Introduction to Differential Geometry

2024/2025

Academic Year

ENG

Instruction in English

5

ECTS credits

Delivered at:

Big Data and Information Retrieval School

Course type:

Elective course

When:

4 year, 3 module

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.