Math Forum / Mathematics / Undergraduate Math / August 2006

I never had real issues with mathematics taught at school, but I
strongly believe that mathematics taught at school, simply isn't real
mathematics.
However, I have BIG problems with what I think real mathematics is,

Please see this image
http://img2.tapuz.co.il/forums/1_83887672.gif
I need to prove alpha using phi.

I have a certain subseries of the harmonic series. So we don't take the
sum of the inverses of all natural numbers, but only those of numbers
containing at most 9 different digits in their decimal representation.
This series converges, but I want to show that an upper bound is 180.

I'm looking to study some topology.  I've had real analysis 1 and am sitting in on real analysis 2 at the undergraduate level.  I have two Dover books but last time I read either I had no idea what was going on.  Does any one have a good suggestion of a topology book that would ...

how does the givens transformation work for a complex vector?  i've got it
working for real vectors fine but cant get it to work if the vector is
complex.  i cant find anything on this in any books either.  how is the
method amended for complex vectors?

Is it possible to establish isomorphism for < N, + >  and < Z, + >?  They
are both countably infinite, but the Z group is a "larger infinity" since it
also includes negatives of the N group, so how could you establish a 1 to 1
relationship?

Hello, First time I post here so I apologize if the subject is not apropiate.  I'm in a little bit of a bind, I'm helping a friend with some homework but I have encountered a problem that I cant solve.
   Translated from spanish;
  Rodolfo paez plans to retire in 20 years he will ...

I found the follwoing algorithm to solve logarithms by hand:
Does anybody know the logic behind it? How can I prove it's correct?
Thanks!
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Let A,B and C be points on the Earth, for example. Suppose A and B are joined by a geodesic (so AB is a geodesic segment). How do you calculate the shortest distance from C to AB? I can easily calucate the distance to the great circle plane... simply take
N = A x B / | A x B |
Then ...

I discovered this interesting question a few months back. It is
relatively easy to solve but the scenario relies completely on chance.
"If a meteorite the size of a golf ball strikes earth at 1/2 the speed
of light, will we survive?"

I have posted at my personal web page http://web.maths.unsw.edu.au/~norman/Rational1.htm
some short pdf papers that might interest teachers of trigonometry. One is called `The Wrong Trigonometry', one is `A Rational Approach to Trigonometry', and another is `Survivor: The ...

Can someone give me a start on this question:  Given Z1 and Z2 are complex
numbers prove that the angle for (Z1-Z2) is equal to the angle between the
real axis and the vector pointing from Z2 to Z1.
When I graph this I can "see" it is the same direction but that is not a

1.I just realize that I don't understand why the definite integral
(riemann integral) is the area under a curve,can some one explain?
Note that i understand why riemann sum is the area,i dont understand
how the connection between riemann sum and definite integral is made.

the measure of angle b, the supplement of angle a, is four times the measure
of angle c, the complement of angle a

f(x,y)= (x^2+2x+3)/sqrt(y)
is the gradient vector < (2x+2)/sqrt(y) , -(x^2+2x+3)/2y^(3/2) > ?
and if the question asks to find the vector tangent to the curve of steepest ascent where x=1 and y=2, do I need to find the vector perpendicular to grad f(2,1) ?
Thanks!