Master the fundamentals of discrete mathematics and proof-writing with MATHEMATICS: A DISCRETE INTRODUCTION! With a clear presentation, the mathematics text teaches you not only how to write proofs, but how to think clearly and present cases logically beyond this course. Though it is presented from a mathematician's perspective, you will learn the importance of discrete mathematics in the fields of computer science, engineering, probability, statistics, operations research, and other areas of applied mathematics. Tools such hints and proof templates prepare you to succeed in this course.

### 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.