Recent content by Barre

Hello. I have been looking at some questions from old exams that I am preparing for, and I have some trouble with the kind of problems that I will now give an example of. Homework Statement Let G = (a,b,c | a^4 = 1, b^2 = a^2, bab^{-1} = a^{-1}, c^3 = 1, cac^{-1} = b, cbc^{-1} = ab)...

Homework Statement A group presentation G = (a,b : a^m = b^n = 1, ba = a^db) defines a group of order mn if and only if d^n \equiv 1 (mod m). Homework Equations One book that I read presents a solution in a way of constructing a group of said order by defining associative binary...

If the class is interesting, and I actually work through the material in the book before the lecture, then it usually is very rewarding to go to a lecture. If I did not have time to read up, then I usually skip the lecture to give myself more time to read and work on my own. In general I...

Did you try earplugs during exams? :D This problem used to be the case for me too. Thankfully, my school is very cool with such mistakes. In one notable example I managed to screw up like that (sign errors, missing terms etcetera) on 6 out of 8 problems on an exam in optics, still receiving an...

Sorry for offtopic, but how much did it take to work through them all? Did you do a reasonable amount of exercises? Do you do this on your free time?

Should this not be a clear 'no' to anyone but the most superficial? PS: Replace Med School with whatever is forced upon you.

Well let's see. We got that if R,M are both Noetherian (satisfying ascending chain conditions on ideals/modules), then we can obtain a filtration 0 = M_0 \subset M_1 \subset M_2 \ldots \subset M_n = M where each factor M_i/M_{i-1} \cong R/P_i for some prime ideal P_i \subset R. We construct this...

I had to work with associated primes of the quotients of M to solve 9b if I remember correctly. I will see if I can prove they are in this case contained in the set of associated primes of M. Thanks.

You are right about which exercise it is. R is supposed to satisfy ACC, yes. Else associated primes would not have to exist. I will look into what 9(b) (the filtration) implies for this problem, thanks. I sort of gave up on using 9b after I 'assumed' that the prime ideals associated with the...

1. Homework Statement R,M are Noetherian. Prove that the radical of the annihilator of an R-moduleM, Rad(ann(M)) is equal to the intersection of the prime ideals in the set of associated primes of M (that is denoted so regretfully that I am not even allowed to spell it out by the system)...

I have nothing to contribute here except noting that this is inspiring for me. I hope in my 50s I will be as eager to learn about science as you are.

Summer is a waste of time if you did not learn anything new :)

In computer engineering I did the standard single/multivariable calculus sequence, linear algebra, linear analysis, statistics and probability, numerical analysis and discrete mathematics. All of those were applied/computational except for discrete mathematics which also served as an...

p/q is in general a rational, but you define it's parity. How does that work?

I think this can be confirmed by invariant factor decomposition (http://en.wikipedia.org/wiki/Finitely-generated_abelian_group) although really Cauchy's theorem should be sufficient for a proof. G \cong Z_{k_1} \times Z_{k_2} \times \ldots \times Z_{k_n} such that k_1 \vert k_2 \vert \ldots...