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Course Description Course Name : Algebra II Course Code : MT-514 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Assoc.Prof.Dr. AHMET TEMİZYÜREK Learning Outcomes of the Course : learns the concepts such as definition of the ring, subring and ring homomorphism . learns the concepts in detail an ideal in a ring, prime and maximal ideals Recognizes prime and irreducible elements in commutative rings and is familiar with the Unique Factorization Domains (UFD) Understands the properties of Euclidean Rings Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : to introduce the basic concepts of the Ring Theory at Graduate level Course Contents : Ring structure, sub-rings and ideals, prime and maximal ideals, decomposition in commutative rings, principal ideal domains (PID), Unique Factorization domains (UFD), Euclidean Domains, decomposition in polynomial rings , polinoamial ring with several variables Language of Instruction : Turkish Work Place : Department of Mathematics , Yusuf UNLU seminar room   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Rings and Ring homomorphisms Reviewing the relevant chapters in the Sources Lecture and discussion 2 Ideals Reviewing the relevant chapters in the Sources Lecture and discussion 3 Prime and maximal ideals Reviewing the relevant chapters in the Sources Lecture and discussion 4 solving problems (problems in the first source pages 120, 133, 134) Solving problems in advance solving problems and discussion 5 Inner direct product and Chinese Remainder Theorem Reviewing the relevant chapters in the Sources Lecture and discussion 6 Decomposition in commutative rings Reviewing the relevant chapters in the Sources Lecture and discussion 7 Solving problems (problems in the first source page 140) Solving problems in advance solving problems and discussion 8 mid-term exam Review of topics discussed in the lecture notes and sources written exam 9 Euclidean Rings Reviewing the relevant chapters in the Sources Lecture and discussion 10 Quotient Rings and Localizations Reviewing the relevant chapters in the Sources Lecture and discussion 11 Quotient Rings and Localizations Reviewing the relevant chapters in the Sources Lecture and discussion 12 Solving problems (problems in page 148) Solving problems in advance solvin problems and discussion 13 Rings and formal power series Reviewing the relevant chapters in the Sources Lecture and discussion 14 Factorization in polynomial rings Reviewing the relevant chapters in the Sources Lecture and discussion 15 Factorization in polynomial rings Reviewing the relevant chapters in the Sources Lecture and discussion 16/17 Final exam Review of the topics discussed in the lecture notes and sources written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Thomas W. Hungerford,´´ Algebra ´´ Springer - Verlag New York (1996) Required Course Material(s)   P.B. Bahattachary, S.K. Jain, S.R. Nagapul ´´ Basic Abstract Algebra´´ Second Edition, Cambridge Üniversity Press. 1994   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 80     Homeworks/Projects/Others 1 20 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 Aquires sufficient knowledge to enable one to do research over and above the undergraduate level 5 2 Learns theoretical foundations of his/her field thoroughly 4 3 Uses the knowledge in his/her field to solve mathematical problems 5 4 Proves basic theorems in different areas of Mathematics 4 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 0 6 Uses technical tools in his/her field 2 7 Works independently in his/her field requiring expertise 4 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 4 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 4 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 2 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 4 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 2 * 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 1 10 10     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 15 15 Total Workload: 138 Total Workload / 25 (h): 5.52 ECTS Credit: 6