An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic that are followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.
The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.
The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.
Table of Contents
Part I Foundations1. Number System
2. Logic and Deduction
3. Sets, Functions, Sequences, Sums
4. Induction, Recursion
5. Elementary Number Theory
Part II Combinatorics
6. Basic Principles of Counting
7. Permutations and Combinations
8. Further Topics in Counting
Part III Discrete Probability
9. Probability of Events
10. Random Variables
Part IV Graphs and Networks
11. Graphs
12. Weighted Graphs
