- Applied Discrete StructuresUpdated 2021 by Alan Doerr, Kenneth Levasseur, University of Massachusetts Lowell.

An Instructor's Guide is available, including

chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; suggested coverage times; detailed solutions to most even-numbered exercises; sample quizzes, exams, and final exams. - Discrete Mathematics An Open Introduction, 3rd edUpdated 2020 by Oscar Levin, University of Northern Colorado.

An introduction to topics in discrete math and as the "introduction to proofs" course for math majors. Four main topics are covered: counting, sequences, logic, and graph theory. Proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions and two additional topics (generating functions and number theory) are also included.

Exercises, activities, and an index. - Combinatorics and Discrete Mathematics202, authored, remixed, and/or curated by LibreTexts.

Modular approach. - Applied Combinatorics2017 by Mitchel T. Keller, Washington and Lee University

William T. Trotter, Georgia Institute of Technology.

Covers the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). Introduces discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other topics. - A Spiral Workbook for Discrete Mathematics2015 by Harris Kwong, SUNY Fredonia. Covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Exercises provided. Topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity.Preface

1 An Introduction

1.1 An Overview

1.2 Suggestions to Students

1.3 How to Read and Write Mathematics

1.4 Proving Identities

2 Logic

2.1 Propositions

2.2 Conjunctions and Disjunctions

2.3 Implications

2.4 Biconditional Statements

2.5 Logical Equivalences

2.6 Logical Quantifiers

3 Proof Techniques

3.1 An Introduction to Proof Techniques

3.2 Direct Proofs

3.3 Indirect Proofs

3.4 Mathematical Induction: An Introduction

3.5 More on Mathematical Induction

3.6 Mathematical Induction: The Strong Form

4 Sets

4.1 An Introduction

4.2 Subsets and Power Sets

4.3 Unions and Intersections

4.4 Cartesian Products

4.5 Index Sets

5 Basic Number Theory

5.1 The Principle of Well-Ordering

5.2 Division Algorithm

5.3 Divisibility

5.4 Greatest Common Divisors

5.5 More on GCD

5.6 Fundamental Theorem of Arithmetic

5.7 Modular Arithmetic

6 Functions

6.1 Functions: An Introduction

6.2 Definition of Functions

6.3 One-to-One Functions

6.4 Onto Functions

6.5 Properties of Functions

6.6 Inverse Functions

6.7 Composite Functions

7 Relations

7.1 Definition of Relations

7.2 Properties of Relations

7.3 Equivalence Relations

7.4 Partial and Total Ordering

8 Combinatorics

8.1 What is Combinatorics?

8.2 Addition and Multiplication Principles

8.3 Permutations

8.4 Combinations

8.5 The Binomial Theorem

A Solutions to Hands-On Exercises

B Answers to Selected Exercises

Index

Publication Date: November 6, 2015

OCLC#: 928028391

ISBN: 978-1-942341-16-1

- Fundamental Approach to Discrete Mathematics by D. P. Acharjya 2009ISBN: 978-8122426076Publication Date: 2009-01-01

- Last Updated: Oct 2, 2023 4:21 PM
- URL: https://libguides.uml.edu/mathematicstextbooks
- Print Page

Subjects: Mathematics