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
x
Exam (4 cr)
Type:
Exam
Grading scale:
0-5
Language:
English