TY  - BOOK
AU  - Ferland,Kevin K.
TI  - Discrete mathematics and applications
T2  - Textbooks in mathematics
SN  - 9781498730655 (hbk. : acidfree paper)
AV  - QA39.3 .F47 2017
U1  - 511/.1 23
PY  - 2017///]
CY  - Boca Raton
PB  - CRC Press, Taylor & Francis Group
KW  - Mathematics
KW  - Textbooks
KW  - Computer science
N1  - "A Chapman & Hall book."; Kevin Ferland

Professor of Mathematics
Bloomsburg University of PA
Bloomsburg PA USA

Kevin Ferland (MR Author ID: 343376) received his Ph.D. in mathematics from Syracuse University in 1999 and is currently a professor of mathematics at Bloomsburg University.
In addition to his textbook, Discrete Mathematics and Applications, he has published several papers on the toughness of graphs. Kevin also enjoys both pursuing the combinatorics of and doing crossword puzzles; Includes bibliographical references and index; Table of Contents

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
ER  -