Mathematical Optimization and Operations Research

          Module 1: Introduction to Mathematical Optimization
Section 1: Overview of Optimization
- Lesson 1: What is Mathematical Optimization?
  Module 1, Section 1, Lesson 1: What is Mathematical Optimization?
- Lesson 2: History and Applications
  Module 1, Section 1, Lesson 2: History and Applications

Section 2: Basic Terminology and Concepts
- Lesson 1: Key Terms in Optimization
  Module 1, Section 2, Lesson 1: Key Terms in Optimization
- Lesson 2: Types of Optimization Problems
  Module 1, Section 2, Lesson 2: Types of Optimization Problems

Section 3: Mathematical Models and Assumptions
- Lesson 1: Modeling Real-World Problems
  Module 1, Section 3, Lesson 1: Modeling Real-World Problems
- Lesson 2: Assumptions in Optimization Models
  Module 1, Section 3, Lesson 2: Assumptions in Optimization Models

Section 4: Introduction to Linear Programming
- Lesson 1: Basics of Linear Equations and Inequalities
  Module 1, Section 4, Lesson 1: Basics of Linear Equations and Inequalities
- Lesson 2: Feasibility and Optimization Concepts
  Module 1, Section 4, Lesson 2: Feasibility and Optimization Concepts

Section 5: Overview of Operational Research
- Lesson 1: Defining Operational Research
  Module 1, Section 5, Lesson 1: Defining Operational Research
- Lesson 2: Practical Examples of Operational Research
  Module 1, Section 5, Lesson 2: Practical Examples of Operational Research

Module 2: Linear Programming Fundamentals
Section 1: Setting Up a Linear Program
- Lesson 1: Identifying Decision Variables and Constraints
  Module 2, Section 1, Lesson 1: Identifying Decision Variables and Constraints
- Lesson 2: Formulating Objective Functions
  Module 2, Section 1, Lesson 2: Formulating Objective Functions

Section 2: Graphical Methods in LP
- Lesson 1: Plotting Constraints on a Graph
  Module 2, Section 2, Lesson 1: Plotting Constraints on a Graph
- Lesson 2: Determining Feasible Regions
  Module 2, Section 2, Lesson 2: Determining Feasible Regions

Section 3: Introduction to the Simplex Method
- Lesson 1: Overview of the Simplex Algorithm
  Module 2, Section 3, Lesson 1: Overview of the Simplex Algorithm
- Lesson 2: Understanding Pivot Operations and Tableaux
  Module 2, Section 3, Lesson 2: Understanding Pivot Operations and Tableaux

Section 4: Interpreting Linear Programming Solutions
- Lesson 1: Recognizing Optimality and Infeasibility
  Module 2, Section 4, Lesson 1: Recognizing Optimality and Infeasibility
- Lesson 2: An Introduction to Sensitivity Analysis
  Module 2, Section 4, Lesson 2: An Introduction to Sensitivity Analysis

Section 5: Practical Applications of LP
- Lesson 1: Solving Resource Allocation Problems
  Module 2, Section 5, Lesson 1: Solving Resource Allocation Problems
- Lesson 2: Cost Minimization Techniques
  Module 2, Section 5, Lesson 2: Cost Minimization Techniques

Module 3: Network Flow and Transportation
Section 1: Basics of Network Flow
- Lesson 1: Introduction to Networks and Graphs
  Module 3, Section 1, Lesson 1: Introduction to Networks and Graphs
- Lesson 2: Fundamental Concepts of Graph Theory
  Module 3, Section 1, Lesson 2: Fundamental Concepts of Graph Theory

Section 2: Flow Networks and Conservation Principles
- Lesson 1: Flow Conservation in Networks
  Module 3, Section 2, Lesson 1: Flow Conservation in Networks
- Lesson 2: Capacity Constraints in Flow Problems
  Module 3, Section 2, Lesson 2: Capacity Constraints in Flow Problems

Section 3: Transportation Problems
- Lesson 1: Formulating Transportation Models
  Module 3, Section 3, Lesson 1: Formulating Transportation Models
- Lesson 2: Solving Transportation Problems
  Module 3, Section 3, Lesson 2: Solving Transportation Problems

