Kaisa_2012_3_photo by Veikko Somerpuro

Enrol

Timetable

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

DateTimeLocation
Wed 5.9.2018
10:15 - 12:00
Mon 10.9.2018
10:15 - 12:00
Wed 12.9.2018
10:15 - 12:00
Mon 17.9.2018
10:15 - 12:00
Wed 19.9.2018
10:15 - 12:00
Mon 24.9.2018
10:15 - 12:00
Wed 26.9.2018
10:15 - 12:00
Mon 1.10.2018
10:15 - 12:00
Wed 3.10.2018
10:15 - 12:00
Mon 8.10.2018
10:15 - 12:00
Wed 10.10.2018
10:15 - 12:00
Mon 15.10.2018
10:15 - 12:00
Wed 17.10.2018
10:15 - 12:00
Mon 29.10.2018
10:15 - 12:00
Wed 31.10.2018
10:15 - 12:00
Mon 5.11.2018
10:15 - 12:00
Wed 7.11.2018
10:15 - 12:00
Mon 12.11.2018
10:15 - 12:00
Wed 14.11.2018
10:15 - 12:00
Mon 19.11.2018
10:15 - 12:00
Wed 21.11.2018
10:15 - 12:00
Mon 26.11.2018
10:15 - 12:00
Wed 28.11.2018
10:15 - 12:00
Mon 3.12.2018
10:15 - 12:00
Wed 5.12.2018
10:15 - 12:00
Mon 10.12.2018
10:15 - 12:00
Wed 12.12.2018
10:15 - 12:00

Other teaching

06.09. - 18.10.2018 Thu 12.15-14.00
01.11. - 29.11.2018 Thu 12.15-14.00
13.12. - 13.12.2018 Thu 12.15-14.00
Erik Elfving
Teaching language: English

Material

J. Väisälä: Topology II
Chapters 0-3
Chapters 4-7
Chapters 8-11
Chapters 12-15
Chapters 16-20
Solutions to the 1st exam

Tasks

Exercise 1 (13.9.2018)

Exercise 2 (20.9.2018)

Exercise 3 (27.9.2018)

Exercise 4 (4.10.2018)

Exercise 5 (11.10.2018)

Exercise 6 (18.10.2018)

Exercise 7 (1.11.2018)

Exercise 8 (8.11.2018)

Exercise 9 (15.11.2018)

Exercise 10 (22.11.2018)

Exercise 11 (29.11.2018)

Exercise 12 (5.12.2018)

Exercise 13 (13.12.2018)

Luentopäiväkirja

Material covered in the lectures:
- week 37: chapter 1 and items 2.1-2.9 from chapter 2.
- week 38: chapter 2 to the end, chapter 3, items 4.1-4.3 from chapter 4.
- week 39: chapter 4 to the end, chapter 5, items 6.1-6.6 from chapter 6.
- week 40: chapter 6 to the end, items 7.1-7.16 from chapter 7.
- week 41: chapter 7 to the end, chapter 8, items 9.1-9.2 from chapter 9.

Remark. The following items have not been discussed, and they are not contained in the material for the exam: 3.15, 3.16, 7.7, 7.8, 7.21, 7.22.

- week 42: chapter 9 to the end.
- week 44: chapter 10.
- week 45: chapter 11, items 12.1-12.11 of chapter 12.
- week 46: chapter 12 to the end (except items 12.24-12.28), items 13.1-13.8 of chapter 13.
- week 47: chapter 13 to the end (except items 13.32-13.40), chapter 14.
- week 48: chapter 15 (except items 15.25-15.30), items 16.1-16.8 of chapter 16.
- week 49: chapter 16 to the end, chapter 17 (except items 17.10-17.11), items 18.1-18.2 of chapter 18.
- week 50: chapter 19.

The material covered in the lectures on week 50 is not included in the material for the 2nd exam. Other exceptions are mentioned above.

Conduct of the course

The 1st midterm exam will take place on Monday, 22nd of October, 10-13, in Exactum D123.

The 2nd midterm exam will take place on Monday, 17th of December, 13-16, in Exactum D123.

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 I

Bachelor studies

The course gives a working knowledge in general topology, also called as point-set topology. Material is fundamental in a wide-range of further studies in mathematics, especially in analysis and geometry.

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

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

Fundamentals of general topology, including: topological spaces and bases, connectedness, compactness, separation and countability axioms, metrization and extension theorems.

Jussi Väisälä "Topologia II", James Munkres "Topology" (Part I)

Lectures and exercise classes

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

Exam, other methods will be described later.