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Course Description Course Name : Algebra I Course Code : MT-515 Course Type : Compulsory Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Assoc.Prof.Dr. AHMET TEMİZYÜREK Learning Outcomes of the Course : Defines the concepts Semigroup, Monoid and group . Defines the group homomorphism and , knows subgroup,some special groups and their properties Knows in detail the structure of normal subgroups cosets and quotient groups Express and proves the isomorphism theorems for groups Knows the concepts of freee groups, free abelian groups, finitely generated abelian groups Knows the action of a group on a set and classification of finite groups of low order Knows the concepts of normal series for groups, Nilpotent groups and solvable groups. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To teach the basic facts in Group Theory required in a graduate program in a detail. Course Contents : Review of the basic concepts of the group theory from undergraduate-level , categories, free products, free objects, free abelian groups, finitely generated Abelian groups, classification of finite groups , Normal series, Nilpotent and solvable groups. 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 Introduction to basic concepts that will be needed in the group theory Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 2 Semigroup, monoid, group and homomorphisms of groups Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 3 Cyclic groups, cosets and counting Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 4 Normal subgroups and quotient groups Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 5 Symmetric, Alternating and dihedral groups Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 6 Categories Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 7 Free objects in the category of groups, generators and relations Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 8 Mid-term exam Review of topics discussed in the lecture notes and sources Written Exam 9 Free abelian groups Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 10 Finitely generated abelian groups Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 11 Action of a group on a set Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 12 Sylow Theorems Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 13 Classification of finite groups of low order. Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 14 Normal series Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 15 Nilpotent and solvable grops Reviewing the relevant chaptes in the Sources Lecture, Problem Solving 16/17 Final exam Review of 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)  P.B. Bahattachary, S.K. Jain, S.R. Nagapul ´´ Basic Abstract Algebra´´ Second Edition, Cambridge Üniversity Press. 1994   Theory and problems of group Theory , SCHAUM´S OUTLINE SERIES McGraw-Hill Book Company 1968 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 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 4 4 Proves basic theorems in different areas of Mathematics 3 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 1 6 Uses technical tools in his/her field 0 7 Works independently in his/her field requiring expertise 3 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 2 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 1 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 3 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 3 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 1 * 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 5 70 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 15 15 Total Workload: 142 Total Workload / 25 (h): 5.68 ECTS Credit: 6