ECONOMICS | |||||
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) | As a world citizen, she is aware of global economic, political, social and ecological developments and trends. | 2 |
2) | He/she is equipped to closely follow the technological progress required by global and local dynamics and to continue learning. | 2 |
3) | Absorbs basic economic principles and analysis methods and uses them to evaluate daily events. | 2 |
4) | Uses quantitative and statistical tools to identify economic problems, analyze them, and share their findings with relevant stakeholders. | 2 |
5) | Understands the decision-making stages of economic units under existing constraints and incentives, examines the interactions and possible future effects of these decisions. | 1 |
6) | Comprehends new ways of doing business using digital technologies. and new market structures. | 2 |
7) | Takes critical approach to economic and social problems and develops analytical solutions. | 1 |
8) | Has the necessary mathematical equipment to produce analytical solutions and use quantitative research methods. | 2 |
9) | In the works he/she contributes, observes individual and social welfare together and with an ethical perspective. | 2 |
10) | Deals with economic problems with an interdisciplinary approach and seeks solutions by making use of different disciplines. | 1 |
11) | Generates original and innovative ideas in the works she/he contributes as part of a team. | 2 |