MATH423 INTRODUCTION TO COMPUTATIONAL TOPOLOGY
| Course Code: | 2360423 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (0.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
Topology studies how a shape or object is connected. In the past few years, there has been an increased interest in the development and use of topological methods for solving various problems in science and engineering. This new line of study is called Computational Topology or Applied Algebraic Topology. Computational topology combines topological results with efficient algorithms to analyze data and solve problems in many fields, including computer graphics and image analysis, neural networks and sensor networks, clustering, robotics, genetics, protein biochemistry, geography, and others. The aim of this course is to give a crash course on topology and geometry with an emphasis on the algorithmic computations for students who are interested in the application side of mathematics.
Course Content
Basic topology, Surfaces and their triangulations, Complexes, Homology, Persistence homology, Morse functions, Discrete Morse Functions, Applications.
Course Learning Outcomes
By the end of semester a successful student will be able to use efficient algorithms to compute homology of a given complex,
and compute persistence homology, relate discrete Morse functions and persistence, sketch persistence diagrams.
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