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Wintersemester 2011/2012

Differenzierbare Mannigfaltigkeiten (BA)/ Differential Geometry (TMP)

Gerasim Kokarev (Mathematisches Institut der LMU) and
James Gray (Fakultät für Physik der LMU)

Course description:
This course provides an introduction to basic concepts in geometry, which are essential to a number of other mathematical and physical disciplines.

It is oriented on students in Mathematics and Physics and covers the modules "Differenzierbare Mannigfaltigkeiten" in the Bachelor Mathematics Programme as well as the module "Differential Geometry" in the Master Programme in Theoretical and Mathematical Physics (TMP).

Mathematics Master students taking this course are also able to get credit points for it.

Bachelor-, Diplom- und Lehramts-Studenten die eine Einführung in die Differentialgeometrie hören wollen, sollten diese Vorlesung besuchen. Für Lehramtstudenten eignet sich diese Vorlesung für das Prüfungsgebiet Geometrie im Staatsexamen.

Pre-requisites:
Modules covering Linear Algebra, Several Variable Calculus, and Point-Set Topology.

Lectures schedule:
Lectures will be given in English twice a week, 8.00-10.00 Wed and 8.00-10.00 Fri, Room B 006

Course outline:
The course includes the standard introductory material on manifolds, vector bundles, Lie groups and Lie algebras; vector fields and flows; differential forms, Stokes theorem, de Rham cohomology; Riemannian metrics, connections, curvature.

Reading list:
1. Conlon, L. Differentiable manifolds: a first course. Birkhäuser Advanced Texts: Basler Lehrbücher. 1993. xiv+395 pp.1
2. Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P. Modern geometry - methods and applications. Part II. The geometry and topology of manifolds. Graduate Texts in Mathematics, 104. Springer-Verlag, New York, 1985. xv+430 pp.2
3. Warner, F. Foundations of differentiable manifolds and Lie groups. Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin, 1983. ix+272 pp.

Exercise classes (Übungen):
There have been made some changes to the time slots for exercise classes!

There will be two exercise groups that will now hold at 8.00-10.00 Tue, Room B006, (for Mathematics BSc/MSc) and 12.00-14.00 Thu, Room B133 (for TMP). Please come to the first group meeting to meet a person who will do the classes.

The problem sets for the exercise classes are typed and posted by Dr Bijan Sahamie on his web-page on Fridays and are due a week later by Friday 10am; the marked homework will be then returned at the classes. Students are encouraged to do as many problems in these sets as possible, since they comprise an important part of the course and similar problems are likely to appear on the exam.

In addition, there will be a series of tutorials, hold at 10.00-12.00 Thu, Room 251, where students can ask questions and discuss the material in an informal atmosphere. They will be given by Peter Uebele.

All questions regarding exercise classes and tutorials are coordinated by Dr Bijan Sahamie. Please contact him directly for any query.

Mid-Term Test:
The test will be delivered by Dr Bijan Sahamie on 16 Dec, Friday, Room B006 at 8.00-10.00. Please bring your student ID along with a photo ID, and make sure that you arrive before 8.00am.

All queries concerning the test and the results should be addressed to Dr Bijan Sahamie.

Final Exam:
The exam will be delivered by Dr Bijan Sahamie on 10 Feb, Friday, Room B006 at 8.00-10.00. Please bring your student ID along with a photo ID, and make sure that you arrive before 8.00am.

The results and comments on solutions are available now. PDF <expired link>

All queries concerning the exam and the results should be addressed to Dr Bijan Sahamie.

Resit (Make-up Exam):
The purpose of a resit is to give a second chance to students who failed the scheduled exam or to allow students, with legitimate reasons for missing the scheduled exam, to fulfill the requirements of the course. The resit can not be taken by students who passed the scheduled exam or have not appeared on it without a strong reason.

If you would like to take the resit please register by sending an email to Dr Bijan Sahamie.
The registration deadline is 22 March.

The resit will hold on 5 Apr, Thursday.

Lecture notes:
The notes on the first few lectures and the programme outline are available now. PDF

Footnotes:
1. There is also a second edition of this book: Conlon, L. Differentiable manifolds. Second edition. Birkhäuser Advanced Texts: Basler Lehrbücher. 2001. xiv+418 pp.
2. A similar more up-to-date text is: Novikov, S. P.; Taimanov, I. A. Modern geometric structures and fields. Graduate Studies in Mathematics, 71. American Mathematical Society, Providence, RI, 2006. xx+633 pp.

http://www.mathematik.uni-muenchen.de/~kokarev/teaching/ws11_12.html
Last modified: 14 March 2011