ARCHITECTURE | |||||
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) | Using the theoretical/conceptual and practical knowledge acquired for architectural design, design activities and research. | |
2) | Identifying, defining and effectively discussing aesthetic, functional and structural requirements for solving design problems using critical thinking methods. | |
3) | Being aware of the diversity of social patterns and user needs, values and behavioral norms, which are important inputs in the formation of the built environment, at local, regional, national and international scales. | |
4) | Gaining knowledge and skills about architectural design methods that are focused on people and society, sensitive to natural and built environment in the field of architecture. | |
5) | Gaining skills to understand the relationship between architecture and other disciplines, to be able to cooperate, to develop comprehensive projects; to take responsibility in independent studies and group work. | |
6) | Giving importance to the protection of natural and cultural values in the design of the built environment by being aware of the responsibilities in terms of human rights and social interests. | |
7) | Giving importance to sustainability in the solution of design problems and the use of natural and artificial resources by considering the social, cultural and environmental issues of architecture. | |
8) | Being able to convey and communicate all kinds of conceptual and practical thoughts related to the field of architecture by using written, verbal and visual media and information technologies. | |
9) | Gaining the ability to understand and use technical information about building technology such as structural systems, building materials, building service systems, construction systems, life safety. | |
10) | Being aware of legal and ethical responsibilities in design and application processes. |