Latest news
Welcome to the course! The schedule for the course can be found in TimeEdit.
2019-03-13: The final homework assignment has been graded. You can pick up your solutions in my office on Friday March 15.
2019-02-28: The third homework assignment is now available below.
2019-02-18: The formulation of Problem 1b of Assignment 2 has been updated.
2019-02-14: The second homework assignment is now available below.
2019-02-04: There was a mistake in the formulation of problem 2b of Assignment 1. The text has now been updated.
2019-01-31: The
first homework assignment is now available below.
Teachers
Course coordinator: Anders Södergren, office L3081, e-mail: andesod(at)chalmers(dot)se
Course literature
English-Swedish mathematical dictionary
Program
Note that minor changes might occur in the program.
Lectures
| Day |
Sections | Contents |
|---|---|---|
| Monday 21/1 |
Short introduction. Arithmetic functions. |
|
| Wednesday 23/1 |
|
Arithmetic functions |
| Friday 25/1 |
|
Arithmetic functions |
| Monday 28/1 |
|
Arithmetic functions |
| Wednesday 30/1 |
|
Elementary results on prime counting |
| Friday 1/2 | Elementary results on prime counting | |
| Monday 4/2 | 7 |
Elementary results on prime counting |
| Wednesday 6/2 | 1,8 |
Dirichlet series |
| Friday 8/2 | 1,8 |
Dirichlet series |
| Monday 11/2 | Dirichlet series and Euler products | |
| Wednesday 13/2 | Dirichlet series and Euler products | |
| Friday 15/2 | The Riemann zeta function |
|
| Monday 18/2 | 17-18 |
The prime number theorem |
| Wednesday 20/2 | 17-18 |
The prime number theorem |
| Friday 22/2 | 8-10 |
The Riemann zeta function |
| Monday 25/2 | 11-13 |
The Riemann zeta function |
| Wednesday 27/2 | 15,17,18 |
The prime number theorem |
| Friday 1/3 | Dirichlet characters and Dirichlet L-functions |
|
| Monday 4/3 | Dirichlet characters and Dirichlet L-functions | |
| Wednesday 6/3 | 1,4 |
The prime number theorem in arithmetic progressions |
| Friday 8/3 | 14,20 |
The prime number theorem in arithmetic progressions |
Recommended exercises
| Week |
Exercises |
|---|---|
| 1 | Exercise sheet 1 |
| 2 | Exercise sheet 2 |
| 3 | Exercise sheet 3 |
| 4 | Exercise sheet 4 |
| 5 | Exercise sheet 5 |
| 6 | Exercise sheet 6 |
| 7 | Exercise sheet 7 |
Course requirements
The learning goals of the course can be found in the course plan.
Assignments
There will be three sets of homework assignments distributed during the course. Each set will consist of 3-5 problems.
NOTE: The following is to clarify the rules for everybody interested
in working with these assignments. You are free to cooperate with
other students and to read whatever literature you can find about the
subject. However, you are expected to formulate your solutions
independently and it is neither allowed to copy from other students
nor to copy solutions form any other source! No credit will be given
to such solutions and if this happens in a systematic fashion you will
be reported for plagiarism.
Examination
To
pass the course you are required to solve at least 50% of the homework
assignments and to pass the oral exam.
At
the time of the exam you are supposed to know all the definitions
and theorems (including proofs) that are from the relevant
sections of the course literature or done in class. You are also
supposed to be able to apply the methods and results of the course
to analyze examples, solve problems and prove theorems.
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.