Geometry III/V
2023/24
Time:0 | Mondays 2pm | in CG218 |
0 | Tuesdays 3pm (weeks 3,5,7,9 and 13,15,17,19) ___ | in MCS2068 |
0 | Fridays 4pm -- | in CG218 |
Lecturer: | Anna Felikson | |
e-mail: | anna dot felikson at durham dot ac dot uk | |
Office hours: _ | Tuesdays 11:30-12:30 | in MCS3006 |
Textbook: |
Further reading and some on-line resources on geometry |
Preliminary course content (subject to change):
Michaelmas topics: Euclidean geometry, spherical geometry, affine and projective geometries;
Epiphany topics: Möbius transformations, hyperbolic geometry, further topics (geometric surfaces, discrete groups).
Schedule:
Assignments:
- There will be 4 sets of marked assignments during each term (to submit through Gradescope on Fridays by 6pm, weeks 3,5,7,9 and 14,16,18,20). --
- There will be also weekly unmarked sets of exercises. Please solve them timely!
- In addition, there will be additional reading material for MSc students, see
here for the instructions.
Week # | Questions | Hints | Due date: Fr 6pm | Solutions | Feedback | |
1-2 | HW 1-2 | Hints 1-2 | October 20 | Solutions | Feedback | Isometries of Euclidean plane |
3-4 | HW 3-4 | Hints 3-4 | November 3 | Solutions | Feedback | Isometries; actions of groups; a bit of spherical geometry |
5-6 | HW 5-6 | Hints 5-6 | November 17 | Solutions | Feedback | Spherical geometry |
7-8 | HW 7-8 | Hints 7-8 | December 1 | Solutions | Feedback | Affine and Projective geometry |
9-10 | HW 9-10 | Hints 9-10 | ----- | Solutions | Projective geometry, Klein model of hyperbolic geometry | |
Week # | Questions | Hints | Due: Fr 6pm | Solutions | Feedback | |
11-12 | HW 11-12 | Hints 11-12 | February 2 | Solutions | Feedback | Möbius geometry, inversion |
13-14 | HW 13-14 | Hints 13-14 | February 16 | Solutions | Feedback | Poincare disc, upper half-plane |
15-16 | HW 15-16 | Hints 15-16 | March 1 | Solutions | Feedback | Computations in UHP, Klein disc and hyperboloid models |
17-18 | HW 17-18 | Hints 17-18 | March 15 | Solutions | Feedback | Classification of isometries. Horocycles and equidistant curves |
Lecture Notes: (Material to be added during the term)
Handouts:
Some tables to review the course:
Additional handout:
(not an essential part of the course, it is non-examinable!)