Schedule, syllabus and examination date

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Course content

The course gives an introduction to algebraic topology, with emphasis on the fundamental group and the singular homology groups of topological spaces.

Learning outcome

After having completed the course

  • you can work with cell complexes and the basic notions of homotopy theory
  • you know the construction of the fundamental group of a topological space, can use van Kampen's theorem to calculate this group for cell complexes, and know the connection between covering spaces and the fundamental group
  • you can define the singular homology groups, and can prove their central properties, such as homotopy invariance, exactness and excision
  • you master the basic homological algebra associated to chain complexes and their homology, and can use simplicial and cellular homology to make effective calculations of homology groups
  • you understand enough category theory to give an axiomatic characterization of singular homology

Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Prerequisites

Recommended previous knowledge

MAT3500 – Topology/MAT4500 – Topology. It may also be useful to have MAT4510 – Geometric structures.

Overlapping courses

10 credits overlap with MAT9530 – Algebraic topology I

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

4 hours of lectures/exercises per week.

Examination

1 mandatory assignment.

Final oral examination.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

Master

Teaching

Every spring

Examination

Every spring

Teaching language

English

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.