Joshi K.D. Foundations of Discrete Mathematics

Hoboken: Wiley, 1991. — 770 p.List of Standard Symbols
Suggested Course CoverageOne. Introduction and Preliminaries
What is Discrete Mathematics?
Typical Problems
Comments about Typical Problems
Review of Logic
Two. Elementary Counting Techniques
Sets and Functions
Cardinalities of Sets
Applications to Counting Problems
Principle of Inclusion and Exclusion
Three. Sets with Additional Structures
Abstraction and Mathematical Structures
Binary Relations on Sets
Order Relations
Algebraic Structures
Four. Boolean Algebras
Definition and Properties
Boolean Functions
Applications to Switching Networks
Applications to Logic
Five. Group Theory
Groups and Subgroups
Cosets of Subgroups
Group Homomorphisms
Permutation Groups
Six. Rings, Fields and Vector Spaces
Basic Concepts and Examples
Special Types of Integral Domains
Vector Spaces
Matrices and Determinants
Seven. Advanced Counting Techniques
Generating Functions of Sequences
Application to Enumeration Problems
Recurrence Relations
Applications of Recurrence Relations
Epilogue: Preview of "Applied Discrete Structures"Answers to Exercises