Discussions - sci.math | Google Groups

	Convergence in topological spaces
	Is the convergence of a sequence defined in a topological space without additional structure on the space? If so, how, since we can't use the concept of distance (a metric)? By Edward Green - 9:41am - 4 new of 4 messages

how to prove $J_{N}$ a cyclic group? $J_{N}$ is the subgroup of $Z*_{N^2}$ contains all the elements whose jacobi symbol with respect to $N$ is 1.

i saw a paragraph said $J_{N}$ is a cyclic group of order 2NN', $J_{N} $ is the subgroup of $Z*_{N^2}$ contains all the elements whose jacobi symbol with respect to $N$ is 1 ($N=pq, p=2p'+1, q=2q'+1, N'=p'q'$), but i don't know why (especially "cyclic")? Will somebody be kind to help me? Moreover, it's said $J_{N}=G*G_{1}*G_{2}$, where $G$ is the subgroup... more »

By challengerlee - 8:14am - 2 new of 2 messages

	finitely generated modules vs.finitely generated algebras
	hello everyone! suppose A is a ring. I'm trying to understand the difference between a finitely generated A-module and a finitely generated A-algebra. what is the general form of each? can you give an example of a finitely generated A-algebra which is not a finitely generated A-module ? thanks michael... more » By michael friedman - 7:29am - 2 new of 2 messages

Topology: Continuity - discrete and indiscrete spaces

Hello, I just started my jourey into Topology and stumpled on the following: (i) Every function from a discrete space into any top. space is continuous. (ii) Every function from any top space into an indiscrete space is continuous. Now, unfortunately I am not quite sure why that is. I hope some experienced traveller can help me out with an explanation!... more »

By BadBedHead@googlemail.com - 7:37am - 2 new of 2 messages

	Can we simplify the partial sum of bionomial coefficients?
	Hello all, Can the following summation be simplified? In terms of j,n and p?Or, Can the summation in the expression be approximated between some lower bound and upper bound? Sum_j = \sum_{k=p+j}^{n} ncr(n,k) where ncr(n,r) returns the "n choose r" number. --- Regards, Sujit P Gujar. IISc Bangalore.... more » By Sujit - 5:09am - 3 new of 3 messages

	power series solution for second order equation
	...[link] Best wishes Torsten. By Torsten Hennig - 3:04am - 1 new of 1 message

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Standardized definitions

Are there any authorized "standard definitions" for terms like e, pi etc? My impression is that there isn't and that a wide variety of definitions are acceptable so long as they are clear and precise and lead to the correct value. So, if a student is asked to prove that the sum (over all positive integers n) of 1/n^2 is pi^2/6, what is to prevent the student from... more »

By pauldepst...@att.net - 12:55am - 13 new of 13 messages

	Happy Fourth of July
	Dear Newsgroup: Happy Fourth of July 2008 to you and to our members. We have variety of articles in mathematics also about Einstein. Join us: Sci.math: [link] Sci.physics: [link] and Sci,comp (public): [link]... more » By Mehran Basti - Jul 3 - 6 new of 6 messages

	sigma rings
	Let X be a set, and define a (Boolean) sigma-ring _S_ as a non-empty class of subsets of X that is closed under the formation of differences and countable unions. Let _E_ be any class of subsets of X, and denote by _S_(_E_) the smallest sigma-ring containing _E_. Let A be a subset of X, and denote by E the generic element of the class... more » By sto - Jul 3 - 5 new of 5 messages