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