Cycle of education: 2019/2020
The name of the faculty organization unit: The faculty Mathematics and Applied Physics
The name of the field of study: Mathematics
The area of study: sciences
The profile of studing:
The level of study: second degree study
Type of study: full time
discipline specialities : Applications of Mathematics in Economics
The degree after graduating from university: master
The name of the module department : Departament of Topology and Algebra
The code of the module: 1489
The module status: mandatory for teaching programme Applications of Mathematics in Economics
The position in the studies teaching programme: sem: 3 / W30 C45 / 5 ECTS / E
The language of the lecture: Polish
The name of the coordinator: Paweł Witowicz, PhD
office hours of the coordinator: wtorek 10:30 - 12 piątek 10:30 - 12
The main aim of study: Getting knowledge about the notions and quantities characterizing curves and surfaces. Getting ability of classifying curves and surfaces and determining their geometric invariants such as curvatures.
The general information about the module: The module concerns a theory of spatial curves and surfaces. The theory of curves cntains the arclength parameter, the Frenet frame, fundamental theorems and theorems involving invariants. The surface theory leads to determining various curvatures (Gauss, mean, normal curvature) and classifying points of a surface. The Riemanian metric and properties of curves contained in a surface are also studied.
1 | John Oprea | Geometria różniczkowa i jej zastosowania | PWN. | 2002 |
2 | Jacek Gancarzewicz, Barbara Opozda | Wstęp do geometrii różniczkowej | Wydawnictwo Uniwersytetu Jagiellońskiego. | |
3 | Biogusław Gdowski | Elementy geometrii różniczkowej z zadaniami | Oficyna Wydawnicza Politechniki Warszawskiej. | 2005 |
1 | Bogusław Gdowski | Elementy geometrii różniczkowej z zadaniami | Oficyna Wydawnicza Politechniki Warszawskiej. | 2005 |
2 | A.N.Pressley | Elementary Differential Geometry | Springer. | 2010 |
1 | Manfredo Do Carmo | Differential Geometry of Curves and Surfaces | Pearson. | 1976 |
Formal requirements: The student satisfies the formal requirements set out in the study regulations
Basic requirements in category knowledge: Knowledge of analysis of several variables, ODE, especially systems of ODE, linear algebra.
Basic requirements in category skills: Ability of calculating integrals, differentiating mappings of several variables, calculating eigenvalues and eigenvectors of matrices.
Basic requirements in category social competences: Ability of individual and group learning.
MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
---|---|---|---|---|---|
01 | A student determines Frenet reper of a regular space curve and its curvature and torsion. | lecture, classes | writing test |
K_W01++ K_U16+ |
P7S_UU P7S_UW P7S_WG |
02 | Lists and explains theorems characterizing curves lying in a plane or within a circle. Uses the theorems to analyze given curves. States the fundamental theorems | lecture, problems classes | writing test, oral exam |
K_W01++ K_W02+++ K_W03+ K_W04++ K_W05++ K_K02++ |
P7S_KK P7S_KO P7S_WG P7S_WK |
03 | Student can assess whether a surface patch is regular, can determine principal curvatures using the shape operator, determines the Gauss curvature of the surface. | lecture, classes | writing test |
K_W01+ K_W03+ K_U10+++ |
P7S_UW P7S_WG |
04 | Student classifies points of a surface. | lecture, problems classes | writing test. oral exam |
K_W02++ K_K02++ |
P7S_KK P7S_KO P7S_WG P7S_WK |
05 | Tells the definitions and theorems included in the lecture. | lecture, problems classes | oral or written exam |
K_W01+++ K_W03+ |
P7S_WG |
Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).
Sem. | TK | The content | realized in | MEK |
---|---|---|---|---|
3 | TK01 | W01, W02,W03, W04, C01 - C04 | MEK01 MEK02 | |
3 | TK02 | W05,W06, C05,C06,C07 | MEK01 | |
3 | TK03 | w07-w09, C08-C10 | MEK03 MEK04 | |
3 | TK04 | W10-W13, C11-C13 | MEK03 MEK04 | |
3 | TK05 | w14-w15, c14-c15 | MEK05 |
The type of classes | The work before classes | The participation in classes | The work after classes |
---|---|---|---|
Lecture (sem. 3) | contact hours:
30.00 hours/sem. |
complementing/reading through notes:
10.00 hours/sem. Studying the recommended bibliography: 5.00 hours/sem. |
|
Class (sem. 3) | The preparation for a Class:
20.00 hours/sem. The preparation for a test: 5.00 hours/sem. |
contact hours:
45.00 hours/sem. |
Finishing/Studying tasks:
3.00 hours/sem. |
Advice (sem. 3) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
3.00 hours/sem. |
|
Exam (sem. 3) | The preparation for an Exam:
15.00 hours/sem. |
The written exam:
2.00 hours/sem. |
The type of classes | The way of giving the final grade |
---|---|
Lecture | Oral or written exam |
Class | Presenting solving of problems, test, presentation. |
The final grade | Degree accounts the exam, test and activity. Degree higher than 4,0 is possible only after having passed an oral exam consisting of giving proofs of selected theorems. |
Required during the exam/when receiving the credit
mek01-04.pdf
zagadnienia_2014-15.pdf
Realized during classes/laboratories/projects
geometria1.odt
geometria2.odt
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : no
1 | P. Witowicz | Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics | 2021 |