Kaisa_2012_3_photo by Veikko Somerpuro

Ilmoittaudu
14.8.2017 klo 09:00 - 13.12.2017 klo 23:59

Aikataulu

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

PäivämääräAikaOpetuspaikka
Ma 4.9.2017
10:15 - 12:00
Ti 5.9.2017
10:15 - 12:00
Ma 11.9.2017
10:15 - 12:00
Ti 12.9.2017
10:15 - 12:00
Ma 18.9.2017
10:15 - 12:00
Ti 19.9.2017
10:15 - 12:00
Ma 25.9.2017
10:15 - 12:00
Ti 26.9.2017
10:15 - 12:00
Ma 2.10.2017
10:15 - 12:00
Ti 3.10.2017
10:15 - 12:00
Ma 9.10.2017
10:15 - 12:00
Ti 10.10.2017
10:15 - 12:00
Ma 30.10.2017
10:15 - 12:00
Ti 31.10.2017
10:15 - 12:00
Ma 6.11.2017
10:15 - 12:00
Ti 7.11.2017
10:15 - 12:00
Ma 13.11.2017
10:15 - 12:00
Ti 14.11.2017
10:15 - 12:00
Ma 20.11.2017
10:15 - 12:00
Ti 21.11.2017
10:15 - 12:00
Ma 27.11.2017
10:15 - 12:00
Ti 28.11.2017
10:15 - 12:00
Ma 4.12.2017
10:15 - 12:00
Ti 5.12.2017
10:15 - 12:00
Ma 11.12.2017
10:15 - 12:00
Ti 12.12.2017
10:15 - 12:00

Muu opetus

06.09. - 18.10.2017 Ke 10.15-12.00
01.11. - 29.11.2017 Ke 10.15-12.00
13.12.2017 Ke 10.15-12.00
Marja Kankaanrinta
Opetuskieli: englanti

Materiaalit

We will cover Chapters 0 - 6 of Joseph J. Rotman's book "An Introduction to Algebraic Topology". In the beginning we will follow the book rather carefully, later on less carefully. Another book that could be of some help, in particular with homology, is the book "Algebraic Topology" by Allen Hatcher. Here is a link to Hatcher's book: https://www.math.cornell.edu/~hatcher/AT/AT.pdf

I taught this class two years ago (fall semester 2015). Here is a link to my lecture notes from that year:
https://wiki.helsinki.fi/display/mathstatKurssit/Introduction+to+algebra...

Here is a proof of Proposition 10.15 (covered in class on Oct 9):

Tehtävät

Homework 1

Solutions 1

Homework 2

Solutions 2

Homework 3

Solutions 3

Homework 4

Solutions 4

Exercise 4.5

Homework 5

Solutions 5

Homework 6

Solutions 6

Homework 7

Solutions 7

Homework 8

Solutions 8

Homework 9

Solutions 9

Homework 10

Solutions 10

Homework 11

Solutions 11

Solutions 11.2

Homework 12

Solutions 12

Kurssin suorittaminen

There will be a final exam worth 30 points on December 13. The exam will be together with the general examination, 4PM - 8PM. In addition you can get up to 4 points for doing homework, a student who does 90 per cent of the homework gets the full 4 points. The homework points will be added to the test score - if you get 22 points on the exam and 3 points on the homework, then your total score will be 25 points out of 30.

Kuvaus

Optional course.

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

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Topology I & II, Algebra I

Basic homotopy theory and homology theory

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

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

Basic notions related to homotopy: fundamental group, examples, applications, covering space theory; basic notions related to homology: chain complexes, singular homology groups, Eilenberg-Steenrod axioms, examples, applications

Joseph J. Rotman: An Introduction to Algebraic Topology; Allen Hatcher: Algebraic Topology (https://www.math.cornell.edu/~hatcher/AT/AT.pdf)

Lectures and exercise classes

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

Exam, other methods will be described later