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Postgraduate course

Manifolds

  • ECTS credits10
  • Teaching semesterSpring
  • Course codeMAT243
  • Number of semesters1
  • LanguageNorsk. Engelsk dersom engelskspråklige studenter deltar.
  • Resources

Teaching semester

Spring

Objectives and Content

Objectives:

The course develops the theory of smooth manifolds.

Content:

One studies smooth manifolds and functions, the tangent/cotangent space, regularity and transversality, constructions on vector bundles, integrability, Riemannian metrics and partition of unity. One develops the theory of flows and locally trivial fibrations.

Learning Outcomes

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

¿ Knows basic definitions concerning elements of smooth manifolds.

¿ Know constructions like the tangent bundle, and the basic theory for this.

¿ Know basic theory for regular values and transversality

¿ Know basic theory for (pre-)vector bundles and the manipulations of these, as for instance normal bundles and Hom-bundles.

¿ Have insight in the theory leading up to the Ehrensmann vibration theorem.

Skills

The student

¿ Can establish concrete properties of smooth manifolds through calculations and theory.

¿ can construct smooth manifolds

  • Has solid experience and training in reasoning with compounded geometric structures like vector bundles

General competence

The student

  • Has insight in the most important properties of manifolds as they are used in mathematics, physics and modelling.

Required Previous Knowledge

None

Recommended Previous Knowledge

MAT121 Linear Algebra, MAT212 Functions of Several Variables and MAT242 Topology

Forms of Assessment

Oral examination

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.

Contact

Contact Information

advice@math.uib.no

Exam information