Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT40620121310	MODULE THEORY	Elective	4	8	5

Level of Course Unit

First Cycle

Objectives of the Course

Give them detailed information about the modules on issues.

Name of Lecturer(s)

Yrd. Doç. Dr. Yıldıray ÇELİK

Learning Outcomes

1	Know the basic concepts of modules.
2	Have some knowledge of homomorphisms and exact sequences.
3	Know the basic properties of Free modules and vector spaces.
4	Have some knowledge of Projective and Injective Modules.
5	Know some properties of Modules over Principal Ideal Domains and use them

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Modules, module homomorphisms and factor modules. Direct sum of modules. Some special module classes. Finitely generated modules. Free modules and submodules of free modules. Decomposition theorems. Prime decomposition of a module.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Module definition and examples.
2	Module homomorfizmleri and full arrays
3	Module homomorfizmleri and full arrays
4	Factor modules
5	Free Modules and Vector Spaces
6	Free Modules and Vector Spaces
7	Submodules of free modules
8	Midterm exam
9	Finitely generated modules
10	Direct sum of modules
11	Tensor products and applications
12	Rings and structure of modules
13	Essential ıdeal region on modules
14	Decomposition theorems.
15	Prime decomposition of a module
16	Final exam

Recommended or Required Reading

T. W. Hungerford, Algebra, Holt, Rinehart and Winston, 1974 J. S. Golan and T. Head, Modules and the structure of rings, Marcel Dekker, 1991 Rings and Modules, Paulo Ribenboim

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	14	4	56
Problem Solving	10	4	40
Brain Storming	10	4	40
TOTAL WORKLOAD (hours)			142

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	2	2	2	3	2	3	3
LO2	3	3	3	3	3	3	3
LO3	2	2	2	3	2	3	3
LO4	3	3	3	3	3	3	3
LO5	2	2	2	2	2	2	2

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High