Combinatorial Optimization Fundamentals

Finding the most efficient route, the perfect matching, or the optimal allocation of scarce resources is at the heart of modern computer science and operations research. This text-based course introduces you to the mathematical foundations and practical algorithms used to solve these complex decision-making problems. You will transition from understanding basic mathematical models to formulating and solving real-world optimization challenges. By studying key concepts and walking through clear, written explanations, you will gain the confidence to analyze network flows, matching problems, and approximation algorithms. What you'll learn: 1. Understand the core principles of linear programming and duality. 2. Formulate and solve classic network flow and maximum flow problems. 3. Explore matching theory and its applications in resource allocation. 4. Learn matroid theory and how greedy algorithms find optimal solutions. 5. Analyze approximation algorithms for tackling computationally difficult NP-hard problems. 6. Practice modeling optimization problems using modern algorithmic frameworks and pseudocode. The course begins with foundational definitions of graphs, complexity, and linear programming before moving into network flows, matching theory, and advanced approximation techniques. It is designed for beginners in computer science, mathematics, or operations research, requiring only basic algebra and introductory programming concepts. Start building your optimization toolkit today through clear, step-by-step written lessons.