Description:
Mathematical discussions and pursuits.
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Mobius inversion and zeta function
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Hi, I was examining the passage where Riemann did the inversion from J(x) to pi(x) to obtain the prime counting function. Well, I really can't understand this. The Mobius inversion formula and the situation he had to face with are quite different. In fact, the theorem says that G(x) = sum{ F(x/n), n < x}... more »
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Computability and Creative Sets
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I am trying to understand computability by reading "Computability Theory" by Cooper. I am stuck on the concept of Creative Set. A creative set, A is defined as:- A is creative if 1. A is c.e. 2. There exists f(e) s.t. W(e) belongs ^A => f(e) belongs ^A-W(e) K = {e st e belongs W(e) is given as an example with creative function... more »
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Convergence in topological spaces
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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)?
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finitely generated modules vs.finitely generated algebras
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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 »
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Topology: Continuity - discrete and indiscrete spaces
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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 »
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Can we simplify the partial sum of bionomial coefficients?
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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 »
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Standardized definitions
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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 »
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