Table of Contents

Module 1: Introduction

Problem O: Introduction
Problem 1: What is a geometry?
Problem 2: Some Classical Finite Geometries
Problem 3: Incidence Matrices
Problem 4: Dual Geometries
Problem 5: Graphs
Problem 6: Isometries

Module 2: Linear Spaces

Problem 7: Subspaces
Problem 8: Linear Spaces
Problem 9: Numerical Relationships Between Points and Lines
Problem 10: Order of a Projective Plane
Problem 11: Dimension
Problem 12: The Exchange Property
Problem 13(a): Linear Transformations
Problem 13(b): Linear Transformations

Module 3: Noneuclidean Geometry

Problem 14: The Projective Plane
Problem 15: The Duality Principle
Problem 16: Finite Hyperbolic Geometries
Problem 17: Infinite Hyperbolic Geometries
Problem 18: Embeddings
Problem 19: History of the Real Projective Plane

Module 4: Projective Geometry

Problem 20: Coordinates and the Real Projective Plane
Problem 21: Projective Coordinate Planes
Problem 22: Affine Coordinate Planes
Problem 23: Pappus' Theorem
Problem 24: Desargues' Theorem
Problem 25: Central Collineations
Problem 26: Desargues' Theorem in Affine Planes
Problem 27: Desargues' Theorem in Projective Planes
Problem 28: Configurations

Module 5: Applications

Problem 29: Graphs
Problem 30: Colorings
Problem 31: The School Girl Problem
Problem 32: The Communication Problem
Problem 33: Walks

Module 6: Quadrangles

Problem 34: Synthetic Geometry
Problem 35: Polarities
Problem 36: Duads and Synthemes