ENGLISH

Journey Into Discrete Mathematics

By Owen Byer; Deirdre L. Smeltzer; Kenneth L. Wantz

Book information

Publisher
Maa Press
Year
2018
ISBN
1470446960, 9781470446963
Language
english
Format
PDF
Filesize
12 MB (12607122 bytes)
Series
AMS/MAA Textbooks 41
Pages
xii+388\402
Time added
2020-05-08 12:33:54

Description

Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject. Cover Title page Copyright Contents Preface What Is Discrete Mathematics? Goals of the Book Features of the Book Course Outline Acknowledgments Chapter 1. Convince Me! 1.1. Opening Problems 1.2. Solutions Chapter 2. Mini-Theories 2.1. Introduction 2.2. Divisibility of Integers 2.3. Matrices Chapter 3. Logic and Sets 3.1. Propositions 3.2. Sets 3.3. Logical Operators and Truth Tables 3.4. Operations on Sets 3.5. Truth Values of Compound Propositions 3.6. Set Identities 3.7. Infinite Sets and Paradoxes Chapter 4. Logic and Proof 4.1. Logical Equivalences 4.2. Predicates 4.3. Nested Quantifiers 4.4. Rules of Inference 4.5. Methods of Proof Chapter 5. Relations and Functions 5.1. Relations 5.2. Properties of Relations on a Set 5.3. Functions 5.4. Sequences Chapter 6. Induction 6.1. Inductive and Deductive Thinking 6.2. Well-Ordering Principle 6.3. Method of Mathematical Induction 6.4. Strong Induction 6.5. Proof of the Division Theorem Chapter 7. Number Theory 7.1. Primes 7.2. The Euclidean Algorithm 7.3. Linear Diophantine Equations 7.4. Congruences 7.5. Applications 7.6. Additional Problems Chapter 8. Counting 8.1. What Is Counting? 8.2. Counting Techniques 8.3. Permutations and Combinations 8.4. The Binomial Theorem 8.5. Additional Problems Chapter 9. Graph Theory 9.1. The Language of Graphs 9.2. Traversing Edges and Visiting Vertices 9.3. Vertex Colorings 9.4. Trees 9.5. Proofs of Euler’s and Ore’s Theorems Chapter 10. Invariants and Monovariants 10.1. Invariants 10.2. Monovariants Chapter 11. Topics in Counting 11.1. Inclusion-Exclusion 11.2. The Pigeonhole Principle 11.3. Multinomial Coefficients 11.4. Combinatorial Identities 11.5. Occupancy Problems Chapter 12. Topics in Number Theory 12.1. More on Primes 12.2. Integers in Other Bases 12.3. More on Congruences 12.4. Nonlinear Diophantine Equations 12.5. Cryptography: Rabin’s Method Chapter 13. Topics in Graph Theory 13.1. Planar Graphs 13.2. Chromatic Polynomials 13.3. Spanning Tree Algorithms 13.4. Path and Circuit Algorithms Hints List of Names Bibliography Index Back Cover

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