COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Module Theory * MT   418 8 3 3 5

Prerequisites and co-requisites 3
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Dr. Lec. Uyesi Zeynep ÖZKURT
Instructors
Dr. Öğr. ÜyesiZEYNEP ÖZKURT1. Öğretim Grup:A
Dr. Öğr. ÜyesiZEYNEP ÖZKURT2. Öğretim Grup:A
 
Assistants
Goals
Understand the definitions and basic theorems of modules, learn the properties of finitely generated and free modules,
Content
Module definition and basic features, Sub-modules, Homomorphisms and Quotient modules, Some special modules, Decomposition theorems, Applications to Finitely generated Abelyen Groups

Learning Outcomes
-


Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Definition of modules and proporties Required readings and solving problems
2 sub modules Required readings and solving problems
3 Homomorphisms and quotient modules Required readings and solving problems
4 Direct sums Required readings and solving problems
5 Finite generated modules Required readings and solving problems
6 Torsion modules Required readings and solving problems
7 Free modules Required readings and solving problems
8 Free modules Required readings and solving problems
9 Mid Term Exam examination
10 Quotient rings and maximal ideals Required readings and solving problems
11 Hilbert bases theorem Required readings and solving problems
12 Submodules of free modules Required readings and solving problems
13 Decomposition theorems Required readings and solving problems
14 Finitely generated abelian groups Required readings and solving problems
15 Exercises Required readings and solving problems
16-17 FINAL EXAM examination

Recommended or Required Reading
TextbookRings, Modules and Linear algebra, B. Hartley and T.O. Hawkes
Additional Resources