| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2006 | General Topology | Spring | 2 | 2 | 3 | 3 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor NERMINE AHMED EL SISSI |
| Course Objectives: | This is an introductory course in topology in which students will learn the basic concepts of point set topology. Topology plays an essential role in modern mathematics as it is linked to almost all other fields in mathematics. Students will acquire a firm understanding of the concepts of topology. Moreover, the course aims to further develop students’ skills of writing proofs and gain confidence in proving properties about abstract objects. |
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The students who have succeeded in this course; • Understand terms, definitions and prove theorems related to topological spaces. • Demonstrate knowledge and understanding of topological concepts such as open and closed sets, interior points, and limit points. • Create new topological spaces from old ones, to name a few: subspaces, product and quotient topologies. • Understand the link between open sets in a topological space and continuous functions defined over the space. • Show how homeomorphisms are used to study the structure of topological spaces. • Apply the properties of topological spaces to study a specific family of topological spaces, namely metric spaces. |
| The course covers the following topics: topological spaces, open and closed sets, Euclidean topology, basis for a topology, limit points, homeomorphisms of topological spaces, continuous mappings, metric spaces, compactness, connectedness, and product topology. |
| Week | Subject | Related Preparation | |
| 1) | Topology on the real line and topological spaces | ||
| 2) | Open sets, finite-closed topology, functions | ||
| 3) | The Euclidean topology | ||
| 4) | Limit points and neighbourhoods | ||
| 5) | Subspaces and homeomorphisms | ||
| 6) | Connectedness and continuous mappings | ||
| 7) | Intermediate Value Theorem | ||
| 8) | Metric Spaces and convergence of sequences | ||
| 9) | Completeness and contraction mappings | ||
| 10) | Compact spaces and the Heine-Borel Theorem | ||
| 11) | Finite Products | ||
| 12) | Projections onto factors of a product | ||
| 13) | Tychonoff's Theorm for finite Products | ||
| 14) | Review | ||
| Course Notes: | Topology Without Tears, Sidney A. Morris, https://www.topologywithouttears.net |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 2 | % 10 |
| Homework Assignments | % 0 | |
| Presentation | 2 | % 5 |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | 2 | % 5 |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentations / Seminar | 3 | 3 | 9 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 7 | 1 | 7 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 5 | 10 |
| Paper Submission | 2 | 3 | 6 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 10 | 10 |
| Total Workload | 126 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |