Analytic Number Theory (AnNum)
Course content
The prime number theorem gives an estimate for the number of primes less than a given value x. This theorem - which we will prove - is intimately related to the location of the zeroes of the famous Riemann zeta function. We shall study the analytic properties of the Riemann zeta functions as well as more general L-function. We consider primes in arithmetic progressions, zero-free regions, the famous Riemann hypothesis, the Lindelöf hypothesis, and related topics.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
Knowledge:
At the end of the course students are expected to have a thourough
knowledge about results and methods in analytic number theory as
described under course content.
Skills:
At the end of the course students are expected to be able
to
- Analyze and prove results presented in analytic number theory
- Prove results similar to the ones presented in the course
- apply the basic techniques, results and concepts of the course to concrete examples and exercises.
Competences:
At the end of the course students are expected to be able to
- Explain and reproduce abstract concepts and results in analytic number theory
- Come up with proofs for result at the course level
- discuss topics from analytic number theory
Weekly: 4 hours of lectures and 2 hours of exercises for 7 weeks.
Complex Analysis (KomAn) or equivalent
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 20 minutes (20-minute preparation time)
- Exam registration requirements
-
To be allowed to take the oral exam the student should have at least 3 out of 4 hand-in exercises approved.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
- Re-exam
-
Same as ordinary exam.
To be eligible for the re-exam, students who did not get 3 out of 4 assignments approved during the ordinary term time can re-submit non-approved assignment. Deadline for this is two weeks before the beginning of the re-exam week.
Criteria for exam assessment
The student must in a satisfactory way demonstrate that they have mastered the learning outcome of the course.
Single subject courses (day)
- Category
- Hours
- Lectures
- 28
- Preparation
- 114
- Exercises
- 14
- Exam
- 50
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK16001U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 2
- Schedulegroup
-
A
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Morten S. Risager (7-776e78666c6a77457266796d33707a336970)
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