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Geometry 2 (Geom2)
Provider: Faculty of Science

Activity no.: 5569-18-07-31 
Enrollment deadline: 19/11/2018
Tilmelding : Geometry 2 (Geom2)
ECTS credits7.50
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time19.11.2018, at: 09:00 -
27.01.2019, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserHans Plesner Jakobsen    E-mail address: jakobsen@math.ku.dk
Teaching languageEnglish partially in English
Semester/BlockBlock 2 ¤ Block 3
Scheme groupB
Exam formOral examination, 30 minutes
Exam formOral examination
Exam detailsOral examination, 30 minutes. 30 minutes of preparation before the exam. A mandatory assignment must be approved before the exam. The assignment is to be handed in no later than two weeks before the exam week. All aids allowed.
Course workload
Course workload categoryHours
Lectures35.00
Theory exercises28.00
Preparation142.00
Exam1.00
Sum206.00
Learning outcome
Knowledge:
Central definitions and theorems from the theory

Skill:
- Decide whether a given subset of R^n is a manifold
- Determine the differential of a smooth map
- Work with tangent vectors, including the Lie algebra of a Lie group
- Utilize topological concepts in relation with manifolds
- Find the Lie bracket of given vector fields
- Work with exterior differentiation and pull-back of differential forms

Competences:
- In general to perform logical reasoning within the subject of the course
- Give an oral presentation of a specific topic within the theory as well as a strategy for solving a specific problem

Content
The following subjects are covered.

1. Differentiable manifolds in Euclidean spaces.
2. Abstract differentiable manifolds.
3. Tangent spaces, differentiable maps and differentials.
4. Submanifolds immersions and imbeddings
5. Vector fields.
6. Lie groups and Lie Algebras (cursory)
7. Differential forms.

8 Integration; Stokes' Theorem

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