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
11.12.2017 at 09:00 - 2.5.2018 at 23:59

Messages

Ilkka Holopainen's picture

Ilkka Holopainen

Published, 27.4.2018 at 10:56

There is a new version of Exercises 11.

Ilkka Holopainen's picture

Ilkka Holopainen

Published, 15.1.2018 at 14:02

There will be no lectures on February 20, 21, 27, and 28 (neither on March 6 and 7).

Ilkka Holopainen's picture

Ilkka Holopainen

Published, 15.1.2018 at 12:00

The first exercise class is on Wednesday, January 24.

Timetable

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

DateTimeLocation
Tue 16.1.2018
12:15 - 14:00
Wed 17.1.2018
12:15 - 14:00
Tue 23.1.2018
12:15 - 14:00
Wed 24.1.2018
12:15 - 14:00
Tue 30.1.2018
12:15 - 14:00
Wed 31.1.2018
12:15 - 14:00
Tue 6.2.2018
12:15 - 14:00
Wed 7.2.2018
12:15 - 14:00
Tue 13.2.2018
12:15 - 14:00
Wed 14.2.2018
12:15 - 14:00
Tue 20.2.2018
12:15 - 14:00
Wed 21.2.2018
12:15 - 14:00
Tue 27.2.2018
12:15 - 14:00
Wed 28.2.2018
12:15 - 14:00
Tue 13.3.2018
12:15 - 14:00
Wed 14.3.2018
12:15 - 14:00
Tue 20.3.2018
12:15 - 14:00
Wed 21.3.2018
12:15 - 14:00
Tue 27.3.2018
12:15 - 14:00
Wed 28.3.2018
12:15 - 14:00
Tue 10.4.2018
12:15 - 14:00
Wed 11.4.2018
12:15 - 14:00
Tue 17.4.2018
12:15 - 14:00
Wed 18.4.2018
12:15 - 14:00
Tue 24.4.2018
12:15 - 14:00
Wed 25.4.2018
12:15 - 14:00
Wed 2.5.2018
12:15 - 14:00

Other teaching

17.01. - 28.02.2018 Wed 14.15-16.00
14.03. - 28.03.2018 Wed 14.15-16.00
11.04. - 02.05.2018 Wed 14.15-16.00
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 and Tuomas Sahlsten: Riemannian geometry
There is a brief review on differential geometry (first 21 pages)

Tasks

Harjoitus 1, Exercise 1 (24.1.2018)

Harjoitus 2, Exercise 2 (31.1.2018)

Harjoitus 3, Exercise 3 (7.2.2018)

Harjoitus 4, Exercise 4 (14.2.2018)

Harjoitus 5, Exercise 5 (14.3.2018)

Harjoitus 6, Exercise 6 (21.3.2018)

Harjoitus 7, Exercise 7 (28.3.2018)

Harjoitus 8, Exercise 8 (11.4.2018)

Harjoitus 9, Exercise 9 (18.4.2018)

Harjoitus 10, Exercise 10 (25.4.2018)

Harjoitus 11, Exercise 11 (2.5.2018)

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 23rd of May.

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