COURSE INFORMATON
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 Type
Course Coordinator Prof.Dr. Hayrullah AYIK
Instructors
Prof.Dr.HAYRULLAH AYIK1. Öğretim Grup:A
Prof.Dr.HAYRULLAH AYIK2. Öğretim Grup:A
 
Assistants
Goals
To grasp the fundamentals of groups, cyclic, abelian groups. Normal subgroups and group homomorphisms. To teach such abstract mathematical concepts and abstract thinking.
Content
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.

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 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
TextbookCebir Dersleri , Halil İbrahim Karakaş
Additional Resources
Soyut Cebir, H.Hilmi Hacısalihoğlu
A first Course in Group Theory , J.B. Fraleigh,