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

Instructors: Dmitry Trushin

Language: English

ECTS credits: 5

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.