Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Homological algebra (HomAlg)

Practical information
Study year 2016/2017
Block 2
Programme level Full Degree Master
Course responsible
  • Beren Sanders (7-75637066677475426f63766a306d7730666d)
  • Department of Mathematical Sciences
Course number: NMAA05100U

Course content

Basic notions in module theory, tensor products of modules, exact sequences. Categories, functors, natural transformations, adjoint functors. Chain complexes and homology, resolutions, exactness of functors and derived functors.

Learning outcome

  • Knowledge: To display knowledge of the course topics and content.
  • Skills: To be able to use the acquired knowledge to perform computations.
  • Competences: At the end of the course the student should
    • Be well versed in the basic theory of modules over a ring (direct sums and products, tensor products, exact sequences, free, projective, injective and flat modules.)
    • Understand the basic methods of category theory and be able to apply these in module categories (isomorphisms of functors, exactness properties of functors, adjoint functors, pushouts and pullbacks).
    • Have a thorough understanding of constructions within the category of chain complexes (homology, homotopy, connecting homomorphism, tensor products, Hom-complexes, mapping cones).
    • Have ability to perform calculations of derived functors by constructing resolutions (Ext and Tor).
    • Be able to interpret properties of rings and modules in terms of derived functors (homological dimensions, regularity).
    • Have ability to solve problems in other areas of mathematics, such as commutative algebra, group theory or topology, using methods from homological algebra.

Recommended prerequisites

Algebra 2 (Alg2), Topologi (Top)

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MSc programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


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Teaching and learning methods

5 hours of lectures and 4 hours of exercises per week for 9 weeks.


No limits




Category Hours
Lectures 45
Theory exercises 36
Preparation 125
English 206


Type of assessment

Continuous assessment
Submission of 3 exercise sets; each set counts for 1/3 of the final grade.


All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

Censorship form

External censorship


30 minutes oral examination with 30 min. preparation time. All aids allowed during the preparation time, but no aids allowed during the examination.

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