Section 4: Shortest Path Problems
- Lesson 1: Basics of Dijkstra's Algorithm
  Module 3, Section 4, Lesson 1: Basics of Dijkstra's Algorithm
- Lesson 2: Practical Applications of Shortest Path Methods
  Module 3, Section 4, Lesson 2: Practical Applications of Shortest Path Methods

Section 5: Minimum Spanning Trees in Networks
- Lesson 1: Introduction to Minimum Spanning Trees
  Module 3, Section 5, Lesson 1: Introduction to Minimum Spanning Trees
- Lesson 2: Overview of Kruskal’s and Prim’s Algorithms
  Module 3, Section 5, Lesson 2: Overview of Kruskal’s and Prim’s Algorithms

Module 4: Optimization Algorithms and Methods
Section 1: Fundamental Optimization Algorithms
- Lesson 1: Introduction to Optimization Algorithms
  Module 4, Section 1, Lesson 1: Introduction to Optimization Algorithms
- Lesson 2: Basics of Gradient Descent
  Module 4, Section 1, Lesson 2: Basics of Gradient Descent

Section 2: Introduction to Heuristic Methods
- Lesson 1: Understanding Heuristics in Optimization
  Module 4, Section 2, Lesson 1: Understanding Heuristics in Optimization
- Lesson 2: Simple Heuristic Examples
  Module 4, Section 2, Lesson 2: Simple Heuristic Examples

Section 3: Fundamentals of Integer Programming
- Lesson 1: What is Integer Programming?
  Module 4, Section 3, Lesson 1: What is Integer Programming?
- Lesson 2: Basic Formulations for Integer Programs
  Module 4, Section 3, Lesson 2: Basic Formulations for Integer Programs

Section 4: Dynamic Programming Essentials
- Lesson 1: Principles of Dynamic Programming
  Module 4, Section 4, Lesson 1: Principles of Dynamic Programming
- Lesson 2: Applying Dynamic Programming to Optimization Problems
  Module 4, Section 4, Lesson 2: Applying Dynamic Programming to Optimization Problems

Section 5: Introduction to Multi-objective Optimization
- Lesson 1: Understanding Trade-Offs in Multi-objective Problems
  Module 4, Section 5, Lesson 1: Understanding Trade-Offs in Multi-objective Problems
- Lesson 2: Basic Example of Multi-objective Optimization
  Module 4, Section 5, Lesson 2: Basic Example of Multi-objective Optimization

Module 5: Practical Problem Solving and Applications
Section 1: Case Studies in Resource Allocation
- Lesson 1: Analyzing Real-World Resource Problems
  Module 5, Section 1, Lesson 1: Analyzing Real-World Resource Problems
- Lesson 2: Developing Resource Allocation Strategies
  Module 5, Section 1, Lesson 2: Developing Resource Allocation Strategies

Section 2: Enhancing Operational Efficiency
- Lesson 1: Identifying Bottlenecks in Operations
  Module 5, Section 2, Lesson 1: Identifying Bottlenecks in Operations
- Lesson 2: Applying Optimization to Improve Efficiency
  Module 5, Section 2, Lesson 2: Applying Optimization to Improve Efficiency

Section 3: Simulation and Scenario Analysis
- Lesson 1: Fundamentals of Simulation Methods
  Module 5, Section 3, Lesson 1: Fundamentals of Simulation Methods
- Lesson 2: Scenario Analysis for Decision Making
  Module 5, Section 3, Lesson 2: Scenario Analysis for Decision Making

Section 4: Project-Based Learning in Optimization
- Lesson 1: Planning and Defining a Project
  Module 5, Section 4, Lesson 1: Planning and Defining a Project
- Lesson 2: Integrating Optimization Techniques in Projects
  Module 5, Section 4, Lesson 2: Integrating Optimization Techniques in Projects

Section 5: Review and Future Directions
- Lesson 1: Recap of Essential Concepts
  Module 5, Section 5, Lesson 1: Recap of Essential Concepts
- Lesson 2: Assessment, Evaluation, and Next Steps
  Module 5, Section 5, Lesson 2: Assessment, Evaluation, and Next Steps