MTK771 - GEOMETRIC TOPOLOGY
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| GEOMETRIC TOPOLOGY | MTK771 | Any Semester/Year | 3 | 0 | 3 | 12 |
| Prequisites | None | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Discussion Problem Solving | |||||
| Instructor (s) | Assoc. Prof. Dr. Sinem Onaran | |||||
| Course objective | The aim of the course is to give an introductory course in geometric topology and to teach the construction tecniques of manifolds. | |||||
| Learning outcomes |
| |||||
| Course Content | Knot theory Invariants of knots, knot polynomials Classification of Surfaces Simplicial complexes and simplicial surfaces Euler characteristic of surfaces Diffeomorfisms of surfaces Mapping class groups of surfaces | |||||
| References | ? A First Course in Geometric Topology and Differential Geometry, Ethan D. Bloch ? Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant, N. Saveliev | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | Knots, links, isotopy, Reidemeister moves |
| Week 2 | Types of knots, knot invariants |
| Week 3 | Knot polynomials: Alexander-Conway polynomial, the classical Alexander polynomial |
| Week 4 | Knot polynomials: the Kauffman bracket polynomial, the Jones polynomial |
| Week 5 | Surfaces, surfaces with boundary |
| Week 6 | Oriented, non-oriented surfaces |
| Week 7 | Classification of oriented, non-oriented surfaces |
| Week 8 | Midterm |
| Week 9 | Proof of the classification of oriented, non-oriented surfaces |
| Week 10 | Simplicial complexes, regular complexes |
| Week 11 | Euler characteristic of surfaces |
| Week 12 | Diffeomorphisms of surfaces |
| Week 13 | Mapping class groups of surfaces |
| Week 14 | Mapping class groups of surfaces |
| Week 15 | Final preparation |
| Week 16 | Final exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 6 | 30 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Midterms | 1 | 30 |
| Final exam | 1 | 40 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 0 | 60 |
| Percentage of final exam contributing grade succes | 0 | 40 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 14 | 12 | 168 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 6 | 20 | 120 |
| Midterms (Study duration) | 1 | 15 | 15 |
| Final Exam (Study duration) | 1 | 15 | 15 |
| Total Workload | 36 | 65 | 360 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1. Deepens the concepts of mathematics in the level of expertise. | X | ||||
| 2. Grasps the inter-disciplinary interaction related to the area; reaches original results by using the specialist knowledge in analyzing and evaluating new ideas. | X | ||||
| 3. Gains the ability to think independently and develops theoretical concepts. | X | ||||
| 4. Develops original mathematical models by using interrelations between mathematics and other disciplines and applies them to other disciplines. | |||||
| 5. Uses high level research methods in studies in the area. | X | ||||
| 6. Develops a new idea, method and/or application independently, finds a solution, and contributes to the progress in the area by carrying out original studies. | |||||
| 7. Fulfills the leader role in the environments where solutions are thought for the area and/or inter-disciplinary problems. | |||||
| 8. Develops continually the skills of creativity, decision making and problem solving. | X | ||||
| 9. Defends original opinions by communicating with experts in the area. | |||||
| 10. Uses a foreign language- at least C1 Level-, communicates with foreign colleagues and follows the international literature. | X | ||||
| 11. Follows the latest developments in the information and communication technologies and uses them in the area. | |||||
| 12. Does research in national and international research groups. | |||||
| 13. Makes strategic decision in the solution of problems in the area. | |||||
| 14. Protects the rights of other researchers in regards to ethics, privacy, ownership and copyright. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest