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. On the other hand, the lecture slides are complete. They are .pdf files which can be downloaded and printed.

Lecture Notes for Beutelspacher & Rosenbaum

1. Synthetic Geometry
1. Foundations - (slides .pdf file)
2. The Axioms of Projective Geometry
3. Structure of Projective Geometry - (slides .pdf file)
4. Quotient Geometries - (slides .pdf file)
5. Finite Projective Spaces - (slides .pdf file)
6. Affine Geometries - (slides .pdf file)
7. Diagrams
- (slides .pdf file)
2. Analytic Geometry
1. The Projective Space P(V) - (slides .pdf file)
2. The Theorems of Desargues and Pappus - (slides .pdf file)
3. Coordinates - (slides .pdf file)
4. Finite Fields (.pdf file)
5. The Hyperbolic Quadric of PG(3,F) - (slides .pdf file)
6. Normal Rational Curves - (slides - next 2 sections also .pdf file)
7. The Moulton Plane - (slides in above file)
8. Spacial Geometries are Desarguesian - (slides in above file)
3. Representation Theorems
1. Central Collineations - (slides .pdf file)
2. Representation of Projective Spaces - (slides .pdf file)
3. Representation of Collineations - (slides .pdf file)
4. Quadratic Sets
1. Fundamental definitions - (slides .pdf file)
2. The index of a quadratic set - (slides in above file)
3. Quadratic sets in spaces of small dimension - (slides .pdf file)
4. Quadratic sets in finite projective spaces - (slides in above file)
5. Elliptic, parabolic and hyperbolic quadratic sets - (slides .pdf file)
6. The Klein quadratic set - (slides .pdf file)
7. Quadrics - (slides .pdf file)
8. Plücker coordinates

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

• Affine Planes; Transformations of the Affine Plane
• Completion of the Affine Plane; Homogeneous Coordinates for the Real Projective Plane
• Desargues Axiom; Axioms for Projective Space; Principle of Duality
• Elements of Group Theory; Automorphisms of the Fano Plane
• Fano's Axiom; Harmonic Points; Perspectivities and Projectivities
• The Fundamental Theorem; Geometry of Complex Numbers; Pappus' Theorem
• Division Rings; The Quaternions; A noncommutative division ring with characteristic p
• Pⁿ(R); the Automorphism group of Pⁿ(R)