Discrete mathematics and applications

著者

    • Ferland, Kevin

書誌事項

Discrete mathematics and applications

Kevin Ferland

（Textbooks in mathematics）

CRC Press, c2017

2nd ed

  • : hardback

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注記

"A Chapman & Hall Book"

Includes bibliographical references (p. 905) and index

内容説明・目次

内容説明

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

目次

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 Coe cients 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

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