# Mathematics: A Discrete Introduction, 3rd Edition

• Edward R. Scheinerman
• ISBN-10: 0840049420
• ISBN-13: 9780840049421
• 504 Pages | Hardcover
• Previous Editions: 2006, 2000
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# Overview

MATHEMATICS: A DISCRETE INTRODUCTION teaches students the fundamental concepts in discrete mathematics and proof-writing skills. With its clear presentation, the text shows students how to present cases logically beyond this course. All of the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective. Students will learn that discrete mathematics is very useful, especially those whose interests lie in computer science and engineering, as well as those who plan to study probability, statistics, operations research, and other areas of applied mathematics.

## Features

• Self-Tests: A self-test appears at the end of every chapter. The problems are of various degrees of difficulty, and complete answers appear in Appendix B.

• Induction: The sections on mathematical induction have been reworked with new motivational material, more examples, and more problems. The induction section is now essentially independent of the proof by smallest counterexample section.

• The book includes sections covering topics such as recurrence relations and combinatorial proof.

• The introductory section, "Joy," motivates students by describing the pleasure of doing mathematics.

• Proof Templates: Proof templates appear throughout the book and give students the basic skeleton of the proof as well as boilerplate language.

• Growing Proofs: The author teaches students how to write proofs by instructing them to begin their proofs by first writing the first sentence and next writing the last sentence. Students then work the proof from both ends until they meet in the middle.

• Mathspeak: Marginal notes explain many of the idiosyncrasies of mathematical English.

• Hints: Appendix A contains an extensive collection of hints (and some answers when necessary) that point students in the correct direction.

• Flexible Coverage: The topics can be arranged in various ways, allowing instructors to take a computer science and engineering focus, an abstract algebra focus, a discrete structures focus, or a broad focus.

Edward R. Scheinerman

Edward R. Scheinerman is Professor in the Department of Applied Mathematics and Statistics at The Johns Hopkins University. Dr. Scheinerman's research interests include discrete mathematics; especially graph theory, partially ordered sets, random graphs, and combinatorics, as well as applications to robotics and networks.

1. FUNDAMENTALS.
Joy. Speaking (and Writing) of Mathetimatics. Definition. Theorem. Proof. Counterexample. Boolean Algebra. Self Test.
2. COLLECTIONS.
Lists. Factorial. Sets I: Introduction, Subsets. Quantifiers. Sets II: Operations. Combinatorial Proof: Two Examples. Self Test.
3. COUNTING AND RELATIONS.
Relations. Equivalence Relations. Partitions. Binomial Coefficients. Counting Multisets. Inclusion-Exclusion. Self Test.
4. MORE PROOF.
Contradiction. Smallest Counterexample. Induction. Recurrence Relations. Self Test.
5. FUNCTIONS.
Functions. The Pigeonhole Principle. Composition. Permutations. Symmetry. Assorted Notation. Self Test.
6. PROBABILITY.
Sample Space. Events. Conditional Probability and Independence. Random Variables. Expectation. Self Test.
7. NUMBER THEORY.
Dividing. Greatest Common Divisor. Modular Arithmetic. The Chinese Remainder Theorem. Factoring. Self Test.
8. ALGEBRA.
Groups. Group Isomorphism. Subgroups. Fermat's Little Theorem. Public-Key Cryptography I: Introduction. Public-Key Cryptography II: Rabin's Method. Public-Key Cryptography III: RSA. Self Test.
9. GRAPHS.
Graph Theory Fundamentals. Subgraphs. Connection. Trees. Eulerian Graphs. Coloring. Planar Graphs. Self Test.
10. PARTIALLY ORDERED SETS.
Partially Ordered Sets Fundamentals. Max and Min. Linear Orders. Linear Extensions. Dimension. Lattices. Self Test.
APPENDICES.
Lots of Hints and Comments; Some Answers. Solutions to Self Tests. Glossary. Fundamentals.
Index.

# New to this edition

• This edition has been revised based on input from reviewers and users, as well as the author's understanding of the course. This includes correcting and adding to the existing content.
• Featuring more than 25% increase in problems. Some of these new problems, which are included in problem sets and chapter tests, are interrelated to develop ideas across chapters, providing a stronger understanding of the materiel.

# Supplements

All supplements have been updated in coordination with the Main title.
Please see Main title page for new to this edition information.

## Instructor Supplements

Instructor's Manual  (ISBN-10: 1133942997 | ISBN-13: 9781133942993)