Emmy Noether’s 133rd birthday.

To do mathematics is hard enough, to do it well even harder, but to do it better than most and be discriminated against by a phalanx of morons for decades takes a special kind of toughness and mental acuity. Today we honor Amalie Emmy Noether, one of the greatest mathematicians of the twentieth century.

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Emmy Noether fought persistent sexism to obtain a Ph.D in 1907 even though she was not allowed to take classes, nor draw a paycheck when she taught classes after her doctorate. Being Jewish she eventually fled the rising drumbeat of Nazism and arrived at Bryn Mawr College in Pennsylvania in 1933. Tragically she died shortly after following medical complications. She was only 53.

Among her many accomplishments include significant contributions to algebraic invariants and number fields. A class of algebraic objects — Noetherian rings — are named after her. Her work on differential invariants in the calculus of variations leading to Noether’s theorem has been called, “one of the most important mathematical theorems ever proved in the development of modern physics”. You can find out more about her on Wikipedia:

http://en.wikipedia.org/wiki/Emmy_Noether

Her many champions included Albert Einstein and David Hilbert. Today Google honors Emmy Noether with a doodle. Go check it out!

https://www.google.com/?gws_rd=ssl

Presidential Dream Course lecture: Dr. Peter Sarnak

We are honored to have Dr. Peter Sarnak from Princeton and the Institute for Advanced Study come to Norman to give a public lecture entitled, “Sums of Squares and Hilbert’s 11th Problem”.

sarnak

Dr. Peter Sarnak, Eugene Higgins Professor of Mathematics

When: Thursday, March 12th 2015, 4:30 pm

Where: Nielsen 270

Here is a bio of Dr. Sarnak:

http://en.wikipedia.org/wiki/Peter_Sarnak

BP Trading Simulation, March 4th, 2015.

BP, the oil company, has other interests besides oil. They run a trading platform for which they are looking for students with strong analytical abilities, specifically students trained in mathematics, physics or engineering. This is a great opportunity to see what employment at this arm of the company is like, so be sure to come with a copy of your resume. There are even prizes for the top three finishers!

OU Trading Sims Flyer - A&S-1

When: Wednesday, March 4th, 2015; 5:00 pm to 6:30 pm.

Where: Adams Hall (Business College), first floor.

Contact: Adrienne Jablonski to sign up, Arts & Sciences (Ellison 234, ajablonski@ou.edu)

Gabriel’s Wedding cake.

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?

cake

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:

cake2

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?