issuhub.com

Schaum's Outline of Discrete Mathematics, Third Edition (Schaum's Outlines)

(Martin Jones) #1

  • CHAPTER 1 Set Theory

    • 1.1Introduction

    • 1.2Sets and Elements, Subsets

    • 1.3Venn Diagrams

    • 1.4Set Operations

    • 1.5Algebra of Sets, Duality

    • 1.6Finite Sets, Counting Principle

    • 1.7Classes of Sets, Power Sets, Partitions

    • 1.8Mathematical Induction

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 2 Relations

    • 2.1Introduction

    • 2.2Product Sets

    • 2.3Relations

    • 2.4Pictorial Representatives of Relations

    • 2.5Composition of Relations

    • 2.6Types of Relations

    • 2.7Closure Properties

    • 2.8Equivalence Relations

    • 2.9Partial Ordering Relations

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 3 Functions and Algorithms

    • 3.1Introduction

    • 3.2Functions

    • 3.3One-to-One, Onto, and Invertible Functions

    • 3.4Mathematical Functions, Exponential and Logarithmic Functions

    • 3.5Sequences, Indexed Classes of Sets

    • 3.6Recursively Defined Functions

    • 3.7Cardinality

    • 3.8Algorithms and Functions

    • 3.9Complexity of Algorithms

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 4 Logic and Propositional Calculus viii CONTENTS

    • 4.1Introduction

    • 4.2Propositions and Compound Statements

    • 4.3Basic Logical Operations

    • 4.4Propositions and Truth Tables

    • 4.5Tautologies and Contradictions

    • 4.6Logical Equivalence

    • 4.7Algebra of Propositions

    • 4.8Conditional and Biconditional Statements

    • 4.9Arguments

    • 4.10Propositional Functions, Quantifiers

    • 4.11Negation of Quantified Statements

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 5 Techniques of Counting

    • 5.1Introduction

    • 5.2Basic Counting Principles

    • 5.3Mathematical Functions

    • 5.4Permutations

    • 5.5Combinations

    • 5.6The Pigeonhole Principle

    • 5.7The Inclusion–Exclusion Principle

    • 5.8Tree Diagrams

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 6 Advanced Counting Techniques, Recursion

