Discrete Mathematics and Its Applications

Author: Wei Changhua
Publisher: Wuhan University Press
Book Description:
This book introduces the fundamental knowledge of discrete mathematics, including mathematical logic, set theory, abstract algebra, lattices, Boolean algebra, and graph theory. The distinctive feature of this book is not to demand rigorous logical and rigorous discussions of the mathematical theories involved, but to emphasize the application of these mathematical knowledge in various fields of computer science. In other words, it focuses on how to solve practical application problems in computer science through relevant mathematical theories, methods, and techniques. To this end, this book strives to achieve an organic combination of theoretical descriptions and examples. Moreover, a large number of examples in the book come from practical problems in various fields of computer science, giving readers a sense of authenticity. At the same time, readers can grasp the close relationship between mathematics and computer science from these examples. The conception and writing of this book have spanned nearly a decade, and it can be said that it is an experience report of the authors' many years of teaching and research in computer science, as a gift to the readers.
This book is suitable for undergraduate and graduate students majoring in computer science in colleges and universities as a textbook, and can also be used as a reference for computer professionals engaged in computer application development.
Table of Contents:
Chapter 1: Mathematical Logic
1.1 Propositional Calculus
1.2 Tautologies
1.3 Normal Forms
1.4 Polish Notation and Reverse Polish Notation in Compilation Technology
1.5 Reasoning Theory of Propositional Calculus
1.6 Predicate Calculus
1.7 Reasoning Theory of Predicate Calculus
1.8 Application of Predicate Calculus in Artificial Intelligence
Chapter 2: Set Theory
2.1 Basic Concepts of Set Theory
2.2 Operations on Sets and Venn Diagrams
2.3 Relations and Partial Orders
2.4 Functions
2.5 Recursive Functions
Chapter 3: Abstract Algebra
3.1 Algebraic Systems and Operations
3.2 Isomorphism and Homomorphism
3.3 Congruence
3.4 Product Algebras
3.5 Semigroups and Monoids
3.6 Groups
3.7 Group Codes and Error-Correcting Codes
Chapter 4: Lattices and Boolean Algebra
4.1 Concept of Lattices
4.2 Properties of Lattices
4.3 Lattices as Algebraic Systems
4.4 Sublattices and Homomorphisms of Direct Products
4.5 Special Types of Lattices
4.6 Boolean Algebra
4.7 Boolean Expressions and Boolean Functions
4.8 Application of Boolean Algebra in Logic Circuit Design
Chapter 5: Graph Theory
5.1 Basic Concepts of Graphs
5.2 Matrix Representation of Graphs
5.3 Planar Graphs
5.4 Trees
5.5 Application of Graph Theory in Computer Science