Introduction to Geometric Combinatorics and Discrete Geometry

Geometric combinatorics sits at the fascinating intersection of geometry and discrete mathematics, providing the theoretical backbone for modern computer graphics, robotics, and geographic information systems. This course offers a clear, accessible entry point into understanding how discrete geometric objects interact and how to solve problems involving points, lines, polygons, and polytopes. You will transition from understanding basic spatial arrangements to analyzing complex geometric structures and modern computational applications. Under the guidance of structured written explanations, you will learn to approach unsolved problems in the field and apply combinatorial proofs to spatial configurations. What you'll learn: Understand core concepts of convex hulls, polytopes, and triangulation; Apply combinatorial methods to analyze point configurations and line arrangements; Solve discrete geometry problems using Radon's theorem and Helly's theorem; Explore modern computational applications of geometric algorithms; Analyze open, unsolved problems in contemporary combinatorial geometry. The course begins with essential terminology and foundational definitions of convexity and dimension before moving systematically through arrangements, configurations, and modern algorithmic applications. This course is designed specifically for beginners in discrete mathematics, computer science students, and curious problem solvers with no prior background in advanced geometry. Start your journey into the mathematical structure of space today.