Schedule for 2023. (Intended plan, may be changed.)
N.B. The course will be given on campus (as long as this isn't strictly forbidden).
|1||28/8 13-15||The real numbers||1.1-1.4|
|2||1/9 13-15||Infinite sets, Limits of sequences||1.4-1.6, 2.2-2.3 + Kardinalitet|
|3||4/9 15-17||Limits of sequences||2.4-2.6|
|4||11/9 15-17||Series, The Cantor set||2.7, 3.1|
|14/9||Hand-in round 1 *|
|5||18/9 13-15||The Cantor function, topology||3.2|
|22/9 13-15||Discussion on exercises round 1|
|28/9||Hand-in round 2 *|
|7||2/10 13-15||Limits and continuity||4.2-4.5|
|6/10 13-15||Discussion on exercises round 2|
|15/10||Hand-in round 3 **|
|8||16/10 15-17||Fixed point theorems||Exercise 4.3.9|
|3/11 13-15||Discussion on exercises round 3|
|10||6/11 13-15||Uniform convergence||6.2-6.4|
|7/11||Hand-in round 4 *|
|11||13/11 13-15||Power series||6.5|
|12||20/11 13-15||The Riemann integral||7.2-7.6|
|26/11||Hand-in round 5 ***|
|13||27/11 13-15||The Riemann integral||7.2-7.6+ En konstig kurva|
|4/12 13-15||Discussion on exercises round 4 (and 5)|
|10/12||Hand-in round 6 *|
|16/12 13-15||Discussion on exercises round 5 (and 6)|
** For round 3 it is ok to hand in your solutions in the course's mailbox no later than 15.00 the day after the deadline listed above, or at the very beginning of the lecture starting at 15.15.
** For round 5 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 lecture 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.
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Last updated: 2023-08-16