Information Package / Course Catalogue
Introduction to Module Theory
Course Code: MAT442
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The aim of this course is to introduce the concepts of module theory and to provide the necessary background to study in these areas.

Course Content

Modules, Submodules, Quotient Modules, Module Homomorphisms, Isomorphism Theorems, Exact Sequences, Split Exact Sequences, Direct Products and Direct Sums of Modules, Free Modules

Name of Lecturer(s)
Learning Outcomes
1.To understand the basic concepts of module structure.
2.To understand the connection between internal direct sum and external direct sum.
3.To understand the concept of exact sequence.
4.To understand the concept of split exact sequence.
5.To understand of free modules.
Recommended or Required Reading
1.Aydın, N., Kandamar H., "Soyut Cebir", Kriter Yayıncılık, 2013.
2.Kasch, F., “Modules and Rings”, Academic Press Inc., 1982.
3.Hungerford, T. W., “Algebra”, Springer Verlag; 8th edition, 1997.
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Definition and Examples of Modules
Week 2 - Theoretical & Practice
Definition and Examples of Modules
Week 3 - Theoretical & Practice
Submodules
Week 4 - Theoretical & Practice
Module Homomorphisms
Week 5 - Theoretical & Practice
Quotient Modules
Week 6 - Theoretical & Practice
Isomorphism Theorems
Week 7 - Theoretical & Practice
Isomorphism Theorems
Week 8 - Theoretical & Practice
Exact Sequences
Week 9 - Theoretical & Practice
Exact Sequences
Week 10 - Theoretical & Practice
Split Exact Sequences
Week 11 - Theoretical & Practice
Direct Products and Direct Sums of Modules
Week 12 - Theoretical & Practice
Direct Products and Direct Sums of Modules
Week 13 - Theoretical & Practice
Free Modules
Week 14 - Theoretical & Practice
Free Modules
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Term Assignment1%5
Midterm Examination1%30
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140228
Lecture - Practice140228
Assignment1112
Term Project1112
Individual Work140228
Midterm Examination124226
Final Examination134236
TOTAL WORKLOAD (hours)150
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
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
4
3
3
2
3
OÇ-2
3
3
4
3
3
3
OÇ-3
3
3
4
3
3
2
3
OÇ-4
3
3
4
3
3
3
3
OÇ-5
3
3
4
3
3
3
3
Adnan Menderes University - Information Package / Course Catalogue
2026