Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

Person Responsible for Information Package

Homological Algebra I

Course Code	: MTK625
Course Type	: Area Elective
Couse Group	: Third Cycle (Doctorate Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

Introduction to homological algebra and give some fundamental properties.

Course Content

To introduce categorie theory, to define tensor product and funktors in module theory, to study Ext and Tor funktors, to give homological approach for ring theory.

Name of Lecturer(s)

Learning Outcomes

1.	To introduce fundamental properties in advanced category theory
2.	To introduce homological approche in module theory
3.	To study some special functors
4.	To study some other homological approches
5.	To be able to use mathematical concepts in solving certain types of problems

Categories

Week 2 - Theoretical

Modules (generalities, tensor products, exactness of functors)

Week 3 - Theoretical

Modules (projectives, injectives and flats)

Week 4 - Theoretical

Ext and Tors (complexes and projective resolutions)

Week 5 - Theoretical

Long exact sequences

Week 6 - Theoretical

Flat resolutions and injective resolutions

Week 7 - Theoretical

Consequences

Week 8 - Theoretical

Dimension theory

Week 9 - Theoretical

Change of rings (computational considirations)

Week 10 - Theoretical

Change of rings (matrix rings, polynomials)

Week 11 - Theoretical

Quotients and localization

Week 12 - Theoretical

Additive functors

Week 13 - Theoretical

Derived functors

Week 14 - Theoretical

Long exact sequences (existence)

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	1	%5
Term Assignment	1	%5
Midterm Examination	1	%20
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	0	3	42
Assignment	1	0	6	6
Term Project	1	0	6	6
Individual Work	14	0	5	70
Midterm Examination	1	30	2	32
Final Examination	1	42	2	44
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	3	4	4	4	4	4	4	4	3	4			4	5
OÇ-2	4	3	4	4	4	4	4	4	4	3	4		4	5	5
OÇ-3	4	4	4	4	4	4	3	4	3	3	4			4	5
OÇ-4	4	4	4	4	4	4	4	4	4	3	4			4	5
OÇ-5	4	4	4	4	4	4	3	4	4	3	4		4	5	5

Person Responsible for Information Package

1.	Basic Homological Algebra, M. Scott Osborne, Spinger Verlag,
2.	Homology , Saunders Mclane, Spinger Verlag
3.	Introduction of Homological Algebra, Rotman, J.J.
4.	Relative Homological Algebra, Edgar, E, Enochs, Overtoun M.G. Jenda