Differential Geometry(MAT417)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT417 | Differential Geometry | 8 | 3 | 0 | 0 | 3 | 5 |
| Prerequisites | MAT116, MAT202 |
| Admission Requirements | MAT116, MAT202 |
| Language of Instruction | |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Serap GÜRER serapgurer@gmail.com (Email) |
| Assistant | |
| Objective | Introduction to fundamental theorems and concepts in differential geometry |
| Content | Curves, surfaces, differential forms, first fundamental form, second fundamental form, Christoffel symbols, geodesics, Gauss's theorema egregium theorem, Gauss-Bonnet theorem, differentiable manifolds, tangent bundle, Lie derivative, Lie brackets, Lie groups, de Rham cohomology |
| Course Learning Outcomes |
1. Understand how to study curves and surfaces 2. Understand the notions of differentiable varieties and the questions involved |
| Teaching and Learning Methods | Lectures and problem sets |
| References |
Cours de mathématiques pures et appliquées : Algèbre et géométrie - Ramis, Warusfel, Moulin Géométrie et calcul différentiel sur les variétés - Pham Differential geometry of curves and surfaces - Do Carmo Géométrie différentielle élémentaire - Paulin Notes de cours de Géométrie différentielle - Oancea Géométrie différentielle - Guedj Lectures on the Geometric Anatomy of Theoretical Physics - Schuller |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Differential calculus |
| 2 | Differential forms |
| 3 | Curves |
| 4 | Surfaces |
| 5 | Tensors, quizz |
| 6 | First fundamental form |
| 7 | Second fundamental form |
| 8 | Midterm |
| 9 | Submanifold |
| 10 | Manifold |
| 11 | Tangent bundle |
| 12 | Lie brackets, Lie derivative |
| 13 | Lie group |
| 14 | de Rham Cohomology, quizz |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 14 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 15 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 10 | 5 |
| Presentation | 1 | 5 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 2 | 20 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 14 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 5 | 70 |
| Assignments | 7 | 3 | 21 |
| Midterm Examinations (including preparation) | 2 | 6 | 12 |
| Final Examinations (including preparation) | 1 | 16 | 16 |
| Total Workload | 175 | ||
| Total Workload / 25 | 7.00 | ||
| Credits ECTS | 7 | ||