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Course Description Course Name : Group Theory Course Code : MT 313 Course Type : Optional Level of Course : First Cycle Year of Study : 3 Course Semester : Fall (16 Weeks) ECTS : 5 Name of Lecturer(s) : Prof.Dr. HAYRULLAH AYIK Learning Outcomes of the Course : Understands basic definitions and theorems of group theory. Recognizes some special groups and group constructions. Recognizes normal subgroups and quotient groups. Recognizes permutation groups and counting its elements Understands isomorphism theorems and solves problems using isomorphism theorems. Knows the Sylow Theorems and solves problems using Sylow Theorems. Understands the clasification of small order groups under isomorphism. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : The aim of this course is to understand basic definitions and theorems of group theory, recognize some special groups and groups construction, recognize normal subgroups and quotient groups, recognize permutation groups and counting its elements, understand and solve problems with isomorphism theorems, understand Sylow Theorems and solving problems using Sylow Theorems. Course Contents : Fundamental definitions and theorem of group theory, Some special groups and group construction, Permutation groups and counting its elements, Groups symmetry, Normal subgroups and its properties, Quotient groups, Counting with groups, Isomorphism theorems, Examples of using isomorphism theorems, Group actions, Basic groups, Sylow Theorems and its applications, Clasification of small order groups under isomorphism Language of Instruction : Turkish Work Place : Faculty of Arts and Sciences Annex Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Fundamental definitions and theorem of group theory Review of the relevant pages from sources Lecture and discussion 2 Some special groups and group construction Review of the relevant pages from sources Lecture and discussion 3 Permutation groups and counting its elements Review of the relevant pages from sources Lecture and discussion 4 Symmetry groups Review of the relevant pages from sources Lecture and discussion 5 Normal subgroups and their properties Review of the relevant pages from sources Lecture and discussion 6 Quotient groups Review of the relevant pages from sources Lecture and discussion 7 Counting with groups Review of the relevant pages from sources Lecture and discussion 8 Mid term Exam Review and Problem Solving Written exams 9 Isomorphism theorems Review of the relevant pages from sources Lecture and discussion 10 Examples of using isomorphism theorems Review of the relevant pages from sources Lecture and discussion 11 Group actions Review of the relevant pages from sources Lecture and discussion 12 Simple groups Review of the relevant pages from sources Lecture and discussion 13 Sylow Theorems and their applications Review of the relevant pages from sources Lecture and discussion 14 Classification groups of small order up to isomorphism Review of the relevant pages from sources Lecture and discussion 15 Classification groups of small order up to isomorphism 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)  C. F. Gardiner ´´ A first course in group theory´´ Springer - Verlag, New York Inc. 1980  J.J. Rotman, ´A first course in abstract algebra´ Second Edition, Prentice Hall, 2000. 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 0 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. 1 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 2 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 2 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 0 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 4 8 Is able to mathematically reorganize, analyze and model problems encountered. 4 9 Knows at least one computer programming language 3 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 4 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 3 42 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 25 25 Total Workload: 124 Total Workload / 25 (h): 4.96 ECTS Credit: 5