This page is for older messages that are no longer important to keep on the main page.
2004-05-27 08:10: There will be no strike. Exams can thus proceed.
2004-05-27 07:40: The strike situation: Negotiations are still not over. Until they are, there is no strike, and the exam may proceed. On the news just now they said another half hour might produce an answer.
2004-05-25: Final exam. By now, everybody should have gotten instructions for the exam by email. If you have not, contact me as soon as possible, if not before.
As you will have learned from the email, it is possible that the exam on Thursday will have to be postponed due to a strike. Whether or not this happens, will probably not be known until Thursday morning. Worse yet, I may be cut off from communicating via the web or email until the strike is over. If this happens, watch this space as soon as you hear the strike has ended.
2004-05-19: Final exam.
There have been some difficulties of a bureaucratic nature which are now happily resolved. The problem is that, as it turns out, one can no longer arrange for an oral exam when the student handbook says it's a written one, without asking for permission through the proper channels. Well, I asked, much too late in principle, and got my permission today. To me, this has been a traumatic confrontation with new and inflexible rules. I will have to pay much more attention to such things in the future. Enough said.
So, as planned, there will be an oral exam on Wednesday and Thursday next week (26 and 27 May). Since there are 12 students intending to take the exam, we need both days to manage this.
All those who have not already told me are asked to contact me, preferable by email to hanche@math.ntnu.no, and tell me which day you prefer. If you prefer Thursday, still let me know if Wednesday is possible for you. And, of course, if you have changed your mind and will not take the exam, I am grateful if you let me know.
Each student will be assigned a topic for a ten to fifteen minute mini-presentation to be presented at the start of the exam. Those examined on Wednesday will be told their topic on Monday and those examined on Thursday will be told on Tuesday.
Finally, I shall be present in my office on Friday from 09:00 to 12:00 in case anybody wants to ask questions.
2004-05-07: End of lectures, and final exam. In my previous message here, I said the last lecture might be Thursday 6 May. Instead, I ended lectures on Tuesday 4 May, according to the official schedule. All those present knew of course, but I had neglected to update the web page. I hope nobody showed up for the non-lecture on Thursday.
There will be an oral examination as previouly agreed. I have obtained all the necessary permissions from the students, and I have also found an outside examiner to help with evaluation as required by the rules. Since there are so many of you, we will have to spread the exam over two days. The official exam date is Thursday, 27 May. I hope we can do a number of examinations the day before. The day after is out, as I have to go away for a meeting. Some students asked to have the exam later, in June. This turns out to be impossible, sorry.
The plan is to spend 30 minutes with each student. I will give a topic to each student, perhaps a few days ahead, for the student to give a brief overview of this topic. (At most 15 minutes.) The remaining time will be spent asking various questions. The details still need to be worked out.
Please remember to check back here for updated information in the days ahead.
2004-04-22: The end of lectures. Officially, the last day of lectures is Tuesday 4 May. But since we lose a lecture this Tuesday, I would like to make Thursday 6 May the last lecture instead. It depends a bit how well the next two lectures go.
2004-04-22: Do read about projections: Kreyszig sections 9.5 and 9.6. I will only mention these sections rather briefly when I lecture next Thursday (29 April). My intention is to get into 9.7 as soon as possible.
2004-04-21: No lecture Tuesday 27 April. I will be away Friday – Wednesday, hence no lecture Tuesday.
2004-03-25: No lectures next week. You are welcome to come to my office to ask questions, though. I will also put out some more review questions – soon. A reminder: There is no lecture on Tuesday after Easter. That is, no lecture on 13 April. This means the next regular lecture is Thursday, 15 April. My advice to you is to make sure before then that you have a firm grasp of the material lectured until now, and to have a sneak look at what comes in chapter 9. There will be quite a bit of material to cover in the final lectures.
2004-03-25: Status and plans. This week, I have lectured as much of chapter 7 as I think we will need. (See also my note, above.) After Easter, we shall start on Chapter 9.
2004-03-12: Now is a good time read Kreyszig sections 4.8 and 4.9. Sorry, I forgot to mention this in today's lecture.
2004-02-24: The second midterm week. Next week, I plan to cover little or no new material. Instead, we'll aim at consolidating what we already know. I will try to come up with a slightly extended exercise set.
2004-02-22: The midterm weeks. Lectures will proceed as usual during the midterm weeks. We're doing general topology, but will soon move on to topological vector spaces (with yet another wrote to be written). Our goal is to explain weak convergence and the Banach–Alaoglu theorem in this setting. We shall also present a proof that uniformly convex Banach spaces are reflexive, which will complete the characterisation of the dual spaces of L^{p} spaces.
2004-02-13: Progress and plans. We are done with the notes on sequence spaces and L^{p} spaces plus Kreyszig chapter four up to and including 4.7. We now skip to 4.12 and 4.13. After that, we spend some time on topology (I plan to make some notes), and then we shall work with weak topology and look at the remainder of chapter four.
2004-01-22: Exercises. There is no scheduled time for exercises, so we must steal a little time from the lectures. I certainly will not go through all the suggested exercises, but we may discuss them as the need arises.
From Kreyszig:
4.2: 3, 4, 5, 10. (The result of combining 3 and 10 is far from obvious!)
4.3: 3, 11.
4.5: 5, 8, 9, 10.
2004-01-22: Change of language. I finally got around to translating this to English. I will not translate the older messages, though.
2004-01-04: Pensum er langt fra klart, men de mest sentrale delene vil nok være kapitlene 4 og 9 i Kreyszig. Jeg må nok gjennomgå biter av kapittel 1–3 som ikke er dekket i Lineær analyse. Jeg vil satse på å gjøre noe av det systematisk, og kanskje komme tilbake og ta andre deler ettersom behovet åpenbarer seg. Kapitlene 7 og 8 vil få senere samme behandling.
I tillegg må vi få inn noe punktmengdetopologi og behandle svak topologi og svak konvergens, med Banach–Aloglus teorem og anvendelser. Om vi kopierer fra annen litteratur eller jeg skriver noe selv vet jeg ikke ennå.
2003-12-23: Første forelesning er tirsdag 6. januar. Tema blir transfinit induksjon, som strengt tatt ikke er pensum men er veldig nyttig. Alle bør se dette minst en gang i løpet av livet! Vi får bruk for det i beviset for Hahn–Banach-teoremet. Det blir ingen forelesning torsdag 8. januar. (Vi tar igjen den timen i forbindelse med midtsemesterukene, for eksempel.) Vi starter på pensum for alvor tirsdag 13. januar.
2003-11-12: Ja, det er jeg som skal forelese dette kurset til våren. Det er ikke mye informasjon på denne websiden ennå, som du ser, men det kommer etterhvert som jeg får bestemt meg. Det er ikke så lett å finne en egnet bok: De fleste er enten for avanserte, eller de inneholder ikke alt vi ønsker. I Gerald B. Folland: Real analysis finner man noe av stoffet, men i tildels svært kort form (først og fremst i kapittel 5). En sterk kandidat er Michael Reed & Barry Simon: Methods of modern mathematical physics, bind I: Functional analysis. Jeg vil nok også hente inspirasjon fra John B. Conway: A course in functional analysis, Eberhard Zeidler: Applied functional analysis, Robert J. Zimmer: Essential results of functional analysis og Haïm Brezis: Analyse fonctionelle.