![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
(no subject)
Oct. 14th, 2002 11:39 pmOctober's crispness is in the air. It's a fine sensation, one I distinctly note year-to-year, one made only slightly bittersweet by the knowledge that it indicates that the descent into winter has reached its steepest slope. The liquid amber trees are starting to drop the occassional yellow leaf, yet still today Memorial Glade was well populated by sunbathers; I'm surprised the rain hasn't yet started.
I like Mondays because they are the beginning of the week. I have a lot of "free time" since my co-op workshifts don't start until Thursday; and also I have one of my favorite classes on Mondays, Hilfinger's programming problems course. I like that class because it consists solely of small, semi-challenging problems that we work on and discuss, so it's a class with a bit of friendly competition, and it's something I'm good at. Oh, and it's completely informal, so it takes the stress out of the week. Last night Brandon and I solved one of the problems that essentially requires that one solve a linear diophantine equation in an arbitrary number of variables, for instance ax+by+cz=d given integers a,b,c, and d, and the requirement that all variables be integers. For two variables, the extended Euclidean algorithm solves this directly; the extension to more variables is cute and direct.
My Complex Analysis class is quite confusing. Most of the class doesn't come to lecture anymore, and I doubt that anyone really "gets it." I think we're really lacking the "motivation" that would put some meaning behind the theorems, lacking the sort of explanations that give an intuitive picture of what is going on. I found a book in the library (Bruce Palka's An Introduction to Complex Function Theory) that is far better about this than the course's textbook (Donald Sarason's Notes on Complex Function Theory). It is nice to have both a succinct book and a book rich with exegesis. I think it will help. I keep meaning to gather together a study group from the class, but given that it's the eighth week already, I question whether I'll actually ever get around to that.
We're just getting into some neat results, basically concerning Cauchy's Integral Theorem, which seems to be the meat of Complex Analysis; It seems that the value of a holomorphic function at points within a disc is determined by the integeral around the perimeter of that disc. Also, a holomorphic function is uniquely determined by its values in a subset containing a limit point. That's a nice result, I think... the previous theorems have been so similar to those of Real Analysis that they become somewhat boring.
I like Mondays because they are the beginning of the week. I have a lot of "free time" since my co-op workshifts don't start until Thursday; and also I have one of my favorite classes on Mondays, Hilfinger's programming problems course. I like that class because it consists solely of small, semi-challenging problems that we work on and discuss, so it's a class with a bit of friendly competition, and it's something I'm good at. Oh, and it's completely informal, so it takes the stress out of the week. Last night Brandon and I solved one of the problems that essentially requires that one solve a linear diophantine equation in an arbitrary number of variables, for instance ax+by+cz=d given integers a,b,c, and d, and the requirement that all variables be integers. For two variables, the extended Euclidean algorithm solves this directly; the extension to more variables is cute and direct.
My Complex Analysis class is quite confusing. Most of the class doesn't come to lecture anymore, and I doubt that anyone really "gets it." I think we're really lacking the "motivation" that would put some meaning behind the theorems, lacking the sort of explanations that give an intuitive picture of what is going on. I found a book in the library (Bruce Palka's An Introduction to Complex Function Theory) that is far better about this than the course's textbook (Donald Sarason's Notes on Complex Function Theory). It is nice to have both a succinct book and a book rich with exegesis. I think it will help. I keep meaning to gather together a study group from the class, but given that it's the eighth week already, I question whether I'll actually ever get around to that.
We're just getting into some neat results, basically concerning Cauchy's Integral Theorem, which seems to be the meat of Complex Analysis; It seems that the value of a holomorphic function at points within a disc is determined by the integeral around the perimeter of that disc. Also, a holomorphic function is uniquely determined by its values in a subset containing a limit point. That's a nice result, I think... the previous theorems have been so similar to those of Real Analysis that they become somewhat boring.
