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| MAT4025 | Introduction to Algebraic Topology | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Doç. Dr. Tane VERGİLİ | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is to introduce the fundamental concepts of algebraic topology that is crucial to classify topological spaces by algebraic structures.
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| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Definitions and theorems related with algebraic topology will be covered. | 1,3,5 | | | LO - 2 : | The relation between topology and algebra will be covered. | 1,3,5 | | | LO - 3 : | The ability to characterize topological spaces with algebraic structures by using homotopy and fundamental groups will be gained. | 1,3,5 | | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| continuous maps, product and quotient spaces, identification spaces, homotopy, fundamental group covering spaces, categories and functors |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Continuity and homeomorphism | | | Week 2 | Product and quotient spaces | | | Week 3 | Identification spaces, suspension | | | Week 4 | connected and path connected spaces | | | Week 5 | Homotopy | | | Week 6 | Path Homotopy | | | Week 7 | Fundamental group | | | Week 8 | Contractible spaces and simply connected spaces | | | Week 9 | Midterm | | | Week 10 | Covering spaces | | | Week 11 | Covering spaces and the fundamental group of a circle | | | Week 12 | Homotopy equivalnece, (strong) deformation retract | | | Week 13 | fundamental group computation | | | Week 14 | Seifert-Van Kampen Theorem | | | Week 15 | Categories and functors | | | Week 16 | Final Exam | | | |
| 1 | Munkres, James Raymon. 1975; Topology a First Course, Prentice Hall. Inc. | | | |
| 1 | Karaca, İsmet. 2020; Teorik ve Uygulama Alanları ile Topoloji, Palme Yayınevi.
| | | 2 | Rotman, Joseph. 1988; An Introduction to Algebraic Topology, Springer-Verlag New York Inc.. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 25/11/2021 | 2 saat | 50 | | End-of-term exam | 16 | 18/01/2022 | 2 saat | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 7 | 14 | 98 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 14 | 1 | 14 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 182 |
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