite Sets
 8.9 SchroderBernstein Theorem
 8.10 Countable Sets
 8.11 The Continuum
 8.12 Diagonal Arguments
 8.13 Set Theory Revisited
 8.14 Functions and Permutations
 9. Automata
 10. Program Verification
 11. Design of Algorithms
 Bibliography
 Copyright
Product information
 Title: Discrete Mathematics
 Author(s):
 Release date: November 2007
 Publisher(s): Pearson India
 ISBN: 9788131717943
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