Comprehensive Table of Contents

Section 1: Discrete Concepts

1. An Introduction to Discrete Mathematics
   1. Types of Discrete Problems
      1. Determining Existance
      2. Counting
      3. Optimization
2. Sets
   1. Set Operations & Concepts
      1. Elements
      2. Union
      3. Intersection
      4. Difference
      5. Complimentation
      6. The Universal Set
      7. De Morgan's Laws
      8. The Venn Diagram
3. Relations
   1. Equivalence Relations
   2. Identity Relations
   3. Congruence Relations
   4. Recurrence Relations
4. Ordered Sets
   1. Partially Ordered Sets
      1. The Hasse Diagram
      2. Minimal & Maximal Elements
   2. Totally Ordered Sets
5. Computation & Counting Techniques
   1. Permutations
   2. Combinations (Combinatorial Analysis)

Section 2: Probability & Statistics

Section 3: Data Structures

1. An Introduction to Structured Data
   1. Arrays vs Pointers
2. Types of Data Structures
   1. Stacks
   2. Queues
   3. Linked Lists
   4. Graphs
   5. Trees

Section 4: Coding Theory

1. The Euclidean Algorithm
2. The RSA Method
3. Error-Detecting & Error-Correcting Codes
4. Matrix Codes
5. Network Flows

Section 5: Computational Theory

1. An Introduction to the Theory of Computation
2. Languages
   1. Regular Languages
   2. Context-Free Languages
3. Grammars
   1. Regular Grammars
4. Automata
   1. Finite Automata
      1. Deterministic Finite Accepters
      2. Nondeterministic Finite Accepters
   2. Pushdown Automata
5. Turing Machines
6. The Limits of Algorithmic Computation