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 | Natural & Applied Sciences Master's Degree |
| 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. |
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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 | |
|---|---|
| Major Area Courses | |
| Supportive Courses | X |
| 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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
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 | ||