MATH-F310: Differential Geometry I


Room: P.2NO 707.
Time: As a rule, Tuesdays 10:00-12:00. However, 23.09 16:00-18:00 and 03.11 14:00-16:00.

Course content: This course is the first part of the Differential Geometry course. In particular, basic notions and methods of differential geometry such as surfaces, smooth manifolds, vector fields etc. appearing both in various branches of mathematics and physics will be introduced and developed.

Lecture notes: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7.
Older lecture notes explaining abstract manifolds in more details.

Evaluation: The final mark consists of 80% for a written exam and 20% for homeworks.

Mock exam: To test yourself, try to solve (and write down clearly!) as much as possible in 3 hrs. Two solutions of your choice may be checked if submitted by 06.12 at the latest.
Solutions of the problems for the mock exam.

Exam: The written exam takes place on 17.01.2022 in P.FORUM.F - Auditoire TITS, 16:00 - 20:00. Notice the following:

  • Please have a photo ID (for example, your ULB-Card) with you.
  • The exam will last 3hrs. Of course you can leave earlier if you are finished earlier.
  • As a rule, you should write your solutions in English. However, if you feel that you cannot write in English, please do write in French. In the latter case, keep in mind that it is in your interest to be brief and write clearly.
  • You may bring only a pen and a bottle of water (a drink) to the exam.
  • Please do not bring any paper to the exam.
  • Please be particularly attentive to details while answering questions in Part A. For example, the formulation of a theorem should contain all hypotheses, a definition should be correct AND complete.
  • You may be asked to prove a theorem (proposition, lemma, corollary) that was discussed during the lectures. You will not be asked to reproduce long proofs (containing more than 2 steps), however you may be asked to reproduce individual steps from long proofs.


S.Montiel, A.Ros. Curves and Surfaces, AMS.
D.Barden, C.Thomas. An introduction to differential manifolds, Imperiall College Press.
J.Lee. Introduction to smooth manifolds, Springer Verlag.
L.Tu. An introduction to manifolds, Springer Verlag.


Room: P.2NO 707.    Time: Fridays, 16:00-18:00.

Excercise sheet 1 (Deadline: 07.10)
Excercise sheet 2 (Deadline: 14.10)
Excercise sheet 3 (Deadline: 21.10)
Excercise sheet 4 (Deadline: 28.10)
Excercise sheet 5 (Deadline: 4.11)
Excercise sheet 6 (Deadline: 11.11)
Excercise sheet 7 (Deadline: 02.12)
Excercise sheet 8 (Deadline: 09.12)
Excercise sheet 9 (Deadline: 16.12)
Excercise sheet 10
Excercise sheet 11