Discrete Mathematics and Applications

Kevin Ferland (Autor)

Buch | Hardcover

916 Seiten

2017 | 2nd edition
Crc Press Inc (Verlag)
978-1-4987-3065-5 (ISBN)

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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

Kevin Ferland

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

Erscheinungsdatum	10.07.2017
Reihe/Serie	Textbooks in Mathematics
Zusatzinfo	196 Tables, black and white; 893 Illustrations, black and white
Verlagsort	Bosa Roca
Sprache	englisch
Maße	178 x 254 mm
Gewicht	2000 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4987-3065-5 / 1498730655
ISBN-13	978-1-4987-3065-5 / 9781498730655
Zustand	Neuware