|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Algebra III *||MT 311||5||3||3||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. Gonca AYIK|
Determining basic properties of rings, recognizing the structure of field, recognizing ideals of rings and their structures, determining the properties of the ring homomorphism, recognizing division rings, integral domains, recognizing rings of integers and their properties, recognizing polinomial rings and their properties and deciding on the reduciblaty of polinomial.
Definitions and elementary properties of rings and fields, ideal and homomorphism, Quotion rings, Integral domain, Construction of the fields of quotients, Rings of polynomial, Factoring polynomials, Irreducibility Criteria
|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||Definition of rings and example of rings||Review of the relevant pages from sources|
|2||Basic properties of rings||Review of the relevant pages from sources|
|3||Definition of fields and example of fields||Review of the relevant pages from sources|
|4||Ideals of rings and examples||Review of the relevant pages from sources|
|5||Homomorphism of rings||Review of the relevant pages from sources|
|6||Division rings||Review of the relevant pages from sources|
|7||Integral domain||Review of the relevant pages from sources|
|8||Midterm exam||Review and Problem Solving|
|9||Charasterictic of integral domains and their properties||Review of the relevant pages from sources|
|10||Rings of integers and its properties||Review of the relevant pages from sources|
|11||Polynomial rings and its properties||Review of the relevant pages from sources|
|12||Polynomial rings and its properties||Review of the relevant pages from sourcesReview of the relevant pages from sources|
|13||Reducibility in polynomial rings||Review of the relevant pages from sources|
|14||Test about reducibility on polynomial rings||Review of the relevant pages from sources|
|15||Introduction to Number Theory||Review of the relevant pages from sources|
|16-17||Final Exam||Review and Problem Solving|
|Recommended or Required Reading|
|Textbook||A Book of Abstract Algebra, Charles Pinter, Mc Graw Hill. |
Soyut Cebir Dersleri Cilt II, Hülya Şenkon, İstanbul Üniversitesi Fen Fakültesi Yayınları.