ISBN-10:
0840049420
ISBN-13:
2900840049420
Pub. Date:
03/01/2012
Publisher:
Cengage Learning
Mathematics: A Discrete Introduction / Edition 3

Mathematics: A Discrete Introduction / Edition 3

by Edward A. Scheinerman

Hardcover

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Overview

Mathematics: A Discrete Introduction / Edition 3

Intended for computer science and engineering students, this textbook introduces basic logic, collections, counting and relations, permutations and symmetry, discrete probability theory, number theory, cryptography, graphs, and partially ordered sets. Detailed proofs are provided for the theorems and propositions. The second edition adds sections on combinatorial proofs and recurrence relations. Annotation ©2005 Book News, Inc., Portland, OR

Product Details

ISBN-13: 2900840049420
Publisher: Cengage Learning
Publication date: 03/01/2012
Edition description: NE
Pages: 624
Product dimensions: 8.40(w) x 11.00(h) x 0.90(d)

About the Author

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.

Table of Contents

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.

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