Foundations of Discrete Structures and Optimization

Mastering the mathematical foundations of decision-making is crucial for solving complex problems in computer science and operations research. This text-based course guides you through the essential concepts of discrete structures and optimization, translating complex formulas into clear, actionable logic. You will transition from understanding basic mathematical models to confidently formulating and solving optimization problems. By analyzing real-world constraints, scheduling tasks, and executing algorithmic solutions, you will build a strong analytical foundation suitable for academic exams and practical applications alike. What you'll learn: Understand the fundamental terminology of discrete structures and mathematical modeling; Formulate and solve linear programming problems using graphical, Simplex, and Dual Simplex methods; Analyze sensitivity to understand how changes in constraints impact optimal solutions; Apply integer programming techniques to solve discrete decision-making problems; Solve transportation and assignment models to optimize resource distribution; Master network analysis using PERT and CPM techniques for project scheduling; Explore modern algorithmic perspectives on optimization used in data science today. The course begins with foundational definitions of discrete structures and mathematical modeling before advancing to step-by-step written walkthroughs of optimization algorithms. You will work through structured text explanations and written practice scenarios that reinforce your analytical skills. This course is designed for beginners in operations research, computer science students, and those preparing for competitive academic exams, requiring no prior advanced mathematical background. Start reading today to master the core principles of optimization and discrete structures.