[PDF] Discrete Mathematics an Introduction to Proofs and Combinatorics by Kevin Ferland Book Free Download

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Discrete Mathematics an Introduction to Proofs and Combinatorics

Download Discrete Mathematics an Introduction to Proofs and Combinatorics by Kevin Ferland Book Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for students who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory.

Discrete Mathematics an Introduction to Proofs and Combinatorics by Kevin Ferland Book Free Download

Book Details:

Title Of The Book Discrete Mathematics an Introduction to Proofs and Combinatorics
Author’s Name Kevin Ferland
Publishers Kevin Ferland
File Size 8.5 MB
File Type PDF

Table Of Content:

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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