Linear and Integer Programming Fundamentals

Mathematical optimization is a cornerstone of modern decision-making, computer science, and operations research. This comprehensive text-based guide introduces you to the core principles of linear and integer programming from the ground up. You will build a rigorous conceptual foundation, learning how real-world resource allocation and scheduling problems translate into formal mathematical models, how polyhedral geometry governs optimal solutions, and how foundational algorithms operate. What you'll learn: - Understand foundational definitions, terminology, and standard versus canonical problem formulations - Formulate linear programming (LP) and integer programming (IP) models for real-world scenarios - Explore geometric foundations including polyhedra, polytopes, and extreme point vertices - Apply algebraic criteria to characterize vertices and basic feasible solutions - Analyze finite solvability concepts, including Fourier-Motzkin elimination - Connect linear optimization to discrete structures like graph matching polytopes - Modernize workflows by translating mathematical formulations into contemporary solver-ready notation The course begins with foundational vocabulary and geometric intuition before guiding you through formal algebraic definitions, solvability principles, and combinatorial applications. Each concept is broken down with step-by-step written explanations and practical formulation exercises. This course is designed for beginners in operations research, computer science, or applied mathematics. No prior optimization background is required, only basic comfort with introductory linear algebra concepts. Start reading today to master the mathematical foundations of optimization.