Topics in Probability
Course content
We will cover various topics in probability theory, such as weak convergence theory, Gaussian processes, Levy processes, Feller processes, or concentration inequalities with the precise content varying each year, and depending on the interests of the participants.
Fall 2024: A tentative plan for this year is to give an introduction to the theory of concentration inequalities. These inequalities express certain surprising features of collections of independent variables.
They play a prominent role in empirical process theory, high-dimensional statistics and machine learning. Highlights are the Borell-TIS inequality for Gaussian processes, the Brunn-Minkowsky inequality and its relation to the isoperimetric problem, and Talagrand's convex distance inequality.
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject
MSc Programme in Mathematics-Economics
Knowledge: To display knowledge of the course topics and content.
Skills: To be able to use the acquired knowledge to perform computations, and to read and understand current research papers.
Competencies: The student should be able to apply the theory to solve problems of moderate difficulty within the topics of the course
5 hours of lectures and 3 hours of exercise class for 7 weeks.
Sand2, and possibly Brownian Motion – alternatively VidSand2 (or
Stok 3) from previous years.
Academic qualifications equivalent to a BSc degree is
recommended.
Written feedback in the form of comments to the compulsory assignements.
Oral feedback during exercise classes, as a response to the contribution of the students to the solution process of the exercises.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 30 minutes (30-minute preparation time)
- Exam registration requirements
-
To participate in the exam the compulsory assignment must be approved and valid
- Aid
- All aids allowed
All aids allowed during preparation
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
- Re-exam
-
Same as the ordinary exam.
If the compulsory assignment was not approved before the ordinary exam it must be (re)submitted and approved. It must be re(submitted) at the latest three weeks before the beginning of the re-exam week.
Criteria for exam assessment
The student should convincingly and accurately demonstrate the
knowledge, skills and competences described under Intended learning
outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 35
- Preparation
- 149
- Theory exercises
- 21
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK24009U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 2
- Schedulegroup
-
C
- 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
- Ernst Hansen (8-6a776d6673786a73457266796d33707a336970)
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Kursusinformation for indskrevne studerende