Geometry and computation WM-MA-S2-E1-CG

This course covers the geometry of curves and surfaces and employs Python symbolic and graphical packages to solve related problems and visualize various examples. If time permits, some more advanced topics, such as mesh processing and surface fairing will be discussed.

(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się

mathematics

(in Polish) Grupa przedmiotów ogólnouczenianych

(in Polish) nie dotyczy

(in Polish) Opis nakładu pracy studenta w ECTS

For the lecture: class attendance 30 hours, participation in tests/exams outside of class 3 hours, consultations 2 hours, preparation for classes 5 hours, preparation for tests/exams 10 hours, All together 50 h, equivalent to 2 ECTS credits For the laboratory: class attendance 30 hours, consultations 5 hours, preparation for classes 20 hours, preparation for tests/exams 20 hours, All together 75 h, equivalent to 3 ECTS credits

Subject level

intermediate

Learning outcome code/codes

For the laboratory: MA2_U13, MA2_U14, MA2_U15, MA2_U21, MA2_U24; MA2_K02, MA2_K08 For the lecture: MA2_W04, MA2_W05, MA2_W06, MA2_W07, MA2_W16

Type of subject

optional with unlimited choices

Preliminary Requirements

Linear Algebra, Basic calculus

Course coordinators

Omid Makhmali

Learning outcomes

U1: The student will be able to analyze the geometry of curves and surfaces, express their differential invariants, and use them to prove equivalence or inequivalence of a pair of curves or surfaces (MA2_U13, MA2_U14, MA2_U15, MA2_U21)

U2: This course serves as a gateway into extrinsic and intrinsic differential geometry of manifolds. (MA2_U13, MA2_U14, MA2_U15, MA2_U21)

U3: The student will be able to use Python to perform symbolic and numerical calculations needed to find differential invariants of curves and surfaces and prove their (in)equivalence, and visualize them. (MA2_U13, MA2_U14, MA2_U15, MA2_U21)

K1: The student can get involved with and contribute to many active communities around open-source projects in Python, in particular SageMath. (MA2_K02, MA2_K08)

K2: Many industries and institutions can significantly benefit from skills that are developed to solve well-known mathematical problems. In the case of analytic and geometric problems, Python language and its open-source libraries have a lot to offer. (MA2_K02, MA2_K08)

W1: Students develop a good understanding of differential geometry of shapes and spaces and can distinguish between their intrinsic and extrinsic properties. (MA2_W04, MA2_W05, MA2_W06, MA2_W07, MA2_W16)

W2: Students develop an understanding of an abstract space, which is essential in physics, astronomy and advanced mathematics. (MA2_W04, MA2_W05, MA2_W06, MA2_W07, MA2_W16)

W3: A variety of unsolved problems and research projects will be mentioned throughout the course, as well as links to other areas of advanced mathematics and physics. (MA2_W04, MA2_W05, MA2_W06, MA2_W07, MA2_W16)

Assessment criteria

For all learning outcomes, the following assessment criteria are adopted for all forms of verification:

grade 5: fully achieved (no obvious shortcomings),

grade 4.5: achieved almost fully and criteria for awarding a higher grade are not met,

grade 4: largely achieved and the criteria for a higher grade are not met,

grade 3.5: largely achieved - with a clear majority of positives - and the criteria for granting a higher grade are not met,

grade 3: achieved for most of the cases covered by the verification and criteria for a higher grade are not met,

grade 2: not achieved for most of the cases covered by the verification.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of WM-MA-S2-E1-CG in USOSweb