MSCI, a local company, will visit the Math Club and talk about career opportunities for math majors. MSCI is a leading provider of investment support tools.
When: Wednesday, 02/25/2015, 5:00 pm
Where: PHSC 1105
Food?: Yep, free pizza!
We now post a mathematical puzzle and ask you all to make sense of it. A little bit of Calculus is needed to do the computations, but resolving the puzzle probably only requires persistence and ingenuity.
So what is Gabriel’s wedding cake? Is it this?
Well sort of. Let us begin by defining a function over the set of numbers from 1 to infinity. Call it f(x). f(x) = 1 on [1,2], f(x) = 1/2 on (2,3], f(x) = 1/3 on (3,4] and so on; f(x) = 1/n on (n, n+1]. This is a step function where the length of each step is 1 and the steps descend by smaller widths going to zero. Now rotate this function about the X-axis to generate the “cake” i.e., an infinite stack of cylinders, each of height 1 but radii 1/n as n goes to infinity. It looks something like this:
Ok, so what’s the big deal? Well from Calculus one can compute the volume and surface area of this curious, infinitely stacked cake. The volume is just an infinite sum of numbers, Pi*r^2*h, where r = 1/n and h = 1. So we are basically adding up Pi times the sum of the squares of reciprocals of natural numbers. This famous sum is the value of the zeta function at s=2 and Euler showed it is equal to Pi^2/6. So the volume of the cake is Pi^3/6 or just under 5 cubic units.
On the other hand the surface area, which includes parts of the top and all of the sides works out to include the harmonic series (the exact expression is left to you) which is the infinite sum, 1 + 1/2 + 1/3 + 1/4 + … which we know diverges to infinity. So there you have it: finite volume with infinite surface area!
In other words: a cake you can eat, but cannot frost!! How do we explain this paradox?
The first Math Club meeting of the spring semester is upon us. The speaker is Dr. Henry Segerman of Oklahoma State University. He specializes in visualizing geometric objects and 3-d printing.
Title: “Sculptures of 4-D objects”
When: Wednesday, January 21st, 5:30 pm
Where: PHSC (Physical Sciences) Room 1105
Food: Free Pizza!
We continue our Spotlight series where we highlight one of the member of the OU Math Department. This edition of Spotlight shines a light on one of our most accomplished graduate students, Elizabeth Pacheco
Short bio (in her own words): Elizabeth is a fifth year graduate student in the math department at OU. She has a B.S. in Mathematics from the University of North Texas. She is studying (configuration spaces and Leavitt path algebras) under the guidance of Dr. Murad Ozaydin.
The blog caught up with Elizabeth to get her thoughts on mathematics, graduate study, cats and other important topics.
The blog is back!
We start with an announcement for students to apply to an REU opportunity at San Diego State University. Students spend a summer conducting research and are paid a stipend of $5000 for the whole summer while working with enthusiastic, like minded fellow students from around the country.
Deadline: March 6th.
More information here: