Sign in  |  Register
Advanced search
Publication Cover

CITATION

Lipschutz, Seymour and Lipson, Marc. Schaum's Outline of Discrete Mathematics, Revised Third Edition. US: McGraw-Hill, 2009.

Schaum's Outline of Discrete Mathematics, Revised Third Edition

Authors: Seymour Lipschutz and Marc Lipson

Published:  August 2009

eISBN: 9780071615877 0071615873 | ISBN: 9780071615860
Open eBook
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Chapter 1 Set Theory
  • 1.1 Introduction
  • 1.2 Sets and Elements, Subsets
  • 1.3 Venn Diagrams
  • 1.4 Set Operations
  • 1.5 Algebra of Sets, Duality
  • 1.6 Finite Sets, Counting Principle
  • 1.7 Classes of Sets, Power Sets, Partitions
  • 1.8 Mathematical Induction
  • Solved Problems
  • Supplementary Problems
  • Chapter 2 Relations
  • 2.1 Introduction
  • 2.2 Product Sets
  • 2.3 Relations
  • 2.4 Pictorial Representatives of Relations
  • 2.5 Composition of Relations
  • 2.6 Types of Relations
  • 2.7 Closure Properties
  • 2.8 Equivalence Relations
  • 2.9 Partial Ordering Relations
  • Solved Problems
  • Supplementary Problems
  • Chapter 3 Functions and Algorithms
  • 3.1 Introduction
  • 3.2 Functions
  • 3.3 One-to-One, Onto, and Invertible Functions
  • 3.4 Mathematical Functions, Exponential and Logarithmic Functions
  • 3.5 Sequences, Indexed Classes of Sets
  • 3.6 Recursively Defined Functions
  • 3.7 Cardinality
  • 3.8 Algorithms and Functions
  • 3.9 Complexity of Algorithms
  • Solved Problems
  • Supplementary Problems
  • Chapter 4 Logic and Propositional Calculus
  • 4.1 Introduction
  • 4.2 Propositions and Compound Statements
  • 4.3 Basic Logical Operations
  • 4.4 Propositions and Truth Tables
  • 4.5 Tautologies and Contradictions
  • 4.6 Logical Equivalence
  • 4.7 Algebra of Propositions
  • 4.8 Conditional and Biconditional Statements
  • 4.9 Arguments
  • 4.10 Propositional Functions, Quantifiers
  • 4.11 Negation of Quantified Statements
  • Solved Problems
  • Supplementary Problems
  • Chapter 5 Techniques of Counting
  • 5.1 Introduction
  • 5.2 Basic Counting Principles
  • 5.3 Mathematical Functions
  • 5.4 Permutations
  • 5.5 Combinations
  • 5.6 The Pigeonhole Principle
  • 5.7 The Inclusion–Exclusion Principle
  • 5.8 Tree Diagrams
  • Solved Problems
  • Supplementary Problems
  • Chapter 6 Advanced Counting Techniques, Recursion
  • 6.1 Introduction
  • 6.2 Combinations with Repetitions
  • 6.3 Ordered and Unordered Partitions
  • 6.4 Inclusion–Exclusion Principle Revisited
  • 6.5 Pigeonhole Principle Revisited
  • 6.6 Recurrence Relations
  • 6.7 Linear Recurrence Relations with Constant Coefficients
  • 6.8 Solving Second-Order Homogeneous Linear Recurrence Relations
  • 6.9 Solving General Homogeneous Linear Recurrence Relations
  • Solved Problems
  • Supplementary Problems
  • Chapter 7 Probability
  • 7.1 Introduction
  • 7.2 Sample Space and Events
  • 7.3 Finite Probability Spaces
  • 7.4 Conditional Probability
  • 7.5 Independent Events
  • 7.6 Independent Repeated Trials, Binomial Distribution
  • 7.7 Random Variables
  • 7.8 Chebyshev’s Inequality, Law of Large Numbers
  • Solved Problems
  • Supplementary Problems
  • Chapter 8 Graph Theory
  • 8.1 Introduction, Data Structures
  • 8.2 Graphs and Multigraphs
  • 8.3 Subgraphs, Isomorphic and Homeomorphic Graphs
  • 8.4 Paths, Connectivity
  • 8.5 Traversable and Eulerian Graphs, Bridges of Königsberg
  • 8.6 Labeled and Weighted Graphs
  • 8.7 Complete, Regular, and Bipartite Graphs
  • 8.8 Tree Graphs
  • 8.9 Planar Graphs
  • 8.10 Graph Colorings
  • 8.11 Representing Graphs in Computer Memory
  • 8.12 Graph Algorithms
