Differential Geometry (BSc)

Owner	Bachelor Wiskunde
Coordinator	prof. dr. S. Shadrin
Part of	Exchange Programme Faculty of Science, specialisation BSc Mathematics, year 1Bachelor Wiskunde, year 3Dubbele bachelor Wis- en Natuurkunde, year 3

Course manual 2021/2022

Course content

This course is an introduction to the theory of smooth manifolds and differential-geometric structures on them. We'll discuss smooth manifolds, smooth maps, tangent and cotangent bundles, submanifolds, Whitney's embedding and approximation theorems, more general tensors, differential forms, integration, de Rham cohomology, integral curves and manifolds, Lie derivatives, Lie groups, and Lie algebras. 

Study materials

Literature

• John M. Lee. Introduction to smooth manifolds. Second Edition. Graduate Texts in Mathematics 218. Springer

Objectives

• The student is able to work with differentiable manifolds in coordinates and in coordinate-free way
• The student is able to reproduce arguments and constructions in differential geometry
• The student is able to connect topological properties and differential-geometric structures
• The student is able to perform differential-geometric computation in particular examples

Teaching methods

• Lecture
• Seminar

Learning activities

Attendance

Programme's requirements concerning attendance (OER-B):

• Each student is expected to actively participate in the course for which he/she is registered.
• If a student can not be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
• It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
• In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. In case of personal circumstances, as described in OER-A Article A-6.4, an other arrangement will be proposed in consultation with the study advisor.

Assessment

Item and weight	Details
Final grade
30% Tussentoets
50% Tentamen	Must be ≥ 5.5
20% Huiswerk

Naast eindtentamen en de tussentoets krijgen de studenten 12 keer huiswerk. Het cijfer voor het huiswerk is de gemiddelde van de beste 10 (uit 12) huiswerkcijfers. Het is ook vereist om ten minste 5,5 voor het tentamen te krijgen om het vak te halen. 

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Additional information

Analysis on R^n, Topology

Processed course evaluations

Below you will find the adjustments in the course design in response to the course evaluations.

Contact information

Coordinator

• prof. dr. S. Shadrin

Staff

• Bjarne Kosmeijer MSc