Бакалавриат
2024/2025
Введение в дифференциальную геометрию
Статус:
Курс по выбору (Прикладная математика и информатика)
Направление:
01.03.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
4-й курс, 3 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
32
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
5
Контактные часы:
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.