MATH-F310: Differential Geometry I


Room: P.OF.2068-2070;     Time: Mondays, 10:00-12:30.
Room: P.A2.222;     Time: Thursdays, 10:00-12:30.

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

Lecture notes (Last updated: 17 DEC 2021)

Evaluation: The final mark consists of 80% for a written exam and 20% for homeworks.
Mock exam: If you wish to test yourself before the real exam, download and print the mock exam and allow yourself 2h30min for solving. Notice that the mock exam covers only Sections 2 and 3 of the lecture notes. The real exam will cover all material of the course.
Exam: The written exam takes place on 18.01.2022 in P.FORUM.G (Auditoire DOLLO), 9:20 - 12:30 (approx.).
Notice the following:

  • First and foremost, make sure that you are healthy on the day of the exam. Should you have any symptoms of Covid-2019, please do not take any unnecessary risk and stay home. In this case please also contact me by e-mail.
  • It is mandatory to wear a mask during the exam.
  • 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.
  • The admission to the room will begin at 09:25 on the day of the exam. Please be there on time, however do not come earlier than 09:20.
  • 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.
  • The problems in Parts C and D of the exam will be related to the material of Sections 1-4 of the lecture notes. However, questions in Parts A and B may be related to the material of Sections 5 and 6.
  • 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.


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.
A.Shastri. Elements of differential topology, CRC Press.


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

Excercise sheet 1 (Deadline: 05.10)
Excercise sheet 2 (Deadline: 12.10)
Excercise sheet 3 (Deadline: 19.10)
Excercise sheet 4 (Deadline: 26.10)
Excercise sheet 5 (Deadline: 09.11)
Excercise sheet 6 (Deadline: 16.11)
Excercise sheet 7 (Deadline: 30.11)
Excercise sheet 8 (Deadline: 07.12)
Excercise sheet 9 (Deadline: 14.12)