COURSE INFORMATON
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 Type
Course Coordinator Prof.Dr. Gonca AYIK
Instructors
Prof.Dr.GONCA AYIK1. Öğretim Grup:A
Prof.Dr.GONCA AYIK2. Öğretim Grup:A
 
Assistants
Goals
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.
Content
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

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
X
10
Uses effective scientific methods and appropriate technologies to solve problems
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
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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
TextbookA Book of Abstract Algebra, Charles Pinter, Mc Graw Hill.
Soyut Cebir Dersleri Cilt II, Hülya Şenkon, İstanbul Üniversitesi Fen Fakültesi Yayınları.
Additional Resources