Course - Manifolds - TMA4190
TMA4190 - Manifolds
About
Examination arrangement
Examination arrangement: Written examination
Grade: Letters
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| Written examination | 100/100 | 4 timer |
Course content
Elementary general topologi. Inverse function theorem. Manifolds, differentiable structures. Regular/critical points, imbeddings, submersions and immersions. The rank theorem. Tangent bundles, flows, vector fields, and integrability. Projective spaces and matrix groups.
Learning outcome
1. Knowledge. The student has knowledge of the fundamental concepts and methods in differential topology, and examples of manifolds, such as projective spaces and matrix groups.
2. Skills. The student is able to apply his or her knowledge of differential topology to formulate and solve problems of a geometrical nature in mathematics, theoretical physics and cybernetics, by the use of dynamical systems on manifolds and other tools.
Learning methods and activities
Lectures and exercises. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments. Written examination. Retake of examination may be given as an oral examination.
Recommended previous knowledge
The course is based on TMA4100/05/15/ Calculus 1/2/3 or equivalent. For students who have their background from mathematical sciences: The course is based on MA1101 Basic Caluculus I, MA1102 Basic Calculus II, MA1103 Vector Calculus, MA1201 Linear Algebra and Geometry, MA1202 Linear Algebra with Applications, MA2105 Complex Function Theory with Differential Equations, or eqivalent.
Course materials
Will be announced at the start of the course.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| SIF5034 | 7.5 |
Version: 1
Credits:
7.5 SP
Study level: Second degree level
Term no.: 1
Teaching semester: SPRING 2014
Language of instruction: English, Norwegian
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- Mathematics
- Technological subjects
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: Written examination
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD Written examination 100/100 2014-05-30 09:00
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Room Building Number of candidates
Examination arrangement: Oral examination
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Summer KONT Oral examination 100/100 2014-08-13
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Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"