Monday 10:15-12:00 Aud 8

Tuesday 13:15-15:00 Aud 5

Friday 9:15-10:00 Aud 8

Tuesday 15:15-17:00 room A104

Friday 10:15-12:00 room A101

ISBN 978-87-7078-458-0, Polyteknisk Boghandel.

(preliminary plan)

17/11 Monday 1.1-1.5

18/11 Tuesday 1.6-1.8

21/11 Friday 2.1-2.3

24/11 Monday 2.4-2.7

25/11 Tuesday 2.7-2.10

28/11 Friday 2.11

1/12 Monday 3.1-3.5

2/12 Tuesday 3.5-3.8

5/12 Friday 3.8-3.10

8/12 Monday 4.1-4.3

9/12 Tuesday 4.4-4.6

12/12 Friday 4.7-4.10

15/12 Monday 5.1-5.5

16/12 Tuesday 5.6-5.8

19/12 Friday 5.9-5.11

22/12 Monday No lecture. (See about a mandatory written assignment below)

2/1 Friday No lecture.

5/1 Monday 6.1-6.4

6/1 Tuesday 6.5-6.8

9/1 Friday 6.9-6.10

20/1 Tuesday 13:15-15:00 Aud 8 Question session.

The exercise classes are conducted by Massimilano Ungheretti

18/11 Tuesday No exercise class

21/11 Friday P1

25/11 Tuesday P2

28/11 Friday P3

2/12 Tuesday P4

5/12 Friday P5+E1

9/12 Tuesday P6+E2

12/12 Friday P7+E3

16/12 Tuesday P8+E4

19/12 Friday P9+E5+E6

2/1 Friday No exercise class. (See about a mandatory written assignment below)

6/1 Tuesday P10+E7+E8

9/1 Friday P11+E9+E10

13/1 Tuesday P12+E11+E12+E13+E14 Note: Double class: 13:15-17:00, room 1-0-37 (DIKU)

16/1 Friday. If there is interest: Selected exam question presentations. 10:15-12:00, room 1004 (DIKU)

P1: 1.1-1.4, Exercises 1.1-1.7. 3,4,5,7

P2: 1.5-1.8, Exercises 1.8-1.17. 11,12,13,15,17

P3: 2.1-2.5, Exercises 2.1-2.10. 4,5,6,7,9,10

P4: 2.6-2.10, Exercises 2.11-2.16. All

P5: 3.1-3.6, Exercises 3.1-3.5. 2,3,4

P6: 3.7-3.10, Exercises 3.6-3.10. 6,7,8,10

P7: 4.1-4.4, Exercises 4.1-4.8. 2,3,4,5

P8: 4.5-4.8, Exercises 4.9-4.15. 10,11,12,13

P9: 5.1-5.6, Exercises 5.1-5.5. 2,3,4

P10: 5.7-5.10, Exercises 5.6-5.12. 8,9,10,11

P11: 6.1-6.5, Exercises 6.1-6.7. 1,3,4,6

P12: 6.6-6.9, Exercises 6.8-6.14. 10,12,13,14

The scope of the exam is as follows: The student draws a question from the following list, and is allowed approximately 30 minutes of preparation. The examination lasts 25 minutes, of which 15-20 minutes will be spent on the presentation. After that questions will be asked in the entire curiculum of the course. At the end the student receives a grade.

The official language of the exam is English (but Danish will be accepted as well).

E2: Abstract manifolds. Projective space.

E3: The Grassmann manifold.

E4: The tangent space of an abstract manifold

E5: Smooth maps and their differentials

E6: Submanifolds

E7: Submersive maps and level sets

E8: The orthogonal group is a Lie group

E9: Partition of unity

E10: Embedding in Euclidean space

E11: The components of a manifold

E12: Vector fields and Lie brackets

E13: The Lie algebra of a Lie group

E14: The Lie algebra of GL(n,R)