Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 November 6, 2015 Vol. 14, No. 5

 Next week's colloquium will  take a look at wavelets

Title: Wavelets: Unlocking the Mysteries of Time, Frequency, and Amplitude
Speaker: Paul Pearson, Hope College     
Time:  Tuesday, November 10 at 11:00-11:50 am
Place:  Vanderwerf 102

One of the most important scientific problems in the digital era is how to analyze time-dependent data.  In this talk we will discuss how to extract frequency and amplitude content from time signals using waves.  In particular, we will use Haar wavelets, Daubechies wavelets, and windowed Fourier transforms to provide answers to the following questions:  Is it possible to convert an audio recording into sheet music?  Is it possible to determine what kind of birds are singing in a recording?  Is it possible to analyze brain activity via an EEG (Electroencephalogram) signal and tell if a person's eyes were open or closed?  Using an EEG, is it possible to determine if a surgery patient has the right anesthesia level?  This talk will be accessible to all (prerequisite knowledge: finding the average of two numbers). 

Generating functions is the focus of colloquium 

Title: Generating Functions and Recurrence Relations 
Speaker: Anil Venkatesh, Ferris State    
Time:  Tuesday, November 17 at 4:00-4:50 pm
Place:  Vanderwerf 102

A generating function is a formal power series whose coefficients encode information about a sequence of numbers.  Given a recursively defined sequence of numbers, generating functions can often be used to deduce an explicit formula for the n-th term of the sequence.  In fact, generating functions were first introduced by Abraham de Moivre in 1730 as a tool for solving a general class of recurrence relation problems.  In this talk, we review the properties of various ordinary generating functions and the sequences they correspond to, drawing connections to the Taylor series lessons in Calculus 2.  We then use generating functions to solve recurrence relations in the spirit of deMoivre, culminating in an explicit formula for the n-th Fibonacci number.

Upcoming Colloquia

After the next fortnight, there are only two colloquia currently on the schedule for the semester.
  • Tuesday, December 1, 4:00pm, Hope students
  • Thursday, December 10, 11:00am, Tim Pennings, Davenport University  

Math Club News

Bring your friends, your games, and your friends' games to the 2nd floor of Graves Hall on Saturday, November 14th at 7pm for Math Club Game Night! Math Club will also provide games to play.

Dr. Cinzori reports the mathematical formula for fun, F, at game nights is F = MATh, where M is the number of math students in attendance, A is the person's anxiety level in the past two weeks, T is the time spent playing games with friends at game night, and h is Planck's constant (of course!). Cinzori points out that since A is large and h is small, they basically cancel each other, and fun at game nights is directly proportional to the number of people attending and the time spent playing games. