Exercises Analysis on Manifolds  (MRI Master Class, Mastermath)

See also: theory


Fall semester 2009
The first weeks you are welcome to attend the intensive reminder on the basic theory of manifolds.

We suggest to do the exercises in the order listed. You should do at least three of them.
The take home exercise should be handed in for grading during next week's exercise class.
 
(01) Week 39, sep 23
1.5: 2, 3, 9, 7, 12, 8, 4. Take home exercise: 1.5.1.
 
(02) Week 40, sep 30
2.1.4, 2.1.6, prove Example 2.2.5, 2.3.1, 2.3.6, 2.4.6, 2.4.4. Take home exercise: 2.3.5.
 
(03) Week 41, oct 7
3.8.7, 3.7.2, 3.7.3, 3.1.2, 3.5.3. Take home exercise: 3.6.3.
 
(04) Week 42, oct 14
4.1.5, 4.1.6, 4.1.15, 4.3.4, 4.1.12, 4.2.4, 4.1.7, 4.3.11. Take home: 4.3.13.
 
(05) Week 43, oct 21
5.1.1, 5.1.4, 5.1.5, 5.2.6, 5.2.8. Take home: 5.1.6.
 
(06) Week 44, oct 28
6.2.4, 6.2.5, 6.1.5, 6.1.10, 6.1.11. Take home: 6.2.4 (revised) and 3.8.7 (extended).
Week 45, nov 4
No lecture.
(07) Week 46, nov 11
7.3.4, 7.3.5, 7.3.7, 7.5.4, 7.5.5. Take home 7.3.9 + 7.3.10.
The take home exercise for lecture 7 was formulated too sketchily for those not familiar with the definition of sheaf. I have therefore made a revised version.
Note that the exercise needs Lemma 7.3.8 in stronger form.
It this take home exercise is too abstract to your taste, you are perfectly welcome to instead hand in the following alternative take home exercise, which is more concrete.
 
We will change the formula of the exercise class. From now on take home exercises will be much more concrete.
Also, for Lecture 8 (November 18) no take home exercise will be given. On November 25, there will be a 45 minutes lecture, and 2 hours of exercise class, with exercises done on the blackboard.
 
(08) Week 47, nov 18
No take home exercise
 
(09) Week 48, nov 25:
2 hours exercise class, from 11:00 - 12:45. The following exercises will be discussed in front of the blackboard:
  • Ex. 1.5.1 (Gijs, 15 minutes)
  • Ex. 3.6.3 (Ionut, 30 minutes) Solution to Exercise 3.6.3, written by Ionut
  • Break
  • Ex. 4.3.13 (Gijs, 15 minutes, only last item)
  • Sheaf property of ps.d.o.'s modulo smoothing (Ivan, 30 minutes)
    • Take home exercise Lecture 9, deadline December 7.
     
    (10) Week 49, dec 2
    Take home exercise: 10.4.1. Deadline for handing in: December 12.
     
    (11) Week 50, dec 9
    Take home exercise 10.6.7. Deadline for handing in: before Christmas.
     
    (12) Week 51, dec 16
    Last exercise class, no new exercises.
    Dates for oral examination have been fixed. If you have not fixed a date yet, please send an email to E.P. van den Ban.
     
    Last update: 21/6-2009