(in Polish) Struktury geometryczne na rozmaitościach

General data

Course ID:	1000-1S22GSM
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	(unknown)
Name in Polish:	Struktury geometryczne na rozmaitościach
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Seminars for Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Main fields of studies for MISMaP:	mathematics
Type of course:	elective seminars
Prerequisites (description):	Knowledge of obligatory subjects from 1st and 2nd year, including Linear algebra, Analysis I and II, Topology, Ordinary Differential Equations. A basic knowledge of Differential Geometry is an advantage but not necessary.
Mode:	Classroom
Short description:	The idea of the seminar is to introduce some basic concepts and results of modern differential geometry.
Full description:	Smooth manifolds carrying additional structure are basic objects in many branches of mathematics and physics, including Control Theory, Riemannian Geometry, Lagrangian and Hamiltonian Mechanics, Field Theory, General Relativity. In the seminar we want to introduce/recall some basic differential geometric notions, including tangent and cotangent bundles, vector and tensor fields, fiber bundles, jets. Later, we would like to dig deeper into one or more specific topics according to the preferences of the students. Some proposals of these specific topics are: -foundations of Riemannian geometry, Levi-Civita connection, Riemannian curvature -sub Riemannian geometry, normal and abnormal geodesics and the problem of smoothness of length minimizing curves -Geometric Control Theory, emphasizing results about accessibility such as Frobenius, Chow’s-Rachewski and Sussmann theorems -Theory of product-preserving functors and its relation with Weil algebras -structure of jet bundles and geometry of partial differential equations
Bibliography:	Lee, Introduction to smooth manifolds Lee, Riemannian Manifolds: An Introduction to Curvature Kolar, Michor, Slovak, Natural Operations in Differential Geometry Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications Saunders, The Geometry of Jet Bundles Spivak, A Comprehensive Introduction to Differential Geometry. Volumes I-V
Learning outcomes:	The intended outcome is that a student will acquire a foundation in the differential geometry used across a variety of modern fields of contemporary research.
Assessment methods and assessment criteria:	Evaluation based on a given seminar talk and active participation in the classes.

This course is not currently offered.

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Copyright by University of Warsaw.