ECTS - An Introduction to Low Dimensional Topology
An Introduction to Low Dimensional Topology (MATH577) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| An Introduction to Low Dimensional Topology | MATH577 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Discussion, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | The aim of this course is to introduce the basic techniques to work with manifolds in low dimensions. To approach this main goal, the knot theory and surfaces, which touches upon many branches of mathematics, will be introduced. Elementary linear algebra and some group theory which are taught in the undergraduate program are sufficient as a background. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Knots, links and their invariants, Seifert surfaces, braids, mapping class groups, Heegaard decompositions, lens spaces and surface homeomorphisms, surgery of 3-manifolds, branched coverings. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Knots, Links and Ribbons | pp. 1-22 |
| 2 | Knot and Link Invariants | pp. 23-46 |
| 3 | Seifert Matrices and Surfaces | pp. 118-144, pp.200-232 (D.Rolfsen) |
| 4 | Braids | pp. 47-66 |
| 5 | 3-Manifolds | pp.67-72 |
| 6 | Heegaard Decompositions of 3- Manifolds | pp. 73-76 |
| 7 | Midterm | |
| 8 | Lens Spaces | pp. 77-82 |
| 9 | Homeomorphisms of Surfaces | pp.83-89 |
| 10 | Mapping Class Groups | pp. 90-94 |
| 11 | Fibred Knots and Links Open Book Decompositions | pp.323-341 (D.Rolfsen) |
| 12 | Surgery on 3-Manifolds | pp. 95-107 |
| 13 | Surgery on 3-Manifolds (Continue) | pp. 108-126 |
| 14 | Branched Coverings | pp. 127-151 |
| 15 | Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. Knots, Links, Braids and 3-Manifolds: An Introductions to the New Invariants in Low-Dimensional Topology, Prasolov, Sossinsky, 1996, AMS. |
|---|
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 3 | 30 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 30 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 5 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Ability to carry out advanced research activities, both individual and as a member of a team | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | |||
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 3 | 5 | 15 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 35 | ||