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Jul. 12th, 2006

I'm thinking of writing to Greg Sorkin, who graduated from Stuy the same year I did, and was in some of my math classes. (nsingman, you may remember him.) He has done a lot of research in CS theory. I would like to know his views on learning abstract math, problem solving, etc. Since he learned from some of the same HS teachers I learned from, I wonder how he feels they influenced him. I also wonder if he had any additional influences (particularly ones I didn't).

FYI, here's some thoughts about problem solving from another Stuy graduate who was also a grad student at UCLA while I was there. We were both in cs281a, the computability and complexity theory class taught by Sheila Greibach (of Greibach normal form).

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( 5 comments — Leave a comment )
nsingman
Jul. 13th, 2006 02:46 pm (UTC)
I do remember Greg, though I didn't know him as well as I knew his co-captain Ashfaq. As far as problem solving went, I found my fellow students (in particular, 1975 graduate Paul Zeitz) to be a greater influence in terms of style and approach.

I don't know Noémi, but I think she'd be very interesting to know. And I envy you taking computability from Greibach. My class was pretty good, and the instructor was okay, but I was the only one in class (which included at least one math major) who really understood what was going on.
gregbo
Jul. 13th, 2006 11:55 pm (UTC)
Ashfaq was in my homeroom and lots of my classes, including math classes. I wrote something about him some time ago in my memories; here's another short story (which has somewhat of a bearing on the topic at hand):

Sometime during my freshman year at the 'tute, perhaps late first semester, he showed up in the lobby of my dorm one day. So we got to talking about our first year college experiences, and I told him how I was taking calculus, physics, etc. (the usual freshman load), and he replied that he was in calculus also – calculus of manifolds.

I wondered what calculus of manifolds was, because I'd never heard of it before. So I looked up information about it, then I wondered how he could have made the jump from high school calculus to calculus of manifolds over the summer. I knew he was a very good student, especially in math, but still ...

Perhaps I should ask you what I was thinking of asking Greg, seeing as you know what CS theory is.
nsingman
Jul. 14th, 2006 03:08 am (UTC)
Stuyvesant had very good AP Calculus classes, as I recall. A 5/5 on Calc BC would let you place out of the first two semesters pretty much anywhere. And folks on the math team went far past that. :-)

Feel free to ask, though I'm a bit (as in, twelve or thirteen years) rusty. :-)
gregbo
Jul. 14th, 2006 07:11 am (UTC)

  • When was the first you heard of CS theory?
  • What do you think influenced your ability to do CS theory most, your experiences in Stuy classes, the math team, or something else (perhaps classes you took elsewhere, puzzles, math camp, science projects)?
  • When you solve CS theory problems, do the solutions come to you as a logical sequence of statements that are axiomatic in nature (like a proof in Euclidean geometry), or is your approach more insight/intuition oriented?


My answers:


  • I'm pretty sure I never heard of it at Stuy or earlier. If it was discussed in the computer classes, I don't remember. I was somewhat aware of finite automata after taking an AI class as a sophomore, and of how parsers worked after a summer job between sophomore and junior year at a compiler company, but I don't think I really gave the issue serious thought until the summer before senior year, when I read Gödel, Escher, Bach.
  • I didn't understand CS theory (Mike Sipser's class) that well when I took it during senior year. I understood it somewhat better after reading a book called Algorithmics by David Harel a few months before starting grad school. I also had some friends at work I could discuss it with.
  • At Stuy, in the unified math curriculum, I was able to use insight and intuition to do algebra and trig. I was able to rely on the axioms to do geometry proofs (Euclidean and affine), so even if I couldn't remember whether an intermediate result was proved, I could usually prove it myself and then use it for what I needed to do. However, the algebraic insight/intuition didn't really carry over in CS theory, and as far as axioms go, Sipser's class wasn't really taught that way. (Greibach's was somewhat more like that.) The way I would sum things up, as far as CS theory goes, is that I can usually follow the logic of a proof, but I can't always come up with the crucial bit of insight that turns a difficult problem into a not-so-difficult one.


BTW, some other observations about how Stuy math was more accessible to me:

  • Math classes met every day (sometimes twice a day).
  • For some things, such as what came from the regents syllabus, there were good review books for practice.
  • Where there was no review material available, homework was assigned and graded regularly, so there was plenty of opportunity for feedback.
  • Tests were given pretty frequently, so it wasn't as if an individual test carried a lot of weight. Also, the lowest score was usually dropped.


FWIW, I took BC calculus along with several other people who were on the math team. I didn't take the AP exam, even though my teacher (Rittermann) tried to persuade me to. I was sort of burned out, and didn't want to add extra load to a busy schedule. Also, I looked over some review problems, and saw some things that either weren't covered or I didn't remember being covered, so I figured I wasn't too prepared for the exam. (At the time I didn't know that it was possible to get a 5 without getting a perfect score.)
nsingman
Jul. 14th, 2006 03:59 pm (UTC)
My undergraduate majors were chemistry and mathematics (I was at Brooklyn College for their BA-MD program, and chemistry was as far away from biology as my parents would let me get). :-) Because of that, I did very little computer science as an undergraduate, and first heard of CS theory as a graduate student during my first attempt ('82-'83). I took a long break because of work and family responsibilities, and then returned ('92-'94) to finish. It was during that second stint that I took a class in computability, and I loved it.

I saw the computability class as essentially a math class, and more abstract than applied (quite reminiscent of abstract algebra, in fact). General mathematical maturity, obtained through high school and undergraduate mathematics, made it reasonably easy going.

As for solving those problems, it's probably a combination of (mostly) following a logical sequence (including the occasional dead end, which makes it seem a bit brute force-like), and then seeing something in the pattern of the solution that suggests the right path. That's my approach to abstract mathematics generally. Of course, I don't always find the right path. :-)
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