**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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