5 ms·

Oh god, I still have nightmares about Herstein. I took an undergrad algebra class from a very old-school prof who thought it would be good for undergrads to be

Oh god, I still have nightmares about Herstein. I took an undergrad algebra class from a very old-school prof who thought it would be good for undergrads to be exposed to some of the problems - they gave all of us quite a bit of trouble.

graycat 10y ago
Herstein is a bit obscure for a first course. Once I was pushed into a course from Herstein. At first it was in group theory below what I'd already done. I asked the prof if he was going to get to group representation theory. He said that that topic was "deep". I told him it was my ugrad honors paper. The course was beneath me, and I saved time and didn't go. For the final exam, he gave me an oral. He asked me something about Galois theory, which is in Herstein and which I learned from there for his exam. His other question was about duality. He wanted me to show that the dual space of the dual space is isomorphic to the original space. That's true and easy to show, mostly just pushing symbols around, and the notation can get a little confusing, but is not true in some cases. Some point set topology courses consider duals of duals, and when there is equality say that the original space is reflexive. Then they want to define the weak topology and the weak* topology, etc. Can see some of this in, say, G. Simmons, Introduction to Topology and Modern Analysis, super nicely written book although I have never seen any applications for it. Pushing around duality in linear algebra can get to adjoint transformations. To me it turns out to be a lot of careful notation for something that turns out to be nearly trivial. Yes, on problems in Herstein, there was one on rings. It took me a while but I got it. I showed it to the prof, and he sent me to another prof who thought that solving that problem was good. He gave me a more difficult related problem, and I made a mess out of it. The problem needed transfinite induction, and I was supposed to understand that but didn't understand it very well. So, I got pissed off: I should have been studying stuff I didn't know, e.g., transfinite induction, instead of wasting time in the Herstein course that had, say, only Galois theory I didn't already know. At that school same thing happened in a topology course: The book was Kelley, famous. Heck as an ugrad, I'd taken that book and given lectures once a week to a prof and did a stack of the exercises. I did all but the chapter on compactness at which time I dropped everything to finish my honors paper. For me to sit in that topology course was stupid. I went to the department chair and tried to get into some material I didn't know but wanted to, especially differential geometry for relativity. He told me no. So, I did my teaching, started violin, met my wife, and left for a good job!

graycat 10y ago

Herstein is a bit obscure for a first course. Once I was pushed into a course from Herstein. At first it was in group theory below what I'd already done. I asked the prof if he was going to get to group representation theory. He said that that topic was "deep". I told him it was my ugrad honors paper. The course was beneath me, and I saved time and didn't go. For the final exam, he gave me an oral. He asked me something about Galois theory, which is in Herstein and which I learned from there for his exam. His other question was about duality. He wanted me to show that the dual space of the dual space is isomorphic to the original space. That's true and easy to show, mostly just pushing symbols around, and the notation can get a little confusing, but is not true in some cases. Some point set topology courses consider duals of duals, and when there is equality say that the original space is reflexive. Then they want to define the weak topology and the weak* topology, etc. Can see some of this in, say, G. Simmons, Introduction to Topology and Modern Analysis, super nicely written book although I have never seen any applications for it. Pushing around duality in linear algebra can get to adjoint transformations. To me it turns out to be a lot of careful notation for something that turns out to be nearly trivial. Yes, on problems in Herstein, there was one on rings. It took me a while but I got it. I showed it to the prof, and he sent me to another prof who thought that solving that problem was good. He gave me a more difficult related problem, and I made a mess out of it. The problem needed transfinite induction, and I was supposed to understand that but didn't understand it very well. So, I got pissed off: I should have been studying stuff I didn't know, e.g., transfinite induction, instead of wasting time in the Herstein course that had, say, only Galois theory I didn't already know. At that school same thing happened in a topology course: The book was Kelley, famous. Heck as an ugrad, I'd taken that book and given lectures once a week to a prof and did a stack of the exercises. I did all but the chapter on compactness at which time I dropped everything to finish my honors paper. For me to sit in that topology course was stupid. I went to the department chair and tried to get into some material I didn't know but wanted to, especially differential geometry for relativity. He told me no. So, I did my teaching, started violin, met my wife, and left for a good job!