Messages - Page 2

Problems for next week are up.

If you want to be a bit ahead of schedule, then consider the weekly problems from last year's ECON4145 web page . However, I have to make adaptations due to the progress -- even due to the allocation of hours in the week.

I have updated today's PDF (merely the C1 to continuous). There won't be any for tomorrow. ¨C NCF

Starting this week, I (NCF) will have to move my consultation hours til Thursday.

• Contact students: please e-mail me, I may have lost your mail addresses.

• PDF for next Tuesday available.

• PDF for last Wednesday updated with that single word (if you have a printout: it is maybe easier to augment that 'multi' into 'multivariate' by hand).

• It was brought to my attention that the lecture schedule isn't complete as book references goes. I have updated somewhat; I may or may not update it further (what now says ¡°rest of chapter 3¡±); the reason why not, is that detailed information may be misleading, as the progress of the constrained optimization part is to be adapted-as-we-go between Maths 2 and Maths 3. I suggest that you use the PDFs (which are updated more often) as an indication on how far we intend to go in each lecture.

I realized that the first of the 'text' problems would be quite hard. I simplified part (e); the general case in n variables would be possible to guess then.

PDF for tomorrow Wednesday available. It is 8 pages, but

• pp1--2 are for information only;
• pp3--4 give the conceptual considerations for tomorrow's topic. Read so you understand the questions that will be asked.
• pp5--6 give the tool to answer these questions -- it will be presented thoroughly in class
• pp7--8 give the concept of linear independence. For tomorrow you only need to know that two vectors are linearly independent if they are non-proportional.

Notice also that the eigenvalue approach to definiteness will not be covered until later (on schedule for October 30th).

Finally, I have corrected the missing 1/2 in today's slides.

¨C NCF

So, I was made aware that I hadn't even given a reference to the reading list for this week. And I'm lagging. To read for tomorrow:

• The PDF I just put out (the first two pages are the physically handed-outs for last time; the Aug 29 is revised too).
• We are not done with quadratic forms, so have a look at that;
• We will review the local 2nd order conditions.
• And maybe the envelope theorem and the extreme value theorem.

For Wednesday:

• Leftovers from Tuesday
• Quadratic forms under linear constraints.

¨C NCF

I realize I didn't make available even the revised .pdf for Wednesday (and certainly not anything for tomorrow). A brief version will be available when I am done with today's teaching. ¨C NCF

Now available: problem set for seminar #01. (The references are to the collection of exam-type problems, available under the exam-type problems on the course front page.)

One of you noticed that the solution to the 2006 exam is missing. I'll see if I can find it somewhere (... I didn't work here then ;-) ).

• Now available: PDFs for Wednesday. Since it is already getting late, I have not included anything on quadratic forms, which was supposed to be tomorrow's topic.

• Consultation hours added to the Administration and teachers document.

Now available: PDFs for Tuesday. I won't print them out for you -- you can have a look at them in advance and decide what to print out or what notes to take from them. This time it is probably pages 4 and 6 that are most interesting (page 4 has new terminology, page 6 has a list of rules).

Confession time again: One of you objected to the linear approximation. Of course you were right, please object heavier next time. Correct formula here.

I was writing a handout for tomorrow, it isn't much -- two pages, and I won't even hand out that sheet, as you probably don't need it in the lecture.

You don't have much time to prepare until tomorrow anyway, so maybe those two pages are just what you would want to have a look at to get an idea where we are heading. For more, read the book.

The rest of that proof: We had this expression. from which we get a ¦Ë^2 coefficient like this, which is positive. Hence we have convexity wrt. ¦Ë, and the maximal value is either at ¦Ë=0 (where we get ||y||^2=1) or at ¦Ë=1 (where we get ||x||^2=1).

I've put up some resources. The 'handout' will be handed out, so you don't need to print it. It does not cover the lecture, it covers the first few minutes to save you from writing.

• Tomorrow's lecture will fix some terminology, and then start on convex sets. You might want to browse the convexity topic on an informal level before the lecture. I will introduce it in an axiomatic way, and I am very much aware that some of you might find it a bit scary; please bear in mind that the more difficult parts are not very exam relevant. (Then why teach those parts? Because I think you might need to have seen this axiomatic manipulation for the purposes of some theoretic microeconomics, including the 2nd theorem of welfare economics.)

¨C NCF