Bachelor
2024/2025
Introduction to Differential Geometry
Type:
Elective course (Applied Mathematics and Information Science)
Area of studies:
Applied Mathematics and Information Science
Delivered by:
Big Data and Information Retrieval School
Where:
Faculty of Computer Science
When:
4 year, 3 module
Mode of studies:
distance learning
Online hours:
32
Open to:
students of one campus
Language:
English
ECTS credits:
5
Contact hours:
40
Course Syllabus
Abstract
Differential geometry is mathematical analysis together with differential equations and linear algebra together with optimization theory. It has always developed under the great influence of physics and has always found applications both in applied sciences and within the abstract areas of mathematics. The course will cover the most basic things. It will outline what a smooth manifold is and how the mappings between them are arranged. Manifolds are nonlinear surfaces of arbitrary fixed dimensions, generalizations of linear spaces. Students will learn how to properly differentiate and integrate on manifolds. Differentiation will lead to covariant derivatives, and integration to the theory of differential forms and de Rham cohomology.