MATS1960 Introduction to manifolds (4 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

Manifolds; differentiable mappings; tangent space; tangent mapping ("push forward"); sub manifolds; vector fields.

Learning outcomes

After passing the course successfully the student

  • knows examples of abstract manifolds
  • can justify the smoothness of a given submanifold
  • knows the abstract version of concepts such as the tangent space and tangent mapping
  • knows the concepts of a vector field and its integral curve

Description of prerequisites

Vector analysis 1 and 2 or Differential geometry of curves and surfaces; Topology

Literature

  • John M. Lee:Introduction to smooth manifolds. Graduate Texts in Mathematics 218, Springer, 2006. ISBN 978-0-387-95448-6

Completion methods

Method 1

Evaluation criteria:
Course exam and exercises
Select all marked parts

Method 2

Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x

Participation in teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English
No published teaching
x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
English
No published teaching