MMA100 Topology Spring 24

Welcome to the course of Topology!

This page contains the program of the course. Below are the weekly plan for lectures and exercise sessions (to be continuously updated).

Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

All lectures and exercise sessions will be held on campus.

Schedule: lectures - Tuesday and Wednesday at 15.15, MVF31

exercise sessions - Friday at 13.15, MVF26.

Weekly plan for lectures

Week 1	Lecture Tuesday	Brief overview. Sections 12 and 13.
Week 1	Lecture Wednesday	Sections 15, 16.
Week 2	Lecture 1	Sections 17, 18.
Week 2	Lecture 2	Sections 19, 20.
Week 3	Lecture 1	Section 23 and a part of 24
Week 3	Lecture 2	Section 24 (the rest of), a part of section 25 (if time permits), and a part of 26.
Week 4	Lecture 1	The rest of section 26; section 27, 28.
Week 4	Lecture 2	Sections 43, 44.
Week 5	Lecture 1	(Parts of) sections 30, 31, 32. Section 33.
Week 5	Lecture 2	Sections 34, 35 and a part of section 20 needed for Urysohn metrization theorem.
Week 6	Lecture 1	Sections 51, 52
Week 6	Lecture 2	a proof that sphere is simply connected (different from the one in the book), a part of section 54, a part of section 55
Week 7	Lecture 1	section 55, a part of section 58 (about homotopy equivalence), section 22
Week 7	Lecture 2	examples of surfaces (from section 60); classification of surfaces ( parts of sections 74, 76, 77)
Week 8	Lecture	Discussion of solutions for exam for 2021. exam2021 (1).pdf In the last problem it should be the square root of x^2 +y^2.

Recommended exercises

Week 1	Ch. 2 Section 13: 1, 3, 4, 7 (excluding R_K), 8. Section 16: 2, 3, 4, 5.
Week 2	ExercisesWeek2-3.pdf SolutionsWeek2-1.pdf ExercisesWeek4.pdf ExercisesWeek5-2 (1).pdf SolutionsToExercisesLeftFromExerciseSession.pdf ExercisesRomWeek5NotDiscussedAtClass.pdf ExercisesWeek7-1.pdf To get used to work with images/preimages you can do Ch.1 Section 2: 2, 3, 4. These exercises we will not discuss at exercises session unless anybody would ask about it.
Week 3	ExercisesWeek3-2.pdf
Week 4	ExercisesWeek4-2.pdf The exercises 1, 2 (except 26.5), 3, 4 can be done already now. The other ones - after the lecture on Tuesday (Febr. 6). SolutionsToExercisesLeftFromExerciseSession.pdf
Week 5	ExercisesWeek5-2 (1).pdf The exercises 1, 2, 5, 7, 8, 9 can be done already now. The other ones - after the lecture on Tuesday. ExercisesRomWeek5NotDiscussedAtClass.pdf
Week 6	ExercisesWeek6-1.pdf Exercises 1, 2, 8 can be done already now. The rest - after the lectures next week.
Week 7	ExercisesWeek7-1-1.pdf Home problems can be done after the lectures on Tuesday and Wednesday.