| GASTRONOMY (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) | - Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources. | |
| 2) | Use of advanced theoretical and practical knowledge within the field. -Interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the field. | |
| 3) | Inform people and institutions, transfer ideas and solution proposals to problems in written and orally on issues in the field. - Share the ideas and solution proposals to problems on issues in the field with professionals and non-professionals by the support of qualitative and quantitative data. -Organize and implement project and activities for social environment with a sense of social responsibility. -Monitor the developments in the field and communicate with peers by using a foreign language at least at a level of European Language Portfolio B1 General Level. -Use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. | |
| 4) | Evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach. -Determine learning needs and direct the learning. -Develop positive attitude towards lifelong learning. | |
| 5) | Act in accordance with social, scientific, cultural and ethic values on the stages of gathering, implementation and release of the results of data related to the field. - Possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also, environmental protection, worker's health and security. | |
| 6) | Conduct studies at an advanced level in the field independently. - Take responsibility both as a team member and individually in order to solve unexpected complex problems faced within the implementations in the field. - Planning and managing activities towards the development of subordinates in the framework of a project |