Discrete Mathematics and Applications: Textbooks in Mathematics
Autor Kevin Ferlanden Limba Engleză Hardback – mai 2017
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
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Specificații
ISBN-13: 9781498730655
ISBN-10: 1498730655
Pagini: 944
Ilustrații: 196 Tables, black and white; 893 Illustrations, black and white
Dimensiuni: 178 x 254 x 51 mm
Greutate: 2 kg
Ediția:2 New edition
Editura: CRC Press
Colecția CRC Press
Seria Textbooks in Mathematics
ISBN-10: 1498730655
Pagini: 944
Ilustrații: 196 Tables, black and white; 893 Illustrations, black and white
Dimensiuni: 178 x 254 x 51 mm
Greutate: 2 kg
Ediția:2 New edition
Editura: CRC Press
Colecția CRC Press
Seria Textbooks in Mathematics
Cuprins
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
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
Descriere
This book 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.