COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Group Theory * MT   313 5 3 3 5

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Hayrullah AYIK
Instructors
Prof.Dr.HAYRULLAH AYIK1. Öğretim Grup:A
Prof.Dr.HAYRULLAH AYIK2. Öğretim Grup:A
 
Assistants
Goals
The aim of this course is to understand basic definitions and theorems of group theory, recognize some special groups and groups construction, recognize normal subgroups and quotient groups, recognize permutation groups and counting its elements, understand and solve problems with isomorphism theorems, understand Sylow Theorems and solving problems using Sylow Theorems.
Content
Fundamental definitions and theorem of group theory, Some special groups and group construction, Permutation groups and counting its elements, Groups symmetry, Normal subgroups and its properties, Quotient groups, Counting with groups, Isomorphism theorems, Examples of using isomorphism theorems, Group actions, Basic groups, Sylow Theorems and its applications, Clasification of small order groups under isomorphism

Learning Outcomes
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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
X
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 Fundamental definitions and theorem of group theory Review of the relevant pages from sources
2 Some special groups and group construction Review of the relevant pages from sources
3 Permutation groups and counting its elements Review of the relevant pages from sources
4 Symmetry groups Review of the relevant pages from sources
5 Normal subgroups and their properties Review of the relevant pages from sources
6 Quotient groups Review of the relevant pages from sources
7 Counting with groups Review of the relevant pages from sources
8 Mid term Exam Review and Problem Solving
9 Isomorphism theorems Review of the relevant pages from sources
10 Examples of using isomorphism theorems Review of the relevant pages from sources
11 Group actions Review of the relevant pages from sources
12 Simple groups Review of the relevant pages from sources
13 Sylow Theorems and their applications Review of the relevant pages from sources
14 Classification groups of small order up to isomorphism Review of the relevant pages from sources
15 Classification groups of small order up to isomorphism Review of the relevant pages from sources
16-17 Final Exam Review and Problem Solving

Recommended or Required Reading
TextbookC. F. Gardiner ´´ A first course in group theory´´ Springer - Verlag, New York Inc. 1980
J.J. Rotman, ´A first course in abstract algebra´ Second Edition, Prentice Hall, 2000.
Additional Resources