Discrete Mathematics

          Module 1: Introduction to Discrete Mathematics

Section 1: Understanding Discrete Mathematics
- Lesson 1: Overview of Discrete Mathematics
  Module 1, Section 1, Lesson 1 Overview of Discrete Mathematics
- Lesson 2: History and Applications
  Module 1, Section 1, Lesson 2 History and Applications

Section 2: Fundamental Concepts and Sets
- Lesson 1: Basics of Set Theory
  Module 1, Section 2, Lesson 1 Basics of Set Theory
- Lesson 2: Introduction to Logic Statements
  Module 1, Section 2, Lesson 2 Introduction to Logic Statements

Section 3: Mathematical Structures
- Lesson 1: Functions and Relations
  Module 1, Section 3, Lesson 1 Functions and Relations
- Lesson 2: Basic Counting Principles
  Module 1, Section 3, Lesson 2 Basic Counting Principles

Section 4: Introduction to Algorithms
- Lesson 1: What is an Algorithm?
  Module 1, Section 4, Lesson 1 What is an Algorithm?
- Lesson 2: Algorithmic Thinking and Problem Solving
  Module 1, Section 4, Lesson 2 Algorithmic Thinking and Problem Solving

Section 5: Developing Problem-Solving Strategies
- Lesson 1: Approaching Problems Step by Step
  Module 1, Section 5, Lesson 1 Approaching Problems Step by Step
- Lesson 2: Practical Examples and Exercises
  Module 1, Section 5, Lesson 2 Practical Examples and Exercises


Module 2: Basic Logic and Proofs

Section 1: Propositional Logic Foundations
- Lesson 1: Introduction to Propositions
  Module 2, Section 1, Lesson 1 Introduction to Propositions
- Lesson 2: Constructing Truth Tables
  Module 2, Section 1, Lesson 2 Constructing Truth Tables

Section 2: Logical Connectives and Equivalence
- Lesson 1: Understanding Logical Connectives
  Module 2, Section 2, Lesson 1 Understanding Logical Connectives
- Lesson 2: Basic Logical Equivalences
  Module 2, Section 2, Lesson 2 Basic Logical Equivalences

Section 3: Introduction to Proof Techniques
- Lesson 1: Direct Proof Methods
  Module 2, Section 3, Lesson 1 Direct Proof Methods
- Lesson 2: Indirect Proof and Contradiction
  Module 2, Section 3, Lesson 2 Indirect Proof and Contradiction

Section 4: Quantifiers and Predicates
- Lesson 1: Basics of Quantifiers
  Module 2, Section 4, Lesson 1 Basics of Quantifiers
- Lesson 2: Using Predicates in Proofs
  Module 2, Section 4, Lesson 2 Using Predicates in Proofs

Section 5: Applying Logic in Mathematical Reasoning
- Lesson 1: Formulating Precise Statements
  Module 2, Section 5, Lesson 1 Formulating Precise Statements
- Lesson 2: Logical Reasoning in Problem Solving
  Module 2, Section 5, Lesson 2 Logical Reasoning in Problem Solving


Module 3: Algorithms and Complexity

Section 1: Introduction to Algorithms
- Lesson 1: Defining an Algorithm
  Module 3, Section 1, Lesson 1 Defining an Algorithm
- Lesson 2: Importance of Algorithms in Mathematics
  Module 3, Section 1, Lesson 2 Importance of Algorithms in Mathematics

Section 2: Writing Pseudocode and Flowcharts
- Lesson 1: Basics of Pseudocode
  Module 3, Section 2, Lesson 1 Basics of Pseudocode
- Lesson 2: Creating Flowcharts for Algorithms
  Module 3, Section 2, Lesson 2 Creating Flowcharts for Algorithms

Section 3: Sorting and Searching Techniques
- Lesson 1: Introduction to Sorting Methods
  Module 3, Section 3, Lesson 1 Introduction to Sorting Methods
- Lesson 2: Fundamentals of Searching Algorithms
  Module 3, Section 3, Lesson 2 Fundamentals of Searching Algorithms

