Kaisa_2012_3_photo by Veikko Somerpuro

Ilmoittaudu

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

PäivämääräAikaOpetuspaikka
Ti 5.9.2017
14:15 - 16:00
Ma 11.9.2017
14:15 - 16:00
Ti 12.9.2017
14:15 - 16:00
Ma 18.9.2017
14:15 - 16:00
Ti 19.9.2017
14:15 - 16:00
Ma 25.9.2017
14:15 - 16:00
Ti 26.9.2017
14:15 - 16:00
Ma 2.10.2017
14:15 - 16:00
Ti 3.10.2017
14:15 - 16:00
Ma 9.10.2017
14:15 - 16:00
Ti 10.10.2017
14:15 - 16:00
Ma 16.10.2017
14:15 - 16:00
Ti 17.10.2017
14:15 - 16:00
Ma 30.10.2017
14:15 - 16:00
Ti 31.10.2017
14:15 - 16:00
Ma 6.11.2017
14:15 - 16:00
Ti 7.11.2017
14:15 - 16:00
Ma 13.11.2017
14:15 - 16:00
Ti 14.11.2017
14:15 - 16:00
Ma 20.11.2017
14:15 - 16:00
Ti 21.11.2017
14:15 - 16:00
Ma 27.11.2017
14:15 - 16:00
Ti 28.11.2017
14:15 - 16:00
Ma 4.12.2017
14:15 - 16:00
Ti 5.12.2017
14:15 - 16:00
Ma 11.12.2017
14:15 - 16:00
Ti 12.12.2017
14:15 - 16:00

Muu opetus

07.09. - 19.10.2017 To 12.15-14.00
02.11. - 30.11.2017 To 12.15-14.00
14.12.2017 To 12.15-14.00
Erik Elfving
Opetuskieli: englanti

Materiaalit

Väisälä: Topology II; Chapters 0-3, Chapters 4-7, Chapters 8-11, Chapters 12-15, Chapters 16-20

J. M. Lee: Introduction to Topological Manifolds, p. 1-15

Tehtävät

Exercise 1 (14.9.2017)

Exercise 2 (21.9.2017)

Exercise 3 (28.9.2017)

Exercise 4 (5.10.2017)

Exercise 5 (12.10.2017)

Exercise 6 (17.10.2017)

Exercise 7 (2.11.2017)

Exercise 8 (9.11.2017)

Exercise 9 (16.11.2017)

Exercise 10 (23.11.2017)

Exercise 11 (30.11.2017)

Exercise 12 (7.12.2017)

Exercise 13 (14.12.2017)

Kurssin suorittaminen

1. kurssikoe on tiistaina 24.10. klo 16-19 salissa D123. Materiaali on Väisälän kirjan luvut 1-8 sekä harjoitukset viikoilta 1-6.

The 1st midterm exam is held on Tuesday, 24th of October, at 16-19 in lecture room D123. The material consists of sections 1-8 in Väisälä's book, and exercises 1-6.

2. kurssikoe on perjantaina 15.12. klo 14-17 salissa D123. Materiaali on Väisälän kirjan luvut 9-17 sekä harjoitukset viikoilta 7-13.

The 2nd midterm exam is held on Friday 15th of December at 14-17 in lecture room D123. The material consists of sections 9-17 in Väisälä's book, and exercises 7-13.

Kuvaus

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.