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Browse College Analysis
Stars indicate particularly interesting answers or
good places to begin browsing.
 Limit of an Infinite Series [7/18/1995]

What is the limit of (n!)^(1/n)?
 Lines, Points, and Infinities [09/01/2001]

What is the cardinality of the set of real numbers between 0 and 1? Is
this cardinality less than, greater than, or equal to the cardinality of
real numbers between 0 and 2?
 Pi to x Million Decimal Places [8/1/1995]

How is pi calculated to x million decimal places?
 PredictorCorrector Methods [09/07/2002]

Could you please explain what a predictorcorrector method is,
possibly using Euler's and Huen's methods as examples?
 Rational and Irrational Numbers [11/12/1997]

Which set is bigger, the set of rational or irrational numbers?
 Rational Numbers [11/24/1997]

Which is greater, the number of rational numbers between 0 and 1 or the
number of rational numbers between 0 and 2?
 0 Raised to a Power [04/25/2002]

What is the limit of 0^n as n approaches infinity? Can you explain why
it equals zero or why it can't equal zero, or if it's undefined?
 Analysis [11/29/1994]

In analysis: If f:[0,1] is continuous. Show that there is an x in [0,1]
such that f(x) = x. Problem #2: If A and B are open and closed sets
respectively, of R^n, show B\A is closed and A\B is open.
 Analysis and the Derivative [01/23/2001]

Suppose that f:RtoR is differentiable at c and that f(c)=0. Show that
g(x):=f(x) is differentiable at c if and only if f'(c)=0.
 Analysis Questions [12/07/1996]

I have been going over some of my professor's old exams and can't figure
out some of the questions.
 BanachTarski Paradox [07/20/2002]

The BanachTarski paradox decomposes a sphere of a fixed radius into a
finite number of parts and then puts them together again to form two
spheres, each with the same radius as the original sphere. How is this
possible?
 Bestfitting Line to a Number of Points [04/25/2001]

I have a number of points on a plane and want to find a line that best
fits through the points, minimizing the sum of squares of the distances
of each point from the line.
 Cardinality, Area, and Probability [09/05/2003]

Divide a rectangle into two regions, one with twice the area of the
other. What is the probability that a point randomly selected will
fall in the larger area? Is it 2/3, because the larger region
contains 2/3 of the area? Or is it 1/2, because the two regions
contain the same number of points?
 Cauchy Sequences [09/11/1997]

I'm trying to prove that every Cauchy sequence has a sequential limit
point.
 Chaos Theory and Converging Sequences [2/14/1996]

I'm investigating a process of dividing and adding  take a number,
divide by 5, add 2, write down the result, repeat the process using the
result  and realise that using this process my sequence will converge
towards 2.5, where nothing else can be done to it. By reversing the
process  adding 2 first then dividing by 5  my sequence will diverge to
what I guess will be infinity. What else can I say?
 Chaotic Functions [10/30/2000]

Can you give some mathematical examples of chaos theory?
 Closure and Compactness in a Metric Space [10/08/2002]

Regard Q, the set of all rational numbers, as a metric space, with
d(p,q)=pq... Show that E is closed and bounded in Q, but that E is
not compact. Is E open in Q?
 Compact Sets [02/04/2001]

Let A be an infinite set in the real numbers with a single accumulation
point in A. Must A be compact?
 Compact Sets and Hausdorff Spaces [03/19/2003]

How do you prove that every compact subset of a metric space is
closed?
 Complex Analysis Geometry Proof [09/28/2004]

I'm looking for a proof that arg z1 + arg z2 = arg(z1z2).
 Complex Integrals and the Residue Theorem [12/18/2000]

How can I calculate the integral over C of (z^2/((z1)^2*(z+1)))dz, where
C is the circle C = {z z  2i = 2}? Can I use the Taylor Series?
 Continuity [11/24/2001]

Suppose f and g are continuous on I = [a,b]... Prove there exists a k
greater than 0 such that f(x) + k is less than or equal to g(x) for all x
in I.
 Continuous but Not Differentiable? [12/27/2003]

I have heard that Weierstrauss found a function that is continuous
everywhere, but differentiable nowhere. How is that possible?
 Continuous Function [05/18/1999]

Is there a way of constructing a continuous function that is nowhere
differentiable?
 Counting Infinite Sets [06/02/1997]

What is the cardinality of all the pieces that are part of the real
number line?
 Definition of the Limit [11/05/2002]

I need some help with the definition of the limit, particularly
choosing delta for a given epsilon.
 Dense and Nowhere Dense Sets [04/25/1999]

Can you define the mathematical terms 'dense' and 'nowhere dense'?
 Deriving the Gamma Function [12/15/2000]

How can you prove that sqrt(pi)/2 = (1/2)!, and what is a fractional
factorial like that equal to?
 Distance between Lines [03/04/1997]

Given the equations of several lines in a room, determine the distance
between them.
 Elliptical Arc Length [11/17/1999]

Is there a series approximation or some other numerical method for
calculating the arc length of an ellipse?
 Epsilon and Delta [04/18/1999]

How can I show that sin(x^2) is not uniformly continuous on the reals?
 Euler Formula: e^(pi*i) = 1 [6/5/1996]

Why does e^(pi*i) = 1?
 Explain Supremum [02/02/1998]

Can you please explain, perhaps with an example, the concept of
"supremum"?
 Fibonacci sequence [1/28/1996]

What is the explicit formula for the Fibonacci numbers?
 Finding Repetitive Patterns in Economic Data [1/28/1995]

What branch/subset of mathematics do I need to learn so that I can write
computer software that will identify and/or search pairs of data for
specific patterns?
 FixedPoint Theorem [05/02/2002]

An intuitive reason why the theorem is true, and a proof.
 Formal Definition of a Limit [08/01/1998]

What is the connection between the open intervals and the informal
definition of the limit?
 Formulas for NDimensional Spheres [10/26/2000]

What is the next term in the sequence pi*r^2, (4/3)pi*r^3, ...? Would it
be the formula for the volume of a 4dimensional sphere?
 Fourier Series and the Zeta Function [08/13/1998]

How do you evaluate Zeta of 2?
 Functions of Complex Variables [02/20/2001]

Do you know of a method of finding f(z) when u(x,y) is known, and f(z) is
analytic in a domain D? Also, how can I show that sin(x) + sin(2x) +
sin(3x) + ... + sin(nx) = 1/2 cot(x/2)cos[(n+1/2)x]/2sin(x/2)?
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