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 Well-ordering
- 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 Inclusion-Exclusion
- 8.8 Infinite Sets
- 8.9 Schroder-Bernstein 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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