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



    Quantifiers



    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



    Divisors



    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



    Relations



    General Relations



    Special Relations on Sets



    Basics of Functions



    Special Functions



    General Set Constructions



    Cardinality



    II Combinatorics



    Basic Counting



    The Multiplication Principle



    Permutations and Combinations



    Addition and Subtraction



    Probability



    Applications of Combinations



    Correcting for Overcounting



    More Counting



    Inclusion-Exclusion



    Multinomial Coecients



    Generating Functions



    Counting Orbits



    Combinatorial Arguments



    Basic Graph Theory



    Motivation and Introduction



    Special Graphs



    Matrices



    Isomorphisms



    Invariants



    Directed Graphs and Markov Chains



    Graph Properties



    Connectivity



    Euler Circuits



    Hamiltonian Cycles



    Planar Graphs



    Chromatic Number



    Trees and Algorithms



    Trees



    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

    Biography

    Kevin Ferland