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Course Description Course Name : Algebra II Course Code : MT 212 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Spring (16 Weeks) ECTS : 7 Name of Lecturer(s) : Prof.Dr. NAİME EKİCİ Learning Outcomes of the Course : Proves properties of groups using basic concepts. Distinguishes between different group structures and computes orders of elements of cyclic groups. Proves whether a given subset is or is not a subgroup. Applies Lagrange´s theorem to solve problems. Proves basic facts about group homomorphisms. Determines whether two given groups are isomorphic. Relates groups to geometric structures. Determines the isomorphism classes of finite abelian groups. Solves various problems using isomorphism theorems. Uses abstract and concrete knowledge to solve problems. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To grasp the fundamentals of groups, cyclic, abelian groups. Normal subgroups and group homomorphisms. To teach such abstract mathematical concepts and abstract thinking. Course Contents : Binary operations, groups, finite groups and group tables, subgroups, cyclic groups, permutation groups, alternating group, isomorphism and Cayley´s theorem, direct product, finitely generated abelian groups, normal subgroups and factor groups, isomorphism theorems. Language of Instruction : Turkish Work Place : Classrooms of Arts and Sciences Faculty   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Groups Review of the relevant pages from sources Lecture and discussion 2 Finite groups and group tables, Subgroups Review of the relevant pages from sources Lecture and discussion 3 Example of groups (The group Zn and dihedral group) Review of the relevant pages from sources Lecture and discussion 4 Permutation groups Review of the relevant pages from sources Lecture and discussion 5 Cyclic groups Review of the relevant pages from sources Lecture and discussion 6 Cyclic groups and cosets Review of the relevant pages from sources Lecture and discussion 7 Lagrange´s Theorem Review of the relevant pages from sources Lecture and discussion 8 Mid-term exam Review of the topics discussed in the lecture notes and sources Written exam 9 Normal subgroups and Factor groups Review of the relevant pages from sources Lecture and discussion 10 Isomorphisms and Automorphisms Review of the relevant pages from sources Lecture and discussion 11 Direct products Review of the relevant pages from sources Lecture and discussion 12 Fundamental Theorem of Finite abelian groups Review of the relevant pages from sources Lecture and discussion 13 Homomorphisms of groups Review of the relevant pages from sources Lecture and discussion 14 Isomorphisms theorems Review of the relevant pages from sources Lecture and discussion 15 Solving problems Review of the relevant pages from sources Lecture and discussion 16/17 Final Exam Review of the topics discussed in the lecture notes and sources again Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Cebir Dersleri , Yazar: Halil İbrahim Karakaş Required Course Material(s)  Soyut Cebir, Yazar:H.Hilmi Hacısalihoğlu  A first Course in Group Theory , Yazar :J.B. Fraleigh,   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 90     Homeworks/Projects/Others 5 10 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 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 1 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. 4 9 Knows at least one computer programming language 4 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 1 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 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 5 5 25     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 20 20 Total Workload: 167 Total Workload / 25 (h): 6.68 ECTS Credit: 7