Mathematics: A Discrete Introduction - Softcover

Edward R. Scheinerman

Softcover

ISBN 10: 0840065280 ISBN 13: 9780840065285

Publisher: Brooks/Cole, 2012

Synopsis

Mathematics: A Discrete Introduction

About this title

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.

Review

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.

Edition details

• Publisher: Brooks/Cole
• Publication date: 2012
• Language: English
• ISBN 10: 0840065280
• ISBN 13: 9780840065285
• Binding: Paperback
• Number of pages: 504