Notes on Discrete Mathematics


File : pdf, 1 MB, 154 pages

by Miguel A. Lerma

TOC

Introduction
1. Logic, Proofs
1.1. Propositions
1.2. Predicates, Quantifiers
1.3. Proofs

2. Sets, Functions, Relations
2.1. Set Theory
2.2. Functions
2.3. Relations

3. Algorithms, Integers
3.1. Algorithms
3.2. The Euclidean Algorithm
3.3. Modular Arithmetic, RSA Algorithm

4. Induction, Recurences
4.1. Sequences and Strings
4.2. Mathematical Induction
4.3. Recurrence Relations

5. Counting
5.1. Basic Principles
5.2. Combinatorics
5.3. Generalized Permutations and Combinations
5.4. Binomial Coefficients
5.5. The Pigeonhole Principle

6. Probability
6.1. Probability

7. Graph Theory
7.1. Graphs
7.2. Representations of Graphs
7.3. Paths and Circuits
7.4. Planar Graphs

8. Trees
8.1. Trees
8.2. Binary Trees
8.3. Decision Trees, Tree Isomorphisms
8.4. Tree Transversal
8.5. Spanning Trees

9. Boolean Algebras
9.1. Combinatorial Circuits
9.2. Boolean Functions, Applications

10. Automata, Grammars and Languages
10.1. Finite State Machines
10.2. Languages and Grammars
10.3. Language Recognition

Appendix A.
A.1. Efficient Computation of Powers Modulo m
A.2. Machines and Languages

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