Discrete Mathematical Structures, Sixth Edition , offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field.

This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.

Klappentext

Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field.This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.

Zusammenfassung

Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field.

This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.

Inhalt

1. 1. Fundamentals

• 1.1 Sets and Subsets
• 1.2 Operations on Sets
• 1.3 Sequences
• 1.4 Properties of Integers
• 1.5 Matrices
• 1.6 Mathematical Structures

1. 2. Logic

• 2.1 Propositions and Logical Operations
• 2.2 Conditional Statements
• 2.3 Methods of Proof
• 2.4 Mathematical Induction
• 2.5 Mathematical Statements
• 2.6 Logic and Problem Solving

1. 3. Counting

• 3.1 Permutations
• 3.2 Combinations
• 3.3 Pigeonhole Principle
• 3.4 Elements of Probability
• 3.5 Recurrence Relations

1. 4. Relations and Digraphs

• 4.1 Product Sets and Partitions
• 4.2 Relations and Digraphs
• 4.3 Paths in Relations and Digraphs
• 4.4 Properties of Relations
• 4.5 Equivalence Relations
• 4.6 Data Structures for Relations and Digraphs
• 4.7 Operations on Relations
• 4.8 Transitive Closure and Warshall's Algorithm

1. 5. Functions

• 5.1 Functions
• 5.2 Functions for Computer Science
• 5.3 Growth of Functions
• 5.4 Permutation Functions

1. 6. Order Relations and Structures

• 6.1 Partially Ordered Sets
• 6.2 Extremal Elements of Partially Ordered Sets
• 6.3 Lattices
• 6.4 Finite Boolean Algebras
• 6.5 Functions on Boolean Algebras
• 6.6 Circuit Design

1. 7. Trees

• 7.1 Trees
• 7.2 Labeled Trees
• 7.3 Tree Searching
• 7.4 Undirected Trees
• 7.5 Minimal Spanning Trees

1. 8. Topics in Graph Theory

• 8.1 Graphs
• 8.2 Euler Paths and Circuits
• 8.3 Hamiltonian Paths and Circuits
• 8.4 Transport Networks
• 8.5 Matching Problems
• 8.6 Coloring Graphs

1. 9. Semigroups and Groups

• 9.1 Binary Operations Revisited
• 9.2 Semigroups
• 9.3 Products and Quotients of Semigroups
• 9.4 Groups
• 9.5 Products and Quotients of Groups
• 9.6 Other Mathematical Structures

1. 10. Groups and Coding

• 10.1 Coding of Binary Information and Error Detection
• 10.2 Decoding and Error Correction
• 10.3 Public Key Cryptology

1. 11. Languages and Finite-State Machines

• 11.1 Languages
• 11.2 Representations of Special Grammars and Languages
• 11.3 Finite-State Machines
• 11.4 Monoids, Machines, and Languages
• 11.5 Machines and Regular Languages
• 11.6 Simplification of Machines