MAI - Matematiska institutionen

TATA34 Lectures

Schedule for 2025. (Intended plan, may be changed.)

Lecture	Date	Subject	Course book	Metric space notes
1	1/9 13-15	The real numbers	1.1-1.4
2	5/9 13-15	Infinite sets, Limits of sequences	1.4-1.6, 2.2-2.3 + Kardinalitet
3	8/9 13-15	Limits of sequences	2.4-2.6
4	15/9 13-15	Series, The Cantor set	2.7-2.8, 3.1
	16/9	Hand-in round 1 *
5	22/9 15-17	The Cantor function, topology	3.2	2.1-2.6
	26/9 13-15	Discussion on exercises round 1
6	29/9 13-15	Topology	3.3-3.4	4, 2.7
	30/9	Hand-in round 2 *
7	6/10 13-15	Limits and continuity, Connected sets	3.4, 4.2-4.4	3, 5, 6
	10/10 13-15	Discussion on exercises round 2
8	13/10 13-15	Fixed point theorems	4.5, Exercise 4.3.9
	15/10	Hand-in round 3 *
9	3/11 13-15	Derivatives	5.2-5.3
10	10/11 13-15	Derivatives, Uniform convergence	6.2-6.4, 5.4
	11/11	Hand-in round 4 *
11	17/11 13-15	Power series	6.5
	21/11 15-17	Discussion on exercises round 3 (and 4)
12	24/11 13-15	The Riemann integral	7.2-7.6
	24/11	Hand-in round 5 *
13	1/12 13-15	The Riemann integral, Curves	7.2-7.6+ En konstig kurva	6.1
	7/12	Hand-in round 6 **
	8/12 13-15	Discussion on exercises round 4 (and 5)
	15/12 13-15	Discussion on exercises round 5 (and 6)

^* It is ok to hand in your solutions in the course's mailbox no later than 10.15 the day after the deadline listed above.
^** For round 6 it is ok to hand in your solutions in the course's mailbox no later than 13.00 the day after the deadline listed above, or at the very beginning of the discussion starting at 13.15.

The book (Abbott) is mainly considering R while I, during the lectures, will discuss many results more generally on metric spaces, in particular Rⁿ, (when it doesn't cost too much). See the notes An introduction to metric spaces, by Andersson-Björn-Wiman for the metric space theory included in this course.

Page responsible: anders.bjorn@liu.se
Last updated: 2025-08-01