|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 Coordinator||Prof.Dr. Hayrullah AYIK|
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.
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
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|Textbook||C. 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.