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Course Description Course Name : Introduction to Algebraic Topology Course Code : MT-561 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Prof.Dr. DOĞAN DÖNMEZ Learning Outcomes of the Course : Learns some problem solving techniques of Algebraic Topology understands the homotopy, homolgy and cohomology functors. translates a topological problem to an algebraic problem using functors. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To grasp the problems and the methods of Algebraic Topology Course Contents : Category,functor, fundamental group, higher homotopy groups, homology 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 Category, covariant and contravariant functors. Category of topological spaces, groups and abelian groups Study the relevant sections in the textbook and solve problems Lecturing 2 Homotopy, relative homotopy, Curves, addition of curves. Fundamental group. Study the relevant sections in the textbook and solve problems Lecturing 3 Fundamental group functor. Seifert-van Kampen theorem Study the relevant sections in the textbook and solve problems Lecturing 4 Homotopy invariance Study the relevant sections in the textbook and solve problems Lecturing 5 Fundamental group of the circle and product spaces. Study the relevant sections in the textbook and solve problems Lecturing 6 Covering spaces, Homotopy lifting in covering spaces. Study the relevant sections in the textbook and solve problems Lecturing 7 Lifting criterion. Study the relevant sections in the textbook and solve problems Lecturing 8 Loop spaces and higher homotopy groups. Study the relevant sections in the textbook and solve problems Lecturing 9 Midterm exam Review the material covered and Solve Problems Written Exam 10 Affine space, standard simplex and affine mappings. Study the relevant sections in the textbook and solve problems Lecturing 11 Singular homology Study the relevant sections in the textbook and solve problems Lecturing 12 Sİngular homology functor. Study the relevant sections in the textbook and solve problems Lecturing 13 Homotopy invariance Study the relevant sections in the textbook and solve problems Lecturing 14 Relation between the fundamental group and the first homology gorup Study the relevant sections in the textbook and solve problems Lecturing 15 Relative Homolgy Study the relevant sections in the textbook and solve problems Lecturing 16/17 Final Exam Review course contents and Solve Problems Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Algebraic Topology M.J. Greenberg, J.R. Harper (1982) Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 70     Homeworks/Projects/Others 3 30 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 3 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 5 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 5 6 Uses technical tools in his/her field 4 7 Works independently in his/her field requiring expertise 3 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 0 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 1 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 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 3 5 15     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 20 20 Total Workload: 143 Total Workload / 25 (h): 5.72 ECTS Credit: 6