Information Package / Course Catalogue
Introduction to Homological Algebra
Course Code: MTK575
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

This course aims to give students the basic concepts of homological algebra, to develop analytical thinking and understanding of abstract concepts. This course aims to gain a systematic approach to define problems and to solve the problems by the discussed topics and their applications.

Course Content

Abel Groups, Rings, Modules, Homomorphisms, Free Modules, Exact Sequences, 5- Lemma ve 3x3 Lemma, Hom Functor, Projektive ve İnjektive Modules, Essential and Superfluous Submodules, Supplements, Category of Complexes, Projektive and İnjektive Resolutions, Derived Functor

Name of Lecturer(s)
Learning Outcomes
1.To be able to comprehend the concepts of abelian group, ring, module and homomorphism.
2.To be able to comprehend the basic concepts of homological algebra.
3.To be able to comprehend abstract concepts.
4.To be able to develop analytical thinking.
5.To be able to gain the skill of interpreting some interrelations among these concepts.
Recommended or Required Reading
1.Rotman, J.J., “An Introduction to Homological Algebra”, Academic Press, 1979
2.Northcott D. G. “An Introduction to Homological Algebra”, Cambridge at the University Press, 1960
Weekly Detailed Course Contents
Week 1 - Theoretical
Abelian Groups
Week 2 - Theoretical
Rings
Week 3 - Theoretical
Modules
Week 4 - Theoretical
Homomorphisms
Week 5 - Theoretical
Free Modules, Exact Sequences
Week 6 - Theoretical
5- Lemma and 3x3 Lemma
Week 7 - Theoretical
Hom Functor
Week 8 - Theoretical
Projective and Injective Modules
Week 9 - Theoretical
Essential and Superfluous Submodules, Supplements
Week 10 - Theoretical
Category of Complexes
Week 11 - Theoretical
Category of Complexes
Week 12 - Theoretical
Projektive and İnjektive Resolutions
Week 13 - Theoretical
Derived Functor
Week 14 - Theoretical
Derived Functor
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment2%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Assignment216236
Individual Work140228
Final Examination150252
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
4
4
4
OÇ-2
4
3
3
OÇ-3
3
3
3
OÇ-4
4
4
3
OÇ-5
3
3
3
Adnan Menderes University - Information Package / Course Catalogue
2026