|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Asst. Prof. Dr. Gül UĞUR KAYMANLI
|
|
Instructors
|
-
|
|
Assistants
|
-
|
|
Resources
|
R1. Ekici, C. (2021). Eğrilerin ve Yüzeylerin Geometrisi. Eskişehir Osmangazi Üniversitesi, Eskişehir.
|
|
Supplementary Book
|
SR1. Block, E. D. (1996). A First Course in Geometric Topology and Differential Geometry. Birkhauser, Boston.
SR2. O`Neil, B. (2006). Elementary differential geometry. Revised second edition. Elsevier/Academic Press, Amsterdam.
SR3. do Carmo, M. P. ( 2016). Differential geometry of curves & surfaces. Dover Publications, Mineola, NY.
SR4. Pressley, A. (2010). Elementary differential geometry. Second edition. Springer Undergraduate Mathematics Series, Springer, Berlin.
SR5. Hacısalihoğlu, H. H. (1998). Diferensiyel Geometri Cilt : 1 (3. Baskı). Hacısalihoğlu Yayınları, Anakara.
SR6. Sabuncuoğlu, A. (2010). Diferensiyel Geometri (4. Baskı). Nobel Akademik Yayıncılık, Ankara.
|
|
Goals
|
To teach basic notions and results of surfaces in classical differential geometry, and to provide necessary substructure to students who wish to study for a master degree in this area.
|
|
Content
|
Orientation on hypersurfaces; The shape operatör; Fundamental forms; The algebraic invariants of the shape operatör; Riemann curvature tensor; Line of curvature, asymptotic line, and its directions; Hyperplane; Hypersphere; Hypercyclinder; Ruled surface; Parallel hypersurfaces; Geodesics on hypersurfaces; Asymptotic curves; Lines of curvature.
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
Having advanced theoretical and applied knowledge in the basic areas of mathematics
|
-
|
|
2
|
Ability of abstract thinking
|
3
|
|
3
|
To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
|
2
|
|
4
|
Associating mathematical achievements with different disciplines and applying them in real life
|
-
|
|
5
|
Ability to work independently in a problem or project that requires knowledge of mathematics
|
-
|
|
6
|
Ability to work harmoniously and effectively in national or international teams and take responsibility
|
-
|
|
7
|
Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
|
3
|
|
8
|
To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
|
-
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
|
2
|
|
11
|
Being able to produce projects and organize events with social responsibility awareness
|
-
|
|
12
|
Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
|
-
|
|
13
|
Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
|
-
|
|
14
|
Being conscious of acting in accordance with social, scientific, cultural and ethical values
|
-
|