GEOMETRY 2, FALL 2011

See also the Study Information System SIS page and (requires login) Absalon

LECTURES

21/11 Monday 1.1-1.3
22/11 Tuesday 1.4-1.6
25/11 Friday 1.7-1.8
28/11 Monday 2.1-2.3
29/11 Tuesday 2.4-2.7
2/12 Friday 2.8-2.10
5/12 Monday 3.1-3.5
6/12 Tuesday 3.6-3.8
9/12 Friday 3.9-3.10
12/12 Monday 4.1-4.3
13/12 Tuesday 4.3-4.5
16/12 Friday 4.6-4.8
19/12 Monday 5.1-5.5
20/12 Tuesday 5.6-5.11
23/12 Friday Cancelled

2/1 Monday Lectures this week are replaced by a mandatory written assignment
3/1 Tuesday Lecture cancelled (but not exercises)
6/1 Friday Lecture cancelled (but not exercises)
9/1 Monday 6.1-6.4
10/1 Tuesday 6.5-6.8
13/1 Friday 6.9-6.10

EXERCISE CLASSES

Exercise classes are used for problem solving, and for presentation of exam questions by participants as preparation for the oral exam. There are 12 problem programs P1-P12, and 12 exam questions E1-E12. The plan below may be revised when the number of students is known - the goal is that every student presents one question.

22/11 Tuesday Exercises cancelled (but not lectures)
25/11 Friday P1
29/11 Tuesday P2
2/12 Friday P3
6/12 Tuesday P4+E1
9/12 Friday P5+E2
13/12 Tuesday P6+E3
16/12 Friday P7+E4
20/12 Tuesday P8
23/12 Friday Cancelled

3/1 Tuesday P9+E5.
6/1 Friday P10+E6
10/1 Tuesday P11+E7
13/1 Friday P12+E8
17/1 Tuesday E9+E10
20/1 Friday E11+E12

MANDATORY EXERCISE ASSIGNMENT

There is one mandatory written assignment during the course. It will be web-posed Monday January 2, and the deadline for return is Friday January 6 at the start of the exercise class.

EXAM

26-27/1 Thursday-Friday: Oral exam

PROBLEM PROGRAMS

Select problems from the following list. The problems cover the mentioned sections.
P1: 1.1-1.4, Exercises 1.1-1.7
P2: 1.5-1.8, Exercises 1.8-1.17
P3: 2.1-2.5, Exercises 2.1-2.10
P4: 2.6-2.10, Exercises 2.11-2.15
P5: 3.1-3.6, Exercises 3.1-3.5
P6: 3.7-3.10, Exercises 3.6-3.10
P7: 4.1-4.4, Exercises 4.1-4.8
P8: 4.5-4.8, Exercises 4.9-4.15
P9: 5.1-5.6, Exercises 5.1-5.5
P10: 5.7-5.10, Exercises 5.6-5.12
P11: 6.1-6.5, Exercises 6.1-6.7
P12: 6.6-6.9, Exercises 6.8-6.14

EXAM QUESTIONS

E1: Manifolds in R^n
E2: Abstract manifolds. Projective space.
E3: The tangent space of an abstract manifold
E4: Smooth maps and their differentials
E5: Submanifolds
E6: The orthogonal group is a Lie group
E7: Partition of unity
E8: Embedding in Euclidean space
E9: Connectedness and components
E10: Vector fields and Lie brackets
E11: The Lie algebra of a Lie group
E12: The Lie algebra of GL(n,R)