Here are the "final marks" (plus some very small comments) after the first exam- well, the ones that I corrected so far (i.e. excluding those of you that needed extra-timem, as I still have to receive those exams from the administration).

And here is the exam, and here are some solutions to the problems from the exam (I may be brief at some point, but I hope this shows some possible and shorter solutions to the problems).

Added on October 25th: the last homework (to be handed in at the start of the exam).

New: the lecture notes- the version of October 23th .

September 26: change in the way I will post the lecture notes (since for some students it seems it was confusing to work with more than 1 file): I will keep one single file, which I will update from time to time. Once some material is posted, I will not make any big change to what was already typed, except for correcting typos (in particular I will make sure that the numbering of the theorems etc will not change). So, in principle, once you printed a part, you do not have to print it again (but, if something looks strange in your copy, do have a look at the file that I keep online, maybe it is just a typo that I already corrected). And here is the last version of the file with:

This is the web-site for the course "Differentieerbare varieteiten" given in blok 1, Fall 2017. Here you will find all the practical informations about the course, changes that take place during the year, lecture notes, etc.

THE LECTURES:

------ Mondays: 9:00 - 10:45, HFG, room 611.

------ Tuesdays: 17:15- 19:00, HFG, room 611.

LECTURER: Marius Crainic.

TEACHING ASSISTANT: Davide Alboresi (D.AlboresiATuu.nl).

THE WERKCOLLEGES:

------ Mondays: 11.00 - 12:45, BBG, room 023.

------ Wednesdays: 911.00 - 12:45, UNNIK, room 209.

HOMEWORKS:

There will be homeworks during the course. Probably around 4-5. They will count for the final mark.

**Note: please do not send your homework by email, unless you aggree with the TA. In any case: please never send the homework to me (the lecturer) by email!!! **

Here is the link where you can find the marks for the homeworks.

- hand in exercises. You will receivce the exercise at the end of the class on Tuesday. You have to hand it in one the next Wednsday, when you arrive at the werkcollege. The everage of the marks for all the homeworks will give one mark HW (maximum 10).

- final exam, for which you will receive a mark E (maximum 10).

Note: you are allowed to bring with you, and use during the exam, three sheets of A4 papers (= six pages) containing definitions, theorems, etc from the course.

**Coordinates of the exam:** The exam will take place on Wednesday, November 8th, between 09.00 - 12.00, in RUPPERT Blauw. The retake will take place on Wednesday, January 3rd 2018, between 09.00 - 12.00, in the math building (HFG), room 611B.

** Final mark:** The final mark will be obtained by combining E (exam mark) and HW (homework mark), by the formula:

max{(7 E+ 3 HW)/10, (17E+ 3H)/20}

I will keep one single file, which I will update from time to time. Once some material is posted, I will not make any big change to what was already typed, except for correcting typos (in particular I will make sure that the numbering of the theorems etc will not change). So, in principle, once you printed a part, you do not have to print it again (but, if something looks strange in your copy, do have a look at the file that I keep online, maybe it is just a typo that I already corrected). the lecture notes (the version of October 10th) .

♣ **WEEK 37/Lecture 1 (September 11):** Reminder on Topology.

Exercises for the werkcollege: read the lecture notes (see above) and try to redo the exam from the last year's course on Topology.

♦ **WEEK 37/Lecture 2 (September 12):** Reminder on Analysis.

Exercises for the werkcollege + the homework: in this file.

Homework:

♦ **WEEK 38/Lecture 3 (September 18):** Ended the reminder on Analysis.

Exercises for the werkcollege:

♦**WEEK 38/Lecture 4 (September 19):** Manifolds and smooth maps; R^n, S^n.

Exercises for the werkcollege:

Homework: here.

♦ **WEEK 39/Lecture 5 (September 25):** The projective spaces, submanifolds.

Exercises for the werkcollege:

♦ **WEEK 39/Lecture 6 (September 26):** More examples (Lie groups); start discussing the tangent space.

Exercises for the werkcollege:

Homework: Homework for October 4th.

♦ **WEEK 40/Lecture 7 (October 2):**

Exercises for the werkcollege:

♦ **WEEK 40/Lecture 8 (October 3):**

Exercises for the werkcollege:

Homework: Homework for October 11.

♦ **WEEK 41/Lecture 9 (October 9):**

Exercises for the werkcollege:

♦ **WEEK 41/Lecture 10 (October 10):**

Exercises for the werkcollege:

Homework: Homework for October 18.

♦ **WEEK 42/Lecture 11 (October 16):**

Exercises for the werkcollege:

♦ **WEEK 42/Lecture 12 (October 17):**

Exercises for the werkcollege:

Homework:

♦ **WEEK 43/Lecture 13 (October 23):**

Exercises for the werkcollege:

♦ **WEEK 43/Lecture 14 (October 24):**

Exercises for the werkcollege:

Homework: Last homework (to be handed in at the start of the exam).

♦ **WEEK 44/Lecture 15 (October 30):**

Exercises for the werkcollege:

♦ **WEEK 44/Lecture 16 (October 31):**

Exercises for the werkcollege:

Homework:

♠**WEEK 46: EXAM (November 7):** 09.00 - 12.00,Gebouw: RUPPERT, Zaal: Blauw.

♠**WEEK 1/2018: RETAKE EXAM (January 3rd), 09.00 - 12.00, Gebouw: HFG, Zaal: 611B.
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**Enjoy the sphere ** (and not only).