Trent University
Mathematics 3260H
Geometry II: Projective and Non-Euclidean Geometry

Fall 2021

• 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)
• 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]

Fall 2019

• MATH 3260H Course Outline
• Handouts and sources:
  • Euclid's Postulates
  • Hilbert's Axioms
  • A Problem Course on Projective Planes
• 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

Fall 2017

• 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.

Winter 2015

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

Winter 2007 [MATH 326H]

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

Department of Mathematics

Trent University