Table of Contents

Module 1: Introduction

Problem O: An Introduction to Geometric Probability
Problem 1: Buffon's Needle Problem
Problem 2: Bertrand's Problem
Problem 3: Buffon's Needle Problem - II
Problem 4: Invariant Measures - A First Look

Module 2: Convex Sets

Problem 5: Convex Sets
Problem 6: Envelopes
Problem 7: Perimeter and Area
Problem 8: Random Triangles and an Introduction to Density

Module 3: Applications of Convex Sets

Problem 9: Sets of Triples of Points
Problem 10: Densities for Sets of Lines in the Plane
Problem 11: Convex Sets Again and Lines that Intersect Them
Problem 12: The Isoperimetric Inequality and Other Geometric Applications
Problem 13: Separating Convex Sets
Problem 14: Average Length of Chords in a Square
Problem 15: An Application of the Density of Points
Problem 16: Point Picking
Problem 17: Density for Sets of Strips
Problem 18: Buffon's Needle Again

Module 4: Densities

Problem 19: The Group of Rigid Motions
Problem 20: Rigid Motions and Kinematic Density
Problem 21: Rigid Motions and Needles
Problem 22: The Intersection of Convex Sets
Problem 23: Integrals for Kinematic Density