MANAGEMENT OF HEALTH (TURKISH) | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT4053 | Differentiable Manifolds | Fall | 3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | English |
Type of course: | Non-Departmental Elective |
Course Level: | Bachelor’s Degree (First Cycle) |
Mode of Delivery: | Face to face |
Course Coordinator : | |
Recommended Optional Program Components: | None |
Course Objectives: | The differentiable manifolds course aims to give the fundamental knowledge for the studies of graduate students who intends to study at geometry. |
The students who have succeeded in this course; upon succeeding this course 1)be able to test a differentiable structure given on a set 2)be able to give examples of Differentiable structures on a set 3) be able to check differentiablity of a function 4) be able to solve problems involving the derived map of a transformation between two manifolds 5) be able to use the properties of induced topology on a manifold, 6) be able to coordinatize Grassmann manifolds and can evaluate their dimensions, 7) be able to understand the existence problems by using the unity of partition 8)be able to explain the derived function of a function by using the Leibniz rule, 9) be able to explain submanifolds as images under Immersions 10) be able to coordinatize quotient manifolds and calculate their dimensions, 11) be able to construct Klein bottle and Mobius strip as an example of a quotient manifold |
Differentiable (diff.able) functions, Atlas, diff.able structures on a set, Examples of diff.able structures, diff.able manifolds, diff.able functions, The induced topology on a manifold, diff.able varieties, Grassmann manifolds, Manifold structure on a topological space, properties of the induced topology, Topological restrictions on a manifold, Partitions of unity, Partial differentiation, tangent vectors, The invers function Theorem, Leibniz's rule. İmmersions, submanifolds, regular submanifolds, some topological properties of submanifolds. Submersions, The fibres of submersions, Quotient manifolds, Transformation groups, Examples of quotient manifolds. |
Week | Subject | Related Preparation |
1) | Preliminaires | |
2) | Some classical theory of differentiable functions | |
3) | Atlas, differentiable structures on a set | |
4) | Examples of differentiable structures on a set | |
5) | Differentiable manifolds | |
6) | Differentiable functions | |
7) | The induced topology on a manifold | |
8) | Differentiable varieties, Grassmann manifolds | |
9) | Topological restrictions on a manifold, Partitions of unity | |
10) | Manifold structure on a topological space, properties of the induced topology | |
11) | Partial differentiation, tangent vectors, derived linear functions, The invers function Theorem, Leibniz's rule. | |
12) | İmmersions, submanifolds, regular submanifolds, some topological properties of submanifolds. | |
13) | Submersions, The fibres of submersions, Quotient manifolds | |
14) | Transformation groups, Examples of quotient manifolds. |
Course Notes / Textbooks: | Differentiable Manifolds an Introduction ,F Brickell, R. S. Clark. |
References: | . |
Semester Requirements | Number of Activities | Level of Contribution |
Midterms | 2 | % 45 |
Final | 1 | % 55 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 45 | |
PERCENTAGE OF FINAL WORK | % 55 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 7 | 2 | 14 |
Midterms | 2 | 20 | 40 |
Final | 1 | 30 | 30 |
Total Workload | 126 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | To have theoretical and practical knowledge required to fulfill professional roles and functions of Management of Health Scşences field. | 3 |
2) | To act in accordance with ethical principles and values in management, to learn and implement related regulations and guides. | 3 |
3) | To use life-long learning, problem-solving and critical thinking skills. | 3 |
4) | To identify the process of management functions (management and organization, public relations, human resources, cost accounting, marketing) in the Management of Health Sciences field. | 2 |
5) | To take part in research, projects and activities within sense of social responsibility and interdisciplinary approach. | 2 |
6) | To have skills for planning training programs and projects according to health education needs of individual, family and the community. | 2 |
7) | To be sensitive to health problems of the community and to be able to offer solutions. | 2 |
8) | To be able to use effective communication skills; to take responsibility as a team member in collaboration with other professions. | 2 |
9) | To have skills for research, planning and practice about health systems and health information systems field within national and international level. | 2 |
10) | To be able to search for literature in health sciences and management and information sources to access to information and use the information effectively. | 2 |
11) | To be able to monitor occupational information using at least one foreign language, to collaborate and communicate with colleagues at international level. | 2 |
12) | To be a role model with contemporary and professional identity. | 2 |