INTERNATIONAL TRADE AND BUSINESS | |||||
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. |
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) | Has theoretical and practical knowledge on management, business, trade, economy, entrepreneurship, innovation, sustainable development related to International Trade and Business and can use this information | |
2) | Can collect data from different sources in the global business world and successfully apply research techniques, use information and communication technologies. | |
3) | Can analyze opportunities and threats with strategic thinking skills by using different resources and channels in the ever-changing global business world. | |
4) | Can communicate orally and in writing with a good knowledge of English grammar. | |
5) | He / she can transfer the knowledge and skills he / she has acquired in the field to the relevant people in written and oral form and evaluate them critically. | |
6) | Adopts the principles of business ethics with the awareness of professional responsibility and can apply these principles within the framework of legal rules in the field of global trade and business. | |
7) | He / she can collaborate in and out of the field, take responsibility, respect cultural differences and have ethical values. | |
8) | Has sufficient awareness of social rights, justice, cultural values, environmental awareness, occupational health and safety. | |
9) | With the lifelong learning skill acquired, she/he can identify learning needs and improve herself/himself |