  • 8.13 Traveling-Salesman Problem
  • Solved Problems
  • Supplementary Problems
  • Chapter 9 Directed Graphs
  • 9.1 Introduction
  • 9.2 Directed Graphs
  • 9.3 Basic Definitions
  • 9.4 Rooted Trees
  • 9.5 Sequential Representation of Directed Graphs
  • 9.6 Warshall’s Algorithm, Shortest Paths
  • 9.7 Linked Representation of Directed Graphs
  • 9.8 Graph Algorithms: Depth-First and Breadth-First Searches
  • 9.9 Directed Cycle-Free Graphs, Topological Sort
  • 9.10 Pruning Algorithm for Shortest Path
  • Solved Problems
  • Supplementary Problems
  • Chapter 10 Binary Trees
  • 10.1 Introduction
  • 10.2 Binary Trees
  • 10.3 Complete and Extended Binary Trees
  • 10.4 Representing Binary Trees in Memory
  • 10.5 Traversing Binary Trees
  • 10.6 Binary Search Trees
  • 10.7 Priority Queues, Heaps
  • 10.8 Path Lengths, Huffman’s Algorithm
  • 10.9 General (Ordered Rooted) Trees Revisited
  • Solved Problems
  • Supplementary Problems
  • Chapter 11 Properties of the Integers
  • 11.1 Introduction
  • 11.2 Order and Inequalities, Absolute Value
  • 11.3 Mathematical Induction
  • 11.4 Division Algorithm
  • 11.5 Divisibility, Primes
  • 11.6 Greatest Common Divisor, Euclidean Algorithm
  • 11.7 Fundamental Theorem of Arithmetic
  • 11.8 Congruence Relation
  • 11.9 Congruence Equations
  • Solved Problems
  • Supplementary Problems
  • Chapter 12 Languages, Automata, Grammars
  • 12.1 Introduction
  • 12.2 Alphabet,Words, Free Semigroup
  • 12.3 Languages
  • 12.4 Regular Expressions, Regular Languages
  • 12.5 Finite State Automata
  • 12.6 Grammars
  • Solved Problems
  • Supplementary Problems
  • Chapter 13 Finite State Machines and Turing Machines
  • 13.1 Introduction
  • 13.2 Finite State Machines
  • 13.3 Gödel Numbers
  • 13.4 Turing Machines
  • 13.5 Computable Functions
  • Solved Problems
  • Supplementary Problems
  • Chapter 14 Ordered Sets and Lattices
  • 14.1 Introduction
  • 14.2 Ordered Sets
  • 14.3 Hasse Diagrams of Partially Ordered Sets
  • 14.4 Consistent Enumeration
  • 14.5 Supremum and Infimum
  • 14.6 Isomorphic (Similar) Ordered Sets
  • 14.7 Well-Ordered Sets
  • 14.8 Lattices
  • 14.9 Bounded Lattices
  • 14.10 Distributive Lattices
  • 14.11 Complements, Complemented Lattices
  • Solved Problems
  • Supplementary Problems
  • Chapter 15 Boolean Algebra
  • 15.1 Introduction
  • 15.2 Basic Definitions
  • 15.3 Duality
  • 15.4 Basic Theorems
  • 15.5 Boolean Algebras as Lattices
  • 15.6 Representation Theorem
  • 15.7 Sum-of-Products Form for Sets
  • 15.8 Sum-of-Products Form for Boolean Algebras
  • 15.9 Minimal Boolean Expressions, Prime Implicants
  • 15.10 Logic Gates and Circuits
  • 15.11 Truth Tables, Boolean Functions
  • 15.12 Karnaugh Maps
  • Solved Problems
  • Supplementary Problems
  • Appendix A: Vectors and Matrices
  • A.1 Introduction
  • A.2 Vectors
  • A.3 Matrices
  • A.4 Matrix Addition and Scalar Multiplication
  • A.5 Matrix Multiplication
  • A.6 Transpose
  • A.7 Square Matrices
  • A.8 Invertible (Nonsingular) Matrices, Inverses
  • A.9 Determinants
  • A.10 Elementary Row Operations, Gaussian Elimination (Optional)
  • A.11 Boolean (Zero-One) Matrices
  • Solved Problems
  • Supplementary Problems
  • Appendix B: Algebraic Systems
  • B.1 Introduction
  • B.2 Operations
  • B.3 Semigroups
  • B.4 Groups
  • B.5 Subgroups, Normal Subgroups, and Homomorphisms
  • B.6 Rings, Internal Domains, and Fields
  • B.7 Polynomials Over a Field
  • Solved Problems
  • Supplementary Problems
  • Appendix C: Cryptology
  • C.1 Introduction
  • C.2 Terminology and Notation
  • C.3 Affine Codes
  • C.4 Modular Exponentiation
  • C.5 RSA
  • Index