Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 February 19, 2016 Vol. 14, No. 10

Next week's colloquium: Problems Posed by Polya

Title: Problems Posed by Polya
Speaker: Stephanie Edwards, PhD, Mathematics Department, Hope College
Time:  Tuesday, February 23 at 4:00-4:50 pm
Place:  VanderWerf 102

Many open problems in entire function theory, specifically, the distribution of zeros of real entire functions, can be traced back to work by G. Polya.  One of the problems stated in a Polya and Szego text from the early 1900's is: If P is a real polynomial with only real zeros, find the number of non-real zeros of P2+P'.  If one removes the hypothesis that P has only real zeros, the problem becomes quite difficult and was not solved until the 1980's. We will discuss a simple solution to the
P2+P' problem, look at natural questions that arise from the problem, and discuss some open questions that have their roots in Polya.

Upcoming Colloquia

The following colloquia are currently on the schedule for this semester. Others may be added as the semester goes along.
  • Tuesday, March 8, Paul Yu, Grand Valley State University
  • Tuesday, April 19, Eric Nordmoe, Kalamazoo College

Math Game and Pizza Night

Come eat pizza and play games with your fellow math students and the math department on Wednesday, March 2!

We will meet in VZN 247 starting at 6PM for an evening of fun, adventure, and intrigue. Sign up in your math class or outside of VWF 210 (Dr. Koh’s office).

Tanton's 10 Problem Solving Strategies

James Tanton, an ambassador for the Mathematics Association of American, has developed a list of problem solving strategies.  Tanton's 10 Problem Solving Strategies are the typical list you'd find posted in a middle school or high school classroom, but is certainly things problem-solvers at the college level should be doing as well. Each strategy linked below also comes with an explanation and an informative and enjoyable video made by Tanton. More information can be found at the MAA site.

Students travel to the Nebraska Conference for Undergraduate Women in Mathematics

Seven undergraduates, two professors, and a 4th grader recently journeyed via van to Lincoln Nebraska for the Nebraska Conference for Undergraduate Women in Mathematics January 28-31, 2016.  Professors Stephanie Edwards and Paul Pearson, students Sarah Hilsman, Jiyi Jiang, and Grace Weisner from Hope along with students from GVSU and Davenport University attended the conference.  Sarah Hilsman presented a talk, “Real Algebraic Level Curves: A generalization of a theorem of Polya” at the conference based on her research from last summer with Anna Snyder under the direction of Stephanie Edwards.  There were many talks given by undergraduates and panel discussions highlighting careers in mathematics (inside and outside academia), as well as breakout sessions and many opportunities to talk with mathematics graduate students and professors from around the country.

Math in the News: How do you like them apples?

The puzzle shown on the left has Facebook all atwitter lately (but apparently Twitter is not all afacebook) because there has been some controversy as to the correct answer. What do you think? What is the correct answer?

This isn't higher level mathematics and seems to rely on exactly what the pictures of fruit represent. You can see some explanations in the Huffington Post.

Problem Solvers of the Fortnight

In our last POTF we asked if there were any positive integers x, y, and z that simultaneously satisfy the following equations?

3x2 = 2y2 + 4z2 - 54 and 5x2 = 3y2 + 7z2 - 74

If so, find them.  If not, show why not.

Congratulations to Daniel Brune, Richard Edwards, Matt Gira, Monica Ohnsorg, Miles Pruitt, and Kathryn Trentadue -- all of whom put on their thinking caps and correctly solved the Problem in the last issue of America's premiere fortnightly electronic mathematics department newsletter.

Problem of the Fortnight

A vertical circular disk of radius R is partially submerged in a liquid.  The disk rotates, so that the portion that was submerged becomes exposed to the air, allowing the liquid to evaporate.  Assuming that the disk is spinning fast enough so that the liquid stays within the annulus shown in the figure, at what height above the surface of the liquid should the center of the disk be placed in order to maximize the area of the exposed portion of the annulus and thereby maximize the efficiency of the evaporator?

Write your solution on an annulus and drop it in the Problem of the Fortnight slot outside Dr. Mark Pearson's office (VWF 212) by 3:00 p.m. on Friday, February 26.  As always, be sure to include your name, as well as the name(s) of your math professors -- e.g. Carrie DaWonn, Professor A.T. Thu -- on your solution.

Off on a Tangent