Kaisa_2012_3_photo by Veikko Somerpuro

Topics:

Smooth manifolds
Smooth mappings
Tangent vectors, tangent bundle
Cotangent bundle
Tensors
Differential forms
Integration on manifolds
De Rham cohomology
Integral curves and flows
Lie derivatives
Lie algebras and Lie groups

Prerequisites: Vector analysis, topology, linear algebra, differential equations

Enrol

Messages

Ilkka Holopainen's picture

Ilkka Holopainen

Published, 5.2.2020 at 11:39

No home work class on Monday, February 10.

Ilkka Holopainen's picture

Ilkka Holopainen

Published, 13.1.2020 at 9:58

First home work classes on Monday, January 20.

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Mon 13.1.2020
10:15 - 12:00
Thu 16.1.2020
14:15 - 16:00
Mon 20.1.2020
10:15 - 12:00
Thu 23.1.2020
14:15 - 16:00
Mon 27.1.2020
10:15 - 12:00
Thu 30.1.2020
14:15 - 16:00
Mon 3.2.2020
10:15 - 12:00
Thu 6.2.2020
14:15 - 16:00
Mon 10.2.2020
10:15 - 12:00
Thu 13.2.2020
14:15 - 16:00
Mon 17.2.2020
10:15 - 12:00
Thu 20.2.2020
14:15 - 16:00
Mon 24.2.2020
10:15 - 12:00
Thu 27.2.2020
14:15 - 16:00
Mon 9.3.2020
10:15 - 12:00
Thu 12.3.2020
14:15 - 16:00
Mon 16.3.2020
10:15 - 12:00
Thu 19.3.2020
14:15 - 16:00
Mon 23.3.2020
10:15 - 12:00
Thu 26.3.2020
14:15 - 16:00
Mon 30.3.2020
10:15 - 12:00
Thu 2.4.2020
14:15 - 16:00
Mon 6.4.2020
10:15 - 12:00
Thu 16.4.2020
14:15 - 16:00
Mon 20.4.2020
10:15 - 12:00
Thu 23.4.2020
14:15 - 16:00
Mon 27.4.2020
10:15 - 12:00
Thu 30.4.2020
14:15 - 16:00

Other teaching

13.01. - 24.02.2020 Mon 14.15-16.00
09.03. - 06.04.2020 Mon 14.15-16.00
20.04. - 27.04.2020 Mon 14.15-16.00
Jean-Baptiste Casteras, Ilkka Holopainen
Teaching language: English

Material

John M. Lee:
Introduction to smooth manifolds, Springer, 2003.

Lecture notes
Ilkka Holopainen: Johdatus differentiaaligeometriaan (in Finnish)

Lecture notes
Ilkka Holopainen: Introduction to differential geometry

Lecture notes
Ilkka Holopainen and Tuomas Sahlsten: Riemannian geometry

Tasks

Conduct of the course

Exam and exercise classes. The exam will consists of 5 problems (evaluated as 6 pts each).

The first possible exam is on 20th of May, 2020.
Remember to register for the exam in WebOodi at least 10 days before the exam!

You will get extra credit points by solving the home work assignments:
25% = +1p, 35% = +2p, 45% = +3p, 55% = +4p, 65% = +5p ja 75% = +6p

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

Belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Topology II

Bachelor studies

Basics on smooth manifolds

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Basics on smooth manifolds and mappings between manifolds, tangent and cotangent space, tensors, differential forms. Stokes theorem.

Lee: Introduction to smooth manifolds.

Lectures and exercise classes

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later