Lecturer: Roland van der Veen, assistants: Boudewijn Bosch, Bram Brongers and Oscar Koster.

Lectures Mondays 13-15, BB 267, Wednesdays 15-17 BB 267, Tutorials: Wednesdays 13-15, Thursdays 11-13 (at)

This course is meant to introduce various types of geometry, roughly divided into three parts: Euclidean, projective and differential geometry. For a longer description of the course see the Ocasys page.

Organisation:

We will make active use of the Nestor discussion board 'projective space', will you join us there? Posting a question on the discussion board is useful for at least four reasons: 1) Making the effort to formulate your question helps solving it. 2) You may get an answer 3) it helps building a community and promotes interaction 4) You get bonus points (see below).

Assessment: Regular homework sets and a written exam. Homework should be handed in or uploaded to Nestor the Wednesday after it was announced before 1pm. Homework counts as 25% of the total grade, written exam counts for 75%. The homework grade is computed as the average of the 6 best sets handed in. Active participation on the Projective space discussion forum in the first four weeks can earn you up to a full bonus point on your homework grade. In the final four weeks you can again earn a full point on your homework grade so in theory you could get a 12 for your homework.

Literature: We will work through the lecture notes specifically written for this course.

1: Week of Feb. 7 | Euclidean geometry: Polyhedra, simplices, linear algebra, Sec 0.1, 1.1 Tutorial exercises: 0.1: 1,2,3, 1.1:1,2,3,4,5 Differential geometry: Spherical geometry, Sec 3.1 Tutorial exercises: 3.1:4,5,1,2 Homework: 1.1:10 and 3.1:6. Due Wed 16-2 before 1pm. |

2: Week of Feb. 14 | Euclidean geometry: Circumscribed sphere Sec 1.1, Simplicial complexes Sec 1.2 Tutorial exercises: 1.1:13,14, 1.2:1,2,4,5 Differential geometry: Inner products sec 0.1, Riemannian metric, lengths, angles, volumes, Sec 3.2 Tutorial exercises:3.2:1,2,3, 0.1:1 Homework: 1.2:9 and 3.2:5a,b,d,e,g. Due Wed 23-2 before 1pm. |

3: Week of Feb. 21 | Euclidean geometry: Simplicial complexes, Euclidean isometries. Sec 1.2, 1.3 Tutorial exercises:1.2:12,6,10,8, 1.3:1,2,3 Differential geometry: Pull-back metric and Hyperbolic geometry. Tutorial exercises: 3.2:5c,f,h,i 3.2:6,7,8 Homework: 1.2:14 and 3.2:9. Due Wed 2-3 before 1pm. |

4: Week of Feb. 28 | Projective geometry: Perspective drawing, projective space. Tutorial exercises: 2.0:1,2 and 2.2:1 Projective geometry: Projective transformations and Desargues theorem. Tutorial(at 5161.0014b) exercises: 2.1:3,4,5, 1.3:2 Homework: 2.1:2 and 1.3:1. Due Wed 9-3 before 1pm. |

5: Week of Mar. 7 | Projective geometry: Affine and projective hypersurfaces, sec. 2.1,2.2 Tutorial exercises: 2.1:7,8,9 and 2.2:3,4,5 Projective geometry: Affine transformations, classification of quadrics, polarity, Sec 2.2 Tutorial(at 5173.0151) exercises: 2.1:6 and 2.2:1,9 Homework: Exercises 2.2:7a, 2.2.8. Due Wed 16-3 before 1pm. |

6: Week of Mar. 14 | Euclidean geometry: Simplicial complexes, Euclidean Isometries sec 1.2, 1.3. Tutorial exercises: 1.2:12,13,15, 1.3:3,4,5 Differential geometry: Hyperbolic lines, Euclidean Geodesics, sec 3.2,3.3. Tutorial(at 5173.0151) exercises: 3.2:10,12 and 3.3:1 Homework: Exercises 3.2:11 and 3.3:3. Due Wed 23-3 before 1pm. |

7: Week of Mar. 21 | Euclidean geometry: Euclidean Isometries Tutorial exercises: 1.3: 13(skipping f),12,11,10,14. Differential geometry: Riemannian Geodesics. Tutorial(at 5173.0165) exercises:3.3:1 and 3.4:1 Homework: Exercises 1.3:15 and 3.4:2 Due Wed 30-3 before 1pm. |

8: Week of Mar. 28 | Euclidean geometry:Quaternions and Recap Tutorial exercises: Any exercises previously missed Differential geometry: Recap Projective and Riemannian geometry Tutorial(at 5173.0151) exercises: 0.2:4, 2.2:12, 3.4:3,4,5 |

9: Week of Apr. 4 | Catch up session, apr 8, 1-3pm at NB 5113.0202 Mock exam Mock exam solutions |

10: Week of Apr. 11 | Written Exam apr 11, 4-6pm, Exam Hall 1 A16 - G6 Blauwborgje 4, Solutions |

10: Week of June 30 | Retake Exam June 30, 4-6pm, Exam Hall 1 H13 - J14 Blauwborgje 4. |

- Linear algebra reference: Linear algebra by Klaus Jaenich
- 1-page Linear Algebra cheat sheet by Jorge Becerra
- Optimal blur-free camera gliding makes for an interesting real world application of hyperbolic geometry and apparently is the hardest math my colleague Dror Bar-Natan has ever done.
- Normal distributions on R are parametrized by a point (mu,sigma) in upper half space and the Fisher distance between two such distributions is precisely the hyperbolic distance.
- Lecture notes from the course on geometry in 2021 and 2020 (includes some more advanced material, use at your own risk)

- Ceva's theorem
- Nine point circle
- Nine point circle tangencies
- Morley's theorem
- Two projective lines in a projective plane.
- Mathematica: Riemannian Chart routine, Length, pull-back area, ON frame.
- Mathematica: Drawing a simplicial torus.
- Mathematica: Drawing a simplicial Mobius strip.
- Mathematica: computer algebra illustration of Exercises 3.3.4 d).