Inhaltsbeschreibung / course description and syllabus

*16.04.2017*: I will be available to review your results on the April 12 exam (**Klausureinsicht**) on Tuesday, April 18, from 3 to 4pm.*04.04.2017*: The**second final exam date**is April 12, 2017 in RUD 26, 0'310, beginning at 9:00. All the information given below for the March 2 exam applies to this one as well (see the announcement from 21.02.2017).*02.03.2017*: I will be available to review your results on the March 2 exam (**Klausureinsicht**) on Tuesday, March 7, from 1 to 3pm*21.02.2017*: Information on the**final exam**, March 2, 2017:- The exam will take place in RUD 26, 0'310, beginning at 9:00, and will last three hours (though I expect that most people will not need more than two).
- You may bring with you any notes or books that you wish to use as reference during the exam. Electronic aids such as calculators or smartphones will not be allowed.
- There is a practice exam posted below, under the weekly problem sets. The actual exam will be of roughly the same format and same level of difficulty, though it might be shorter. (For the practice exam I have not made an effort to make sure it is doable within two hours, but for the real exam I will.)
- There will be an alternative exam date on April 12, see the Prüfungsangelegenheiten page for details.

*21.02.2017*: I will have**extra office hours**this week and next.- Tuesday 21.02, 15:00 - 16:00 (as usual)
- Wednesday 22.02, 13:00 - 14:00
- Thursday 23.02, 13:00 - 14:00
~~Monday 27.02, 14:00 - 16:00~~(canceled due to illness)- Tuesday 28.02, 13:00 - 16:00 (lengthened to compensate for the Monday cancelation)

*21.02.2017*: The solutions for Problem Sets 13 and 14 are now available below.*16.02.2017*: If you didn't get your graded takehome midterm back yet, you can pick it up in my office.*16.02.2017*: A practice final exam will be posted here by next Tuesday.*9.01.2017*: The class will not meet on Tuesday 17.01.2017 (both lecture and Übung) or Thursday 26.01.2017 (lecture). On Thursday 19.01.2017 the class will meet as usual, but with a substitute lecturer.*9.01.2017*: The take-home midterm is now available (see below under*Problem sets*) and will be due 24.01.2017.*13.12.2016*: The final exam will take place on 2.03.2017 (registration deadline 16.02.2017). The second exam date is 12.04.2017 (registration deadline 29.03.2017). See the math department's Prüfungsangelegenheiten page for administrative details.*13.12.2016*: The take-home midterm will be distributed on January 10 and due two weeks later (January 24).*17.11.2016*: Today's lecture didn't quite cover everything that was planned, and as a result, Problem 4(g) on Problem Set 5 is not doable based only on what was covered in lecture. You need the coordinate formula for computing the exterior derivative, which we'll talk about next Tuesday.*31.10.2016*: The version of Problem Set 2 handed out last week had an error in the reading suggestion (it referred to the 2013 edition of Lee, despite claims to the contrary). A corrected version has now been posted below.*18.10.2016*: Linguistic compromise: the lectures will be in English, but the Übungen / problem classes in German. (Fragen dürfen aber auch in der Vorlesung gern auf Deutsche gestellt werden. And the problem sets will continue to be printed in English.)*17.10.2016*: Die Übung findet in der ersten Semesterwoche nicht statt. / The problem class will not meet in the first week of the semester.

topics covered in the lectures (updated regularly)

- Problem set 1 (distributed 18.10.2016)
- Problem set 2 (distributed 25.10.2016) -- updated version (with error in the suggested reading corrected)
- Problem set 3 (distributed 1.11.2016)
- Problem set 4 (distributed 8.11.2016)
- Problem set 5 (distributed 15.11.2016)
- Problem set 6 (distributed 22.11.2016)
- Problem set 7 (distributed 29.11.2016)
- Problem set 8 (distributed 6.12.2016)
- Problem set 9 (distributed 13.12.2016)
- Problem set 10 (distributed 3.01.2017)
- Take-home midterm (distributed 10.01.2017)
- Problem set 11 (distributed 24.01.2017)
- Problem set 12 (distributed 31.01.2017) -- updated version with minor corrections
- Problem set 13 (distributed 7.02.2017) -- updated version with minor corrections
- Problem set 13 Solutions (for Problem 2 only)
- Problem set 14 (distributed 14.02.2017)
- Problem set 14 Solutions
- Practice exam / Probeklausur:
*Note that while this practice exam is designed to be of a similar format and difficulty to the actual exam, the actual exam may be shorter. It will be designed to be easily doable within two hours, and you will have a third in case you need it.*

- Chapter 1: Title page, preface and introduction
- Chapter 2: Bundles
- Chapter 3: Connections
- Chapter 4: Natural constructions on vector bundles
- Chapter 5: Curvature on bundles
- Chapter 6: Curvature in Riemannian geometry
- Appendix A: Multilinear algebra and index notation
- Appendix B: Lie groups and Lie algebras

- Vorlesungskript von Helga Baum
- For some amazing animations of the Hopf fibration, I recommend Chapter 7 of Dimensions