    • 6.1Introduction

    • 6.2Combinations with Repetitions

    • 6.3Ordered and Unordered Partitions

    • 6.4Inclusion–Exclusion Principle Revisited

    • 6.5Pigeonhole Principle Revisited

    • 6.6Recurrence Relations

    • 6.7Linear Recurrence Relations with Constant Coefficients

      • Relations 6.8Solving Second-Order Homogeneous Linear Recurrence



    • 6.9Solving General Homogeneous Linear Recurrence Relations

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 7 Probability

    • 7.1Introduction

    • 7.2Sample Space and Events

    • 7.3Finite Probability Spaces

    • 7.4Conditional Probability

    • 7.5Independent Events

    • 7.6Independent Repeated Trials, Binomial Distribution

    • 7.7Random Variables

    • 7.8Chebyshev’s Inequality, Law of Large Numbers CONTENTS ix

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 8 Graph Theory

    • 8.1Introduction, Data Structures

    • 8.2Graphs and Multigraphs

    • 8.3Subgraphs, Isomorphic and Homeomorphic Graphs

    • 8.4Paths, Connectivity

    • 8.5Traversable and Eulerian Graphs, Bridges of Königsberg

    • 8.6Labeled and Weighted Graphs

    • 8.7Complete, Regular, and Bipartite Graphs

    • 8.8Tree Graphs

    • 8.9Planar Graphs

    • 8.10Graph Colorings

    • 8.11Representing Graphs in Computer Memory

    • 8.12Graph Algorithms

    • 8.13Traveling-Salesman Problem

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 9 Directed Graphs

    • 9.1Introduction

    • 9.2Directed Graphs

    • 9.3Basic Definitions

    • 9.4Rooted Trees

    • 9.5Sequential Representation of Directed Graphs

    • 9.6Warshall’s Algorithm, Shortest Paths

    • 9.7Linked Representation of Directed Graphs

    • 9.8Graph Algorithms: Depth-First and Breadth-First Searches

    • 9.9Directed Cycle-Free Graphs, Topological Sort

    • 9.10Pruning Algorithm for Shortest Path

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 10 Binary Trees

    • 10.1Introduction

    • 10.2Binary Trees

    • 10.3Complete and Extended Binary Trees

    • 10.4Representing Binary Trees in Memory

    • 10.5Traversing Binary Trees

    • 10.6Binary Search Trees

    • 10.7Priority Queues, Heaps

    • 10.8Path Lengths, Huffman’s Algorithm

    • 10.9General (Ordered Rooted) Trees Revisited

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 11 Properties of the Integers x CONTENTS

    • 11.1Introduction

    • 11.2Order and Inequalities, Absolute Value

    • 11.3Mathematical Induction

    • 11.4Division Algorithm

    • 11.5Divisibility, Primes

    • 11.6Greatest Common Divisor, Euclidean Algorithm

    • 11.7Fundamental Theorem of Arithmetic

    • 11.8Congruence Relation

    • 11.9Congruence Equations

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 12 Languages, Automata, Grammars

    • 12.1Introduction

    • 12.2Alphabet, Words, Free Semigroup

    • 12.3Languages

    • 12.4Regular Expressions, Regular Languages

    • 12.5Finite State Automata

    • 12.6Grammars

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 13 Finite State Machines and Turing Machines

    • 13.1Introduction

    • 13.2Finite State Machines

    • 13.3Gödel Numbers

    • 13.4Turing Machines

    • 13.5Computable Functions

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 14 Ordered Sets and Lattices

    • 14.1Introduction

    • 14.2Ordered Sets

    • 14.3Hasse Diagrams of Partially Ordered Sets

    • 14.4Consistent Enumeration

    • 14.5Supremum and Infimum

    • 14.6Isomorphic (Similar) Ordered Sets

    • 14.7Well-Ordered Sets

    • 14.8Lattices

    • 14.9Bounded Lattices

    • 14.10Distributive Lattices

    • 14.11Complements, Complemented Lattices

    • SolvedProblems

    • SupplementaryProblems



  • CHAPTER 15 Boolean Algebra CONTENTS xi

    • 15.1Introduction

    • 15.2Basic Definitions

    • 15.3Duality

    • 15.4Basic Theorems

    • 15.5Boolean Algebras as Lattices

    • 15.6Representation Theorem

    • 15.7Sum-of-Products Form for Sets

    • 15.8Sum-of-Products Form for Boolean Algebras

    • 15.9Minimal Boolean Expressions, Prime Implicants

    • 15.10Logic Gates and Circuits

    • 15.11Truth Tables, Boolean Functions

    • 15.12Karnaugh Maps

    • SolvedProblems

    • SupplementaryProblems



  • APPENDIX A Vectors and Matrices

    • A.1Introduction

    • A.2Vectors

    • A.3Matrices

    • A.4Matrix Addition and Scalar Multiplication

    • A.5Matrix Multiplication

    • A.6Transpose

    • A.7Square Matrices

    • A.8Invertible (Nonsingular) Matrices, Inverses

    • A.9Determinants

    • A.10Elementary Row Operations, Gaussian Elimination (Optional)

    • A.11Boolean (Zero-One) Matrices

    • SolvedProblems

    • SupplementaryProblems



  • APPENDIX B Algebraic Systems

    • B.1Introduction

    • B.2Operations

    • B.3Semigroups

    • B.4Groups

    • B.5Subgroups, Normal Subgroups, and Homomorphisms

    • B.6Rings, Internal Domains, and Fields

    • B.7Polynomials Over a Field

    • SolvedProblems

    • SupplementaryProblems

    • Index



Free download pdf
Get our desktop app
Company
Features
Documentation
Resources
© ISSUHUB. 2024. All rights reserved.