### Lecture Notes

In this section we will provide some lecture notes for material given in this course. These notes are not complete in the sense that they are only outlines with some details included.

### Lecture Notes for Bennett, *Affine and Projective Geometry*.

- Introduction
- Affine Planes
- Definitions and Examples
- Some combinatorial results
- Orthogonal Latin Squares
- Affine Planes and Latin
Squares
- Projective Planes

- Desarguesian Affine Planes
- The Fundamental Theorem and Addition
on Lines
- Desargues' Theorem
- More Addition on Lines
- Multiplication on Lines of an
Affine Plane
- Pappus' Theorem and Further
Properties

- Introducing Coordinates
- Division Rings and Isomorphisms
- Coordinate Affine Planes
- Coordinatizing Points
- Linear Equations
- The theorem of Pappus

- Coordinate Projective Planes
- Projective Points and
Homogeneous Equations in
**D**^{3}
- Non-homogeneous Coordinates
- Projective Conics
- Pascal's Theorem
- Non-Desarguesian Coordinate Planes
- Some Examples of Veblen-Wedderburn Systems
- A Projective Plane of order 9
- A non-Desarguesian affine plane of
order 9

- Projective Spaces
- Planes in Projective Space
- Dimension and Desargues
Theorem

The following sets of lecture notes do not correspond to the text we are using, and are provided only as an additional reference.

#### Lecture Notes for Beutelspacher & Rosenbaum

- Synthetic Geometry
- Foundations
- The Axioms of Projective Geometry
- Structure of Projective Geometry
- Quotient Geometries
- Finite Projective Spaces
- Affine Geometries
- Diagrams

- Analytic Geometry
- The Projective Space P(V)
- The Theorems of Desargues and Pappus
- Coordinates
- The Hyperbolic Quadric of PG(3,F)
- Normal Rational Curves
- The Moulton Plane
- Spacial Geometries are Desarguesian

- Representation Theorems
- Quadratic Sets
- Fundamental Definitions
- The Index of a Quadratic Set
- Quadratic Sets in Spaces of Small Dimension
- Quadratic Sets in Finite Projective Spaces

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*Last updated January 20, 2003*