Mathematics : a discrete introduction / Edward R. Schneiderman.

1. FUNDAMENTALS
Definition.
Theorem.
Proof.
Counterexample.
Boolean Algebra.

2. COLLECTIONS.
Lists.
Factorial.
Sets I: Introduction,
Subsets. Quantifiers.
Sets II: Operations.

3. COUNTING AND RELATIONS.
Relations.
Equivalence Relations.
Partitions.
Binomial Coefficients.
Counting Multisets.
Inclusion-Exclusion.

4. MORE PROOF.
Contradiction.
Smallest Counterexample.
Introduction.

5. FUNCTIONS.
Functions.
The Pigeonhole Principle.
Composition.
Permutations.
Symmetry.
Assorted Notation.

6. PROBABILITY.
Sample Space.
Events.
Conditional Probability and Independence.
Random Variables.
Expectation.

7. NUMBER THEORY.
Dividing.
Greatest Common Divisor.
Modular Arithmetic.
The Chinese Remainder Theorem.
Factoring.

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.

9. GRAPHS.
Graph Theory Fundamentals.
Subgraphs.
Connection.
Trees. Eulerian Graphs.
Colouring. Planar Graphs.

10. PARTIALLY ORDERED SETS.
Partially Ordered Sets Fundamentals.
Max and Min. Linear Orders.
Linear Extensions.
Dimension.
Lattices.

Includes index.