course-details-portlet

TMA4192 - Differential Topology

About

Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 100/100 4 hours D

Course content

The aim of the course is to introduce fundamental concepts and examples in differential topology. Key concepts that will be discussed include 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, transversality, intersection numbers and cobordism. 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 of 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.

Learning methods and activities

The learning methods and activities depend on the course teacher, but will in general consist of lectures and exercises. The lectures will be given in English if the course is attended by students who don't master a Scandinavian language. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for their written answers. Written examination. Retake of examination may be given as an oral examination.

Further on evaluation

See "Teaching methods and activities".

Course materials

Will be announced at the start of the course.

More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Second degree level

Coursework

Term no.: 1
Teaching semester:  SPRING 2021

No.of lecture hours: 4
No.of specialization hours: 8

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
  • Topology
  • Topology and Geometry
  • Mathematics
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences

Phone:

Examination

Examination arrangement: Written examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Spring ORD Written examination 100/100 D
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.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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