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Homological algebra

Code: 61469
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Pavle Pandžić - Lectures
Lecturers: prof. dr. sc. Pavle Pandžić - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES:
To familiarize students with the categorial methods of homological algebra on examples of working with modules over rings. Considered are the basic notions in homological algebra, like projective and injective resolutions, universal constructions, adjoint functors and derived functors.

COURSE DESCRIPTION AND SYLLABUS:
1. Rings and modules. Free and projective modules.
2. Projective modules over principal domain rings.
3. Dualization and injective modules. Injective modules over principal ideal domains. Cofree modules.
4. Categories and functors. Examples: Hom functor and tensor product of modules.
5. Natural transformation of a functor. Isomorphims and equivalence of categories.
6. Products and coproducts. Universal objects and universal constructions.
7. Adjoint functors. Various examples including reinterpretations of universal construction.
8. Abelian categories. Projective, injective and free objects in Abelian categories.
9. Complexes of modules. Morphisms of complexes. Exact sequencs. Homology and cohomology.
10. Homotopy. Motivation and examples from algebraic topology.
11. Resolution. Derived functors.
12. Ext i Tor functors are derived functors.
13. Computations of Ext i Tor functors. Some applications.

TEACHING AND ASSESSMENT METHODS:
Attending of at least 70% of lectures and examples classes, sloving at least 70% of homework assignments, and passing grade on two mid-term exams.
Literature:
  1. P. J. Hilton, U. Stammbach: A Course in Homological Algebra, 2nd edition, Graduate Texts in Mathematics
  2. C. A. Weibel: An Introduction to Homological Algebra
  3. H. Cartan, S. Eilenberg: Homological Algebra
Prerequisit for:
Enrollment :
Passed : Algebra 2
3. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

4. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics
Consultations schedule: