Math Forum / Mathematics / Undergraduate Math / October 2008

I would like to check and prove or disprove the convergence (firstly
pointwise and then under the uniform/sup metric) of the following two
sequences of functions in the space of bounded functions from [0, 2Pi] to
R=reals).

For given curve we can find out the area bounded by the curve using Simpson's 1/3 rule, I found out the area of the curve.
Now how to divide the area in to 'n' equal parts, so that
total Area=sum of n areas.
Thanks.

So yeah, it's EASY to prove I'm right with non-polynomial
factorization.  Posters disagreeing with me can try to attack my
proof, where remember THEIR argument was that 7 is split up by
functions, so they want something like:

For different values of X,  Y i.e Sin-wave would be either maximum or minimum,I plotted all the points.
With the help of x values I want to find out y values.
I'm thinking like this.Finding out area bounded by the wave,so with the help of 'Area' and 'x' values,finding out y values.

Let R and S be commutative rings with identity and let f be a ring
homomorphism
from R to S.
Suppose that the ideal I of R is generated by the set H. Show that the

As I rant and rave, continually antagonize my audience, and talk about
cutting public funding for basic research, or well, any research at
all, I can imagine mathematicians smiling to themselves.  No way
people will ever listen to such nuttiness and they may smugly feel

Let R be a commutative ring with identity, and let N be the nilradical
of R
Show that the ring R/N has zero nilradical.
Sincerely, Thans

Back when I was naive and stupid, and idealistic, I dreamed of making
great discoveries to advance the state of humanity.
But then I made some discoveries, got years of abuse from
mathematicians, and now all I want to do is make as many academics

Why is it that every subset of a finite metric space is both open and
closed?  Thank you.

I am having a difficult time with this one!
(10x∧3+20-8x-25x∧2) ÷ (-2x+5)
I am not sure if I would swap the 20 and the 25x so that the 20 is at the end.

anyone i need some help a.s.a.p please

I want to solve the below equation and find out value of r.
(1+r)+(1+r)^2+(1+r)^3+.....+(1+r)^n
I will be very grateful.
Regards,

How many primitive elements does GF(81) have?

Um, so I've been ranting this morning as I've been feeling sorry for myself but a poster called Enrico just elevated my mood!
He's shown a cool result related I think to what I call a massive theoretical super structure, which I also call a Diophantine supermap for binary ...