MATH313 METRIC SPACES
| Course Code: | 2360313 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (3.00 - 2.00) |
| ECTS Credit: | 7.5 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of the course students are expected to:
The students will get acquainted with the basic notions of metric spaces like topological properties, continuity/equicontinuity of functions, products, completion, compactness, connectedness, contraction mappings principles and their applications, Tietze extension theorem, Baire's theorem, etc.
Course Content
Metric Spaces. Compactness, connectedness, limits and continuity in metric spaces. Sequences and series in metric spaces, complete metric spaces, completion of a metric space. Sequences and series of functions, uniform convergence. Applications:contraction mappings theorem and its applications, Tietze extension theorem, Baire`s theorem.
Course Learning Outcomes
At the end of the course students are expected to:
- The students will learn the basic results in the field of real anaysis regarding metric spaces and get experience working with metric spaces other than Euclidean space.
- The student will be able to demonstrate competence with topology of metric spaces, like determining a subset of a metric space open/closed or neither.
- The students will get acquainted with the basic topological properties of metric spaces; like compactness, connectedness, etc..
- The student will be able to demonstrate competence with doing proofs by using definitions and basic properties of metric spaces.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution