Course - Introduction to Topology - TMA4190
TMA4190 - Introduction to Topology
About
Examination arrangement
Examination arrangement: Written examination
Grade: Letters
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| Written examination | 100/100 | 4 timer |
Course content
The aim of the course is to introduce fundamental concepts and examples in differential topology and the idea of using algebraic invariants to study geometric objects. The course discusses the inverse function theorem, differentiable structures and smooth manifolds, tangent bundles, embeddings, submersions and regular/critical points. Important examples of spaces are surfaces, spheres, and projective spaces. Other key concepts are homotopy, the fundamental group and covering spaces. Applications presented in the course may range from Brouwer's fixed point theorem to vector fields on spheres. These methods and ideas have been influential to and are used in many other parts of mathematics, but also in physics and other areas of application.
Learning outcome
1. Knowledge. The student has knowledge of fundamental concepts and methods in differential and algebraic topology, and examples of manifolds.
2. Skills. The student is able to apply his or her knowledge of differential and algebraic 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 Calculus 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 (see course description 2013/14), 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 2017
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 2017-06-09 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 2017-08-07
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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"