Geometry 2022

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.


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.


Computer/Mathematica resources