Messages - Page 2

• The Thursday at 14 idea seems not feasible, so for not it is most likely that the schedule will run as it is - and the draft schedule I posted earlier will bump one week downwards.
• Uploaded a note for at least the first part of Tuesday (hope to get a little further and discuss concave programs - will leave a message when new notes are produced).
• Uploaded Eric's notes from previous seminar.

• Most recent lecture note updated: the 2's on page 8 are fixed, and the last application is written out on two new pages 12-13.
  Also, since nobody needed both "landscape" and "portrait", I rationalized away the latter.
• Week 9: not unlikely, there will be seminar on Thursday 14-16, and lecture Friday 12-14. (Objections ASAP, please.)

If so, the rest of the semester could look like the following: 

• Wk 9: optimization 
• Wk 10: trig. functions, 2nd order diff.eq's
• Wk 11: differential eq. systems
• Wk 12: either double/multiple integrals, or difference equations & (discrete-time) dynamic programming
• Wk 13: Easter
• Wk 14: calculus of variations & (continuous-time) optimal control
• Wk 15: optimal control
• Wk 16: multiple integration
• Wk 17: there will then be only one lecture left (not two), and that ca...

The F matrix was missing. Corrected.

See schedule. Yesterday I wrote that the rest of 2-01 will be included, but I postpone that one week. If Eric has strong opinions, there may be further changes. 

Now they should be. (Well, past 13 o'clock without anyone noticing ...)

Schedule updated. When done with the quasiconcaves, I will start on max/min (the unconstrained case: recast the old 2nd derivatives tests with definiteness tools), and then review Lagrange's and Kuhn--Tucker's methods. The precise necessary conditions will have to wait until after the winter break; the ambition for Wednesday is to get as far as to be able to assign problems. 

A very incomplete (but covering Tuesday) draft lecture sheet for max/min uploaded also, but expect that to be expanded and/or revised.

The old ones are not changed, so therefore I have not renamed them - and the old "factsheet" that now has gotten a link from the front page (among the list of lecture notes, where it belongs) is the same as the one I linked to in a previous message. 

So we got as far as to define quasiconcavity and quasiconvexity. Have a look at these questions to get a bit hands-on.

Tomorrow:

• The rest of convex/concave functions (the 7ff notes)
• Quasiconvex/quasiconcave functions (the new note)

... with a hopefully better hint.

Nils.

1) So the time change is implemented.

• In particular, the next lecture is Tuesday at 10:15 - that one is at HH101. We could discuss whether ES1220 is better, but not for the upcoming one.
• The second lecture scheduled for Tuesday is out.
• That leaves us with one lecture missing from the schedule. There cannot be any lecture on Wed. Feb. 28, so we might try Thursday March 1; then possibly 14-16 is a better time? (I cannot commit to that timeslot yet.)

2) Seminar problems updated: added a couple since you have four more days. 

3) Lecture schedule for this week and next: updated to reflect reality. 

4) I should post notes for quasiconcave functions during the week-end. I will give "the graphical definition" for quasiconvexes, but soon change to quasiconcaves, as you probably use that more often.

• Big bugfixes in the uploaded 6 and 7ff (document split to reflect reality).
  Also, a technical mishap gave the "6" narrower margins than 50 percent. But I thought: is that an improvement, visually? Here is the 7ff in a version with the same issue. What do you prefer?
• There was one missing item from today's lecture, a page I accidentally flipped over. Will recap tomorrow.
• Looks like we will change time, then. Major revisions expected by Friday.

Nils

The proposals you got by e-mail clash for at least one person, so tomorrow at 1015 there is seminar - room 1220! More on this week at the end.

New suggestions as permanent replacement for Thu 10-12, are as follows:

• Thursday 14-16
• Friday 10-12
• Friday 12-14

If you already know these are objectionable, please let us know by reply to the previous mail. We will discuss in Wednesday's lecture anyway.
We may reshuflle between lectures and seminars, though. For example, Thu 14-16 works for Eric, but usually not for Yikai/Nils.

So, this week's lectures: 

• Content posted in the schedule
• Draft note posted - if you managed to download the "LS" version before 15 o'clock, then reload, there is one more thing (inverse functions, not only implicit) on page 7.
  (There is only one portrait version.)

