Trent University

Mathematics 3260H

*Geometry II: Projective and Non-Euclidean Geometry*

- MATH 3260H Course Outline [Unofficial summary of the syllabus.]
- Handouts and sources:
- Euclid's Postulates (excerpted from
*Euclid's Elements of Geometry*, edited and translated by Richard Fitzpatrick. - Hilbert's Axioms (adapted from The Foundations of Geometry by David Hilbert)
- Euclid's Postulates Extended
- Axioms for Affine and Projective Planes (adapted from A Problem Course on Projective Planes by Stefan Bilaniuk)

- Euclid's Postulates (excerpted from
- Assignment # 1, 2, 3, 4, 5, 6, τ=2π, 7, 8, 9, 10, 11
- Take-Home Final Examination
- Lectures [All in webm format.] Notes contributed by a student wishing to remain anonymous - thanks!
- Introduction (2021-09-09) [notes]
- Incidence (2021-09-13) [notes]
- Examples of Projective Planes (2021-09-15) [notes]
- Extending an Affine Plane to a Projective Plane (2021-09-16) [notes]
- Some Easy Results (2021-09-20) [notes]
- Counting Points and Lines in a Finite Plane (2021-09-22) [notes]
- When Are Two Projective Planes the Same? (2021-09-23) [notes]
- Free Completion (2021-09-27) [notes]
- Coordinatization (2021-09-29) [notes]
- Coordinatization II (2021-10-06) [notes]
- Coordinatization III (2021-10-07) [notes]
- Collineations (2021-10-13) [notes]
- Collineations II (2021-10-14) [notes]
- Collineations III (2021-10-18) [notes]
- Transitivity (2021-10-20) [notes]
- Transitivity II (2021-10-21) [notes]
- Transitivity III (2021-11-03) [notes]
- Transitivity IV (2021-11-04) [notes]
- Transitivity & Ternary Rings (2021-11-08) [notes]
- Transitivity & Ternary Rings II (2021-11-10) [notes]
- The Elliptic Plane (2021-11-11) [notes]
- Spherical Geometry (2021-11-15) [notes]
- Spherical Geometry II (2021-11-17) [notes]
- The Elliptic Plane II (2021-11-18) [notes]
- The Hyperbolic Plane (2021-11-22) [notes]
- Neutral Geometry (2021-11-24) [notes]
- Neutral Geometry II (2021-11-25) [notes]
- From the Postulates (2021-11-29) [notes]
- From the Postulates II (2021-12-01) [notes]
- From the Postulates III (2021-12-02) [notes]
- Circumference of Circles (2021-12-06) [notes]

- MATH 3260H Course Outline
- Handouts and sources:
- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,

and Solutions to Assignment # 1, 2, 3, 4 - Take-Home Final Examination

- MATH 3260H Course Outline
- Sources
- Assignment # 1, 2, 3, 4, 5, 6, 2π, 7, 8, 9, 10, 11
- Quizzes
- Take-Home Final Examination
- Euclid's axioms and Hilbert's axioms for Euclidean geometry.
- A Problem Course on Projective Planes, version 0.4, by Stefan Bilaniuk.

- MATH 3260H Course Outline
- Readings and Schedule
- Sources
- Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
- Quizzes
- Final Examination

- MATH 326H Course Outline
- Sources
- Problem Set # 1, 2, 3, 4, 5, 6
- Final Examination

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 2021-12-08.