17. Tuesday, July 7, 2009: By the way, the controversial article on Perelman's Fields Medal I mentioned some days ago can be downloaded HERE. And at this link you can see Professor Yau's response to the article.
16. Tuesday, July 7, 2009: Some good references for the last day of lecture are the following: A paper on solving degenerate systems faster, and a paper on computing the complex dimension of an algebraic set.
15. Tuesday, June 30, 2009: An excellent reference for the multivariate resultant construction I introduced today is a paper by Canny and Emiris. You may also want to google Ioannis Z. Emiris' webpage and see his thesis, which is also an excellent reference for multivariate resultants. Related note: he has some very nice papers on computational biology as well.
14. Wednesday, June 24, 2009: Most of the slides I showed today can be downloaded HERE.
13. For those of you curious about complexity theory, there are some very nice notes on the basics, from Scott Aaronson's Spring 2008 Great Ideas in Theoretical Computer Science course at MIT.
12. A rather nice paper by a Fields Medalist (Michael H. Freedman), relating complexity theory to knot theory, is about to appear in the Annals of Mathematics. HERE is a preview. I mention this because we saw in lecture that P=?NP, GRH, and complex feasibility are connected. Now, we have yet another cool connection between complexity theory and deep math.
11. Tuesday, June 23, 2009: HW#3 is not quite ready yet but, in the mean time, here is one problem: Please write a clear proof of Bezout's Theorem, mimicking the proof of the Fundamental Theorem of Algebra presented in class. Should you run in to any difficulties, do please e-mail me, and I'll post hints here.
10. Thursday, June 18, 2009: Sorry for the short notice but afternoon lecture today has been rescheduled for FRIDAY, June 19, 2009, 13:00-14:00. (Please note the non-standard time!) The room should be the same as usual: Blocker 111. (Unless I say otherwise very soon...)
9. Wednesday, June 17, 2009: Due to popular demand, the due date for HW#2 has been postponed to monday (June 22, 2009). I hope the homework doesn't interfere with your weekend too much!
8. Tuesday, June 16, 2009: OK... HW#2 has been re-edited slightly with some hints/simplications for Problem #6. Please re-download HW#2 from Item #5 below. (Note: Some browsers have brain-dead caches and may just give you the old file. So you may wish to close and re-open your browser before you reload.)
7. Tuesday, June 16, 2009: The slides for yesterday's lecture (on June 16, 2009) can be downloaded HERE. Also, HW#2 will be re-edited to fix the Smith normal form confusion, so check back a bit later this evening...
6. Tuesday, June 16, 2009: There is an omission in Problem #6 of HW#2: We haven't covered Smith normal form yet! So I'll be saying a few things about binomial systems and Smith normal form today...
5. Friday, June 12, 2009: Homework #2 can be downloaded HERE.
4. Friday, June 12, 2009: The slides for yesterday's lecture (on June 11, 2009) can be downloaded HERE.
3. Tuesday, June 9, 2009: The slides for today's lecture can be downloaded HERE. Great to finally see you in class!
2. Wednesday, June 3, 2009: You should be aware of MathSciNet, which is a GREAT service provided by the American Mathematical Society (AMS) for looking up research papers. Google and wikipedia are fine for preliminary searching but MathSciNet (http://www.ams.org/mathscinet/search) is the tool of choice. Its database contains reviews of tens of thousands of mathematical papers, most of which are extremely useful. Our university has a subscription, so you can always use MathSciNet from any math department machine.
1. Monday, June 1, 2009: Homework #1 can be downloaded HERE. Here are the links to some of the suggested readings: