2nd Edition

Discrete Mathematics and Applications

By Kevin Ferland Copyright 2017
    944 Pages 893 B/W Illustrations
    by CRC Press

    944 Pages 893 B/W Illustrations
    by Chapman & Hall

    944 Pages 893 B/W Illustrations
    by Chapman & Hall

    Discrete Mathematics and Applications, Second Edition is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book.

    Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.

    • Emphasizes proofs, which will appeal to a subset of this course market

    • Links examples to exercise sets

    • Offers edition that has been heavily reviewed and developed

    • Focuses on graph theory

    • Covers trees and algorithms


    I Proofs

    Logic and Sets

    Statement Forms and Logical Equivalences

    Set Notation


    Set Operations and Identities

    Valid Arguments

    Basic Proof Writing

    Direct Demonstration

    General Demonstration (Part 1)

    General Demonstration (Part 2)

    Indirect Arguments

    Splitting into Cases

    Elementary Number Theory


    Well-Ordering, Division, and Codes

    Euclid's Algorithm and Lemma

    Rational and Irrational Numbers

    Modular Arithmetic and Encryption

    Indexed by Integers

    Sequences, Indexing, and Recursion

    Sigma Notation

    Mathematical Induction, An Introduction

    Induction and Summations

    Strong Induction

    The Binomial Theorem


    General Relations

    Special Relations on Sets

    Basics of Functions

    Special Functions

    General Set Constructions


    II Combinatorics

    Basic Counting

    The Multiplication Principle

    Permutations and Combinations

    Addition and Subtraction


    Applications of Combinations

    Correcting for Overcounting

    More Counting


    Multinomial Coecients

    Generating Functions

    Counting Orbits

    Combinatorial Arguments

    Basic Graph Theory

    Motivation and Introduction

    Special Graphs




    Directed Graphs and Markov Chains

    Graph Properties


    Euler Circuits

    Hamiltonian Cycles

    Planar Graphs

    Chromatic Number

    Trees and Algorithms


    Search Trees

    Weighted Trees

    Analysis of Algorithms (Part 1)

    Analysis of Algorithms (Part 2)

    A Assumed Properties of Z and R

    B Pseudocode

    C Answers to Selected Exercises


    Kevin Ferland