|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Algebra II *||MT 212||4||4||4||7|
|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|
To grasp the fundamentals of groups, cyclic, abelian groups. Normal subgroups and group homomorphisms. To teach such abstract mathematical concepts and abstract thinking.
Binary operations, groups, finite groups and group tables, subgroups, cyclic groups, permutation groups, alternating group, isomorphism and Cayleys theorem, direct product, finitely generated abelian groups, normal subgroups and factor groups, isomorphism theorems.
|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||Groups||Review of the relevant pages from sources|
|2||Finite groups and group tables, Subgroups||Review of the relevant pages from sources|
|3||Example of groups (The group Zn and dihedral group)||Review of the relevant pages from sources|
|4||Permutation groups||Review of the relevant pages from sources|
|5||Cyclic groups||Review of the relevant pages from sources|
|6||Cyclic groups and cosets||Review of the relevant pages from sources|
|7||Lagranges Theorem||Review of the relevant pages from sources|
|8||Mid-term exam||Review of the topics discussed in the lecture notes and sources again|
|9||Normal subgroups and Factor groups||Review of the relevant pages from sources|
|10||Isomorphisms and Automorphisms||Review of the relevant pages from sources|
|11||Direct products||Review of the relevant pages from sources|
|12||Fundamental Theorem of Finite abelian groups||Review of the relevant pages from sources|
|13||Homomorphisms of groups||Review of the relevant pages from sources|
|14||Isomorphisms theorems||Review of the relevant pages from sources|
|15||Solving problems||Review of the relevant pages from sources|
|16-17||Final Exam||Review of the topics discussed in the lecture notes and sources again|
|Recommended or Required Reading|
|Textbook||Cebir Dersleri , Halil İbrahim Karakaş|
Soyut Cebir, H.Hilmi Hacısalihoğlu
A first Course in Group Theory , J.B. Fraleigh,