INTERNATIONAL FINANCE | |||||
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 correctly identify the problems and to be able to ask the correct questions | 2 |
2) | To have the ability for problem solving and to utilize analytical approach in dealing with the problems of finance | 1 |
3) | To understand and grasp the full details of theoretical arguments and counter arguments | 2 |
4) | To be fully prepared for a graduate study in finance and to have lifelong learning awareness | 2 |
5) | To be able to apply theoretical principles of finance to the realities of practical business life | 1 |
6) | To develop solutions for managerial problems by understanding the requirements of international financial markets | 2 |
7) | To think innovatively and creatively in complex situations | 3 |
8) | To be able to make decisions both locally and internationally by knowing the effects of globalization on business and social life | 2 |
9) | To have the competencies of the digital age and to use the necessary financial applications | 2 |
10) | To be able to use at least one foreign language both for communication and academic purposes | 1 |
11) | To understand the importance of business ethics and to take decisions by knowing the legal and ethical consequences of their activities in the academic world and business life | 2 |
12) | To develop an objective criticism in business and academic life and having a perspective to self-criticize | 2 |