Section 4: Recursion Fundamentals
- Lesson 1: Understanding the Concept of Recursion
  Module 3, Section 4, Lesson 1 Understanding the Concept of Recursion
- Lesson 2: Simple Recursive Examples
  Module 3, Section 4, Lesson 2 Simple Recursive Examples

Section 5: Basics of Algorithm Analysis
- Lesson 1: Introduction to Complexity Notation
  Module 3, Section 5, Lesson 1 Introduction to Complexity Notation
- Lesson 2: Analyzing Time and Space Complexity
  Module 3, Section 5, Lesson 2 Analyzing Time and Space Complexity


Module 4: Combinatorics Fundamentals

Section 1: Fundamental Counting Principles
- Lesson 1: The Rule of Product
  Module 4, Section 1, Lesson 1 The Rule of Product
- Lesson 2: The Rule of Sum
  Module 4, Section 1, Lesson 2 The Rule of Sum

Section 2: Introduction to Permutations
- Lesson 1: Understanding Permutations
  Module 4, Section 2, Lesson 1 Understanding Permutations
- Lesson 2: Calculating Permutations in Practice
  Module 4, Section 2, Lesson 2 Calculating Permutations in Practice

Section 3: Introduction to Combinations
- Lesson 1: Basics of Combinations
  Module 4, Section 3, Lesson 1 Basics of Combinations
- Lesson 2: Practical Examples Using Combinations
  Module 4, Section 3, Lesson 2 Practical Examples Using Combinations

Section 4: The Pigeonhole Principle
- Lesson 1: Concept and Explanation of the Pigeonhole Principle
  Module 4, Section 4, Lesson 1 Concept and Explanation of the Pigeonhole Principle
- Lesson 2: Applications of the Pigeonhole Principle
  Module 4, Section 4, Lesson 2 Applications of the Pigeonhole Principle

Section 5: Combinatorial Problem Solving
- Lesson 1: Strategies for Tackling Counting Problems
  Module 4, Section 5, Lesson 1 Strategies for Tackling Counting Problems
- Lesson 2: Practice Problems and Interactive Exercises
  Module 4, Section 5, Lesson 2 Practice Problems and Interactive Exercises


Module 5: Introduction to Graph Theory

Section 1: Graph Terminology and Concepts
- Lesson 1: Basic Terminology in Graph Theory
  Module 5, Section 1, Lesson 1 Basic Terminology in Graph Theory
- Lesson 2: Types and Properties of Graphs
  Module 5, Section 1, Lesson 2 Types and Properties of Graphs

Section 2: Graph Representations
- Lesson 1: Representing Graphs with Diagrams
  Module 5, Section 2, Lesson 1 Representing Graphs with Diagrams
- Lesson 2: Adjacency Lists and Matrices
  Module 5, Section 2, Lesson 2 Adjacency Lists and Matrices

Section 3: Graph Traversal Techniques
- Lesson 1: Introduction to Depth-First Search (DFS)
  Module 5, Section 3, Lesson 1 Introduction to Depth-First Search (DFS)
- Lesson 2: Introduction to Breadth-First Search (BFS)
  Module 5, Section 3, Lesson 2 Introduction to Breadth-First Search (BFS)

Section 4: Trees and Their Applications
- Lesson 1: Understanding Trees as Graphs
  Module 5, Section 4, Lesson 1 Understanding Trees as Graphs
- Lesson 2: Basic Tree Traversal Methods
  Module 5, Section 4, Lesson 2 Basic Tree Traversal Methods

Section 5: Real-World Applications of Graph Theory
- Lesson 1: Graphs in Network Analysis
  Module 5, Section 5, Lesson 1 Graphs in Network Analysis
- Lesson 2: Case Studies and Practical Examples
  Module 5, Section 5, Lesson 2 Case Studies and Practical Examples