Ferland, Kevin K., 1969-
Discrete mathematics and applications / Kevin Ferland. - Second edition. - xxviii, 916 pages : color illustrations ; 27 cm. - Textbooks in mathematics .
"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
9781498730655 (hbk. : acidfree paper)
2016033396
Mathematics--Textbooks.
Computer science--Mathematics--Textbooks.
QA39.3 / .F47 2017
511/.1
Discrete mathematics and applications / Kevin Ferland. - Second edition. - xxviii, 916 pages : color illustrations ; 27 cm. - Textbooks in mathematics .
"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
9781498730655 (hbk. : acidfree paper)
2016033396
Mathematics--Textbooks.
Computer science--Mathematics--Textbooks.
QA39.3 / .F47 2017
511/.1