Nils

• You should by now have received an e-mail on possible change of time. I proposed to move lecture to the seminar slot, and the seminar to the "new" slot. An earlier time on Wednesday appeared to also be a potential candidate, but I did not want to mess it up by suggesting more than two.
• Two updates to the eigenvalues/eigenvectors note (#3):
  • Two useful facts should have been lectured. I will cover that next week, but I put it into the note: new second-to-last page.
  • Last page I wrote the matrix wrong; the numbers I wrote, was from A-4I and not A. A correction has been made, and furthermore, the last page is updated to give A as an example of the previous item.
• Seminar problems posted.
• Feedback suggests that you want those lecture notes, so I'll keep on posting them. Working on next week.

- time: will ask tomorrow
- anything else: please forward to contact students by end of the day.

Problems for next week will be posted tomorrow, and will most likely include
1-05, 1-06 and 1-07, and besides 1-03(b) which I have already assigned but did not review. Furthermore: 
Let A be symmetric. Show that the value of the problems min/max x'Ax subject to x'x = 1, is, respectively, the smallest and largest eigenvalue.
Let A be neg.def., p an integer and A^p a power of A. Show that if p is odd and positive, then A^p is neg.def; decide if the same thing holds if p is even and positive, or if p is odd and negative. (Here, A^-p = (A^-...

Thursday: We can take the 1415 slot.

A supplement note for Thursday is uploaded as portrait and landscape. Later I will likely merge this into the "Lecture 4" note - or maybe split.

Tomorrow: I am missing the last part of eigenvalues/-vectors, and will complete that before I start on the "Lecture 4".

• Due to illness, it is not clear what will happen with these lectures. One possibility is that Eric covers differential eq's.
• A draft note covering the originally planned Wednesday lecture - and surely part of Thursday's - is uploaded.

If so, please let me know. For the first seminar, the "conversion table" is easy: add 1 to the section number.
New 1.2.4 = old 1.3.4
New 1.3.1 = old 1.4.1
New 1.4.1 = old 1.5.1.

Ida Kristine Haavi, idakhaa [ætt] student.sv.uio.no
Sondre Elstad, sondre.elstad [ætt] econ.uio.no

Exercise(s) for you: 

• Complete the last example to a level where you can either rest assured that you don't need any details in class, identify where you fell off ;-) 
• Do the problems for today if you did not already do so.
• Have a look at the rest of the note I posted yesterday, and the slides I linked (only the pages quoted).
• If you still want to do more: Consider a generic 2x2 matrix A with elements a, b, c, d (this space does not support more typography, sorry); calculate p(t) = det(A-tI) and find the zeroes of this polynomial.

I will update the schedule to reflect reality. Problems for Tuesday will be posted tomorrow at latest.

Here: http://www.uio.no/studier/emner/sv/oekonomi/ECON4140/v18/m3_2018lect02draft.pdf

I suppose this is more than enough. 

For tomorrow, do:

• Problem 1-03 from the compendium
• (Easy) A square matrix M = M_t has t as top-left element m₁₁, while no other element depends on t. Let f(t) = det(M_t). What kind of function is f?
• (Somewhat harder, skip if you don't catch it) A square matrix A does not depend on t, but A - t I does (subtract t from each diagonal element of A). Let p(t) = det(A - t I). What kind of function is p?

Lecture notes.

• I updated the one for today. The next will be...

Due to events at Faculty level, some lecture slots had to go. Right now there are too many the first two weeks, but I (Nils) would like to discuss with you which ones to remove. It may be a good idea to use the first week of May, but it depends on, for example, your other exams.

The first weeks are shaping up as follows:

1. First week: lectures 16th/17th/18th (in order to get far enough to assign problems)
2. Second week: seminar the 23rd, lecture 24th and 25th - but it is likely not a good idea to have two lectures on that Thursday. Which one to remove? The last? 
3. Third week: normal as per the schedule.
4. Fourth week: right now it says seminar the 6th and lecture later the same day - is that OK?
5. Fifth week: normal as per the schedule
6. "Teaching-free week": in order to fit everything, there was inserted one during the winter break. If you are fine with extending tea...

See message November 27th; starting this semester, the Department has restricted the use of calculators to one particular simple calculator and/or one particular scientific calculator - provided the course allows for calculator at all.

In Mathematics 2 and 3, you will be allowed to bring either. 

Calculators can be used on some of our ECON-exams. Starting spring 2018 only two different calculator types are authorized for use at the Department of Economics:

• Aurora HC106 - a very simple calculator with most basic functions
• Casio FX-85EX - which is a scientific calculator with 274 functions

It is important that you know whether it is allowed to use a calculator on your exam and which type that is allowed. For more information about resources allowed on your exam, please see “Examination support material” on each course page.

You can buy the calculators at Akademika bookstore at Blindern, or online.