DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Algebra III Course Code : MT 311 Course Type : Compulsory Level of Course : First Cycle Year of Study : 3 Course Semester : Fall (16 Weeks) ECTS : 7 Name of Lecturer(s) : Prof.Dr. GONCA AYIK Learning Outcomes of the Course : Recognizes the structure of ring. Determines basic properties of rings. Recognizes the structure of field. Recognizes ideals of rings and their structures. Determines the properties of the ring homomorphism. Recognizes division rings, integral domains. Recognizes rings of integers and their properties. Recognizes polinomial rings and their properties. Determines the irreduciblility of a polinomial. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : 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. Course Contents : 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 Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Definition of rings and example of rings Review of the relevant pages from sources Lecture and discussion 2 Basic properties of rings Review of the relevant pages from sources Lecture and discussion 3 Definition of fields and example of fields Review of the relevant pages from sources Lecture and discussion 4 Ideals of rings and examples Review of the relevant pages from sources Lecture and discussion 5 Homomorphism of rings Review of the relevant pages from sources Lecture and discussion 6 Division rings Review of the relevant pages from sources Lecture and discussion 7 Integral domain Review of the relevant pages from sources Lecture and discussion 8 Midterm exam Review and Problem Solving Written Exam 9 Charasterictic of integral domains and their properties Review of the relevant pages from sources Lecture and discussion 10 Rings of integers and its properties Review of the relevant pages from sources Lecture and discussion 11 Polynomial rings and its properties Review of the relevant pages from sources Lecture and discussion 12 Polynomial rings and its properties Review of the relevant pages from sources Lecture and discussion 13 Reducibility in polynomial rings Review of the relevant pages from sources Lecture and discussion 14 Test about reducibility on polynomial rings Review of the relevant pages from sources Lecture and discussion 15 Introduction to Number Theory Review of the relevant pages from sources Lecture and discussion 16/17 Final Exam Review and Problem Solving Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  A Book of Abstract Algebra, Charles Pinter, Mc Graw Hill.  Soyut Cebir Dersleri Cilt II, Hülya Şenkon, İstanbul Üniversitesi Fen Fakültesi Yayınları. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 5 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 5 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 3 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 4 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 3 6 Expresses clearly the relationship between objects while constructing a model 4 7 Draws mathematical models such as formulas, graphs and tables and explains them 5 8 Is able to mathematically reorganize, analyze and model problems encountered. 5 9 Knows at least one computer programming language 5 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 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 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 5 4 20     Mid-term Exams (Written, Oral, etc.) 1 20 20     Final Exam 1 25 25 Total Workload: 163 Total Workload / 25 (h): 6.52 ECTS Credit: 7