| Learning Outcomes |
PO |
MME |
| The students who succeeded in this course: |
|
|
| LO-1 |
Learn some important inequalities. Can define the concepts of metric, pseudometric and normed space. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
|
Examination
|
| LO-2 |
Can define the concepts of open set and closed set. Can find interior, exterior, boundary, closure and accumulation points of a set in metric spaces. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
|
Examination
|
| LO-3 |
Can find the distance of a point to a set and the distance between two sets. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
|
Examination
|
| LO-4 |
Can examine equivalence of metrics and convergence of sequences in metric spaces. |
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
|
Examination
|
PO: Programme Outcomes
MME:Method of measurement & Evaluation |
| Course Contents |
| Fundamental Concepts, Absolute Value, Cauchy-Schwarz, Hölder and Minkowski Inequalities, Metric Spaces, Examples, Normed Spaces, Subspaces, Open and Closed Sets, Interior, Exterior, Boundary and Closure of a Set, Distances and Bounded Sets, Neighborhoods and Accumulation Points, Equivalent Metrics, Convergence in Metric Spaces, Examples. |
| Weekly Course Content |
| Week |
Subject |
Learning Activities and Teaching Methods |
| 1 |
Fundamental Concepts |
Lecturing |
| 2 |
Absolute Value |
Lecturing |
| 3 |
Cauchy-Schwarz, Hölder and Minkowski Inequalities |
Lecturing |
| 4 |
Metric Spaces |
Lecturing |
| 5 |
Examples |
Lecturing |
| 6 |
Normed Spaces |
Lecturing |
| 7 |
Subspaces |
Lecturing |
| 8 |
mid-term exam |
|
| 9 |
Open and Closed Sets |
Lecturing |
| 10 |
Interior, Exterior, Boundary and Closure of a Set |
Lecturing |
| 11 |
Distances and Bounded Sets |
Lecturing |
| 12 |
Neighborhoods and Accumulation Points |
Lecturing |
| 13 |
Equivalent Metrics |
Lecturing |
| 14 |
Convergence in Metric Spaces |
Lecturing |
| 15 |
Examples |
Lecturing |
| 16 |
final exam |
|
| Recommend Course Book / Supplementary Book/Reading |
| 1 |
T. Başkan, O. Bizim, İ. N. Cangül, Metrik Uzaylar ve Genel Topolojiye Giriş, Nobel Yayın, Ankara, 2006. |
| 2 |
O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. |
| 3 |
S. A. Kılıç, M. Erdem, Metrik Uzaylar ve Topoloji, Vipaş A.Ş., Bursa, 1999. |
| Required Course instruments and materials |
|
