| CHILD DEVELOPMENT (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 | Spring | 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. |
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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 gain both theoretical and practical knowledge about physical, cognitive, social-emotional aspects of child development. | 4 |
| 2) | To display actions in professional practice based on ethical principles and values. | 5 |
| 3) | To adopt the principle of lifelong learning, using efficient ways for accessing information. | 5 |
| 4) | To know the stages of child development and to be able to use models / theories efficiently for supporting children's cognitive, affective and psycho-motor development. | 5 |
| 5) | To plan, implement and evaluate professional projects, research and events with a sense of social responsibility, | 5 |
| 6) | To be able to use effective communication methods in counseling and child and family-based guidance. | 3 |
| 7) | To be sensitive to the child and family-related issues taking into account the child's stages of development, and to implement strategies for personal development of child and education methods which are vital for leading effective and productive life. | 5 |
| 8) | To use the education and communication materials according to the child development stage, and to create proper educational environment. | 5 |
| 9) | To take responsibilities in the field of child development and education using interdisciplinary approach, and to use information technologies, and to engage in projects and activities. | 5 |
| 10) | To use health information technologies for research in the field of child development. | 5 |
| 11) | To be able to monitor occupational information using at least one foreign language, to collaborate and communicate with colleagues at international level. | 5 |
| 12) | To become a good example for colleagues and society, and represent efficiently the professional identity using advanced knowledge about child development. | 5 |