Linear Programming Foundations for Advanced Mathematics

Linear programming is a foundational pillar of applied mathematics and decision science, essential for solving complex optimization problems in academic research and industry. This text-only course breaks down the rigorous mathematical theory and practical algorithms of linear programming into accessible, step-by-step written explanations. You will transition from understanding core geometric properties to confidently solving multi-variable optimization models. What you will learn: Understand the foundational terminology, convex sets, and geometric properties of linear programming; Formulate real-world scenarios into precise mathematical optimization models; Master the mechanics of the Simplex and Two-Phase Simplex algorithms through structured walkthroughs; Apply duality theory to derive dual problems and perform sensitivity analysis; Explore modern computational concepts including interior-point methods and basic vector-based formulations. This course begins with essential mathematical definitions and graphical methods before progressing systematically to algebraic algorithms, duality, and post-optimality analysis. It is designed for students of mathematics, economics, or data science who want a deep, conceptual understanding of optimization without needing prior exposure to advanced operations research. Start reading today to master the mathematical principles of optimization.