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The exam 171026 with solutions.
Please note some irregularities in our schedule.
Weak 39: No class Monday 25 September. Instead we meet Friday 29 September 10-12.
Weak 40: No class Thursday 5 October. Instead we meet Wednesday 4 October 15-17.
Weak 42: No class Thursday 19 October. Instead we meet Friday 20 October 10-12.
The schedule for the course can be found in
TimeEdit.
Teachers
Course coordinator: Hjalmar Rosengren
Course literature
Lecture notes will be written as the course proceeds.
This draft contains all seven chapters. The file was last updated 27 October 2017.
Note that previous versions contained a mistake in the proof of Lemma 4.2.10 and in the statement of Exercises 4.6.8 and 5.4.1.
Also, Lemma 6.2.3 has been strengthened.
A good reference book for most of the material covered in the course is Serge Lang, Algebra.
Here is a check-list for the course contents.
Here is the solution to Exercise 3.9.5.
Program
Lectures
| Day |
Sections | Contents |
|---|---|---|
| 28/8 |
1.1-1.4 |
Review of group theory |
| 29/8 |
1.5, 2.1-2.2 |
Review of group and ring theory |
| 31/8 |
1.6, 2.3 |
Unique factorization domains |
| 5/9 |
3.1-3.5 |
Modules |
| 7/9 |
3.6-(3.8) |
Tensor products |
| 12/9 |
3.8, 4.1-(4.2) |
More on the exterior product, Modules over a PID (Prop. 4.2.2 and Cor. 4.2.3) |
| 14/9 |
4.2-4.3 |
Modules over a PID |
| 19/9 |
4.4-4.5 |
Canonical forms |
| 21/9 |
3.9-3.10 |
Associative algebra, Grassmann algebra and Plücker relations |
| 26/9 |
5.1-5.2 | Group representations |
| 28/9 |
5.3-5.6 | Character tables |
| 3/10 |
5.7-5.9 | Fourier transform on groups, Frobenius divisibility |
| 4/10 |
(6.1) 6.2 | Representations of the symmetric group |
| 10/10 |
6.3 | Schur-Weyl duality |
| 12/10 |
6.4-6.6 | Characters of the symmetric group |
| 16/10 |
7 | Compact groups, especially SU(2) |
| 17/10 |
Repetition |
|
| 20/10 |
Exercises, Course evaluation |
Recommended exercises
| Day |
Exercises |
|---|---|
| 4/9 |
1.2.4, 1.7.4, 1.7.5, 1.7.12, 2.2.4, 2.3.1, 2.4.1, 2.4.6, 2.4.7, 2.4.8 |
| 11/9 |
3.2.2, 3.5.2, 3.6.1, 3.7.3, 3.7.4, 3.9.1, 3.9.4, 3.9.5, 3.9.8, 3.9.9
|
| 18/9 |
3.8.2, 3.8.3, 3.8.5, 3.8.7, 3.9.11, 3.9.13, 4.1.1, 4.2.1, 4.3.1 |
| 29/9 |
3.10.1, 4.4.1, 4.4.2, 4.6.1, 4.6.3, 4.6.5, 4.6.6, 4.6.8 |
| 2/10 |
5.1.1, 5.1.5, 5.2.1, 5.4.1, 5.5.1, 5.5.2, 5.6.1, 5.10.1, 5.10.2 |
| 9/10 |
1.8.17, 5.9.2, 5.10.2 (again), 5.10.4, 6.1.1, 6.1.2, 6.7.1, 6.7.2 |
| 20/10 |
6.6.1, 6.7.4, 6.7.5, 7.1.2, 7.2.4, 7.3.3 (This session will not give bonus points.) |
Course requirements
The learning goals of the course can be found in the course plan.
Assignments
We will have six problem sessions during the course. If you are participating actively in a session and are prepared to present the solution of at least three problems to the class you will get a bonus point for the exam.
Examination
There will be a written exam at the end of the course. The maximal number of points will be 30. Bonus points from the problem sessions can be added to the result.If you contribute useful feedback on the lecture notes (by email) you will get an extra bonus point, but the maximum number of bonus points is 6. To pass the course you need 15 points and for high pass (VG) 25 points.
Examination procedures
In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.
Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.
At the exam, you should be able to show valid identification.
After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.
At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of
the review will be announced here on the course homepage. Anyone
who can not participate in the review may thereafter retrieve and
review their exam at the
Mathematical Sciences Student office.
Check that you have the
right grades and score. Any complaints about the marking must be
submitted in writing at the office, where there is a form to fill
out.
At re-examination:
Exams are reviewed and retrieved at the
Mathematical Sciences Student office.
Check that you have the
right grades and score. Any complaints about the marking must be
submitted in writing at the office, where there is a form to fill
out.
Old exams
151026
160107
You can find many more old exams
here, but not all problems are appropriate for the current course contents.