MT003 Module Theory

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT003
Name Module Theory
Term 2024-2025 Academic Year
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Yüksek Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Doç. Dr. ZEYNEP ÖZKURT


Course Goal / Objective

Understand the basic definitions and theorems about modules and associate them with different algebraic structures.

Course Content

Modules, Homomorphisms,submodules and quotient modules. Short exact Sequences. Direct products, tensor product. Free, Projective, injective and flat modules. Modules over Principal Ideal Domains. Jordan and Normal Canonical forms.

Course Precondition

no

Resources

David Dummit, Richard Foote Abstract Algebra

Notes

Hungerford, Algebra


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Knows definition of modules and its properties
LO02 Knows submodules, quotient modules and homomorphisms has an idea about the structure of free modules
LO03 Knows the structure of tensor product and properties
LO04 Create an exact sequence
LO05 Defines projective, injective and flat modules
LO06 Has an idea about the structure of modules on principal ideal domain
LO07 Knows the Rational and Jordan canonical forms


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in her area of expertise and other areas of mathematics.
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in his area of ​​expertise and other areas of mathematics.
PLO03 Bilgi - Kuramsal, Olgusal Establishes new mathematical models with the help of the knowledge gained in the field of specialization.
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics. 3
PLO05 Bilgi - Kuramsal, Olgusal It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. 3
PLO06 Bilgi - Kuramsal, Olgusal Effectively uses the technical equipment needed to express mathematics.
PLO07 Bilgi - Kuramsal, Olgusal poses original problems related to field and presents different solution techniques.
PLO08 Bilgi - Kuramsal, Olgusal carries out original and qualified scientific studies on the subject related to its field. 2
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories.
PLO10 Beceriler - Bilişsel, Uygulamalı Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education.
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. 3
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. 4
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 5


Week Plan

Week Topic Preparation Methods
1 Main Definitions Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
2 Quotient modules and Homomorphisms Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
3 Direct sums Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
4 Free modules Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
5 Free modules1 Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
6 Tensor product of modules Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
7 Tensor product of modules1 Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Read the relevant sections in the textbook and solving problems Ölçme Yöntemleri:
Yazılı Sınav
9 Exact Sequences Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
10 Projective modules Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
11 İnjective modules Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
12 Flat Modules Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
13 Modules on principal ideal domain Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
14 Rational Canonical Forms Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
15 Jordan Canonical forms Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
16 Exercises Read the relevant sections in the textbook and solving problems Öğretim Yöntemleri:
Anlatım
17 Term Exams Read the relevant sections in the textbook and solving problems Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 5 70
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 15 15
Final Exam 1 30 30
Total Workload (Hour) 157
Total Workload / 25 (h) 6,28
ECTS 6 ECTS

Update Time: 09.05.2024 11:37