NMAK15005U Advanced Vector Spaces (AdVec)
MSc Programme in Mathematics
MSc Programme in Statistics
This course covers the fundamentals of linear and multilinear algebra as well as more advanced subjects within the field, from a theoretical point of view with emphasis on proofs.
Topics include
1. Fundamentals of finite dimensional vector spaces over a field
2. Duality
3. Direct sums and quotient spaces
4. Multilinear algebra. Tensors and alternating tensors
5. Determinant and trace. The Cayley-Hamilton theorem
6. Generalized eigenspaces and the Jordan normal form
7. Real and complex Euclidean structure
8. Spectral theory of commuting normal operators
9. Positive operators, polar decomposition and calculus of
operators
10.Quadratic forms and conics
Knowledge: Central definitions and theorems from the subjects mentioned in the description of contents.
Skills: To follow and reproduce logical reasoning at an abstract level within the subjects mentioned in the description of contents. To give an oral presentation of a mathematical subject.
Competencies: To apply abstract results from the curriculum to concrete problems
- Category
- Hours
- Exam
- 1
- Lectures
- 35
- Preparation
- 142
- Theory exercises
- 28
- Total
- 206
As
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minOral examination with 30 minutes of preparation before the exam
- Exam registration requirements
A mandatory assignment must be approved before the exam.
- Aid
All aids allowed during the preparation time. No aids allowed for the examination.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
Oral examination, 30 minutes plus 30 minutes of preparation before the exam. If the mandatory assignment has not been approved before the regular exam, the oral re-exam will include problem solving. In this case the timeslots for exam and preparation will each be prolonged by 15 minutes, and the grading will be based on the total performance.
In either case, all aids are allowed during the preparation time, but no aids allowed during the examination.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK15005U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- A
- Course capacity
- no limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Henrik Schlichtkrull (8-78686d716e686d79457266796d33707a336970)