John M. Lee:
Introduction to smooth manifolds, Springer, 2003.
Ilkka Holopainen: Johdatus differentiaaligeometriaan (in Finnish)
Ilkka Holopainen and Tuomas Sahlsten: Riemannian geometry
There is a brief review on differential geometry (first 21 pages)
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)
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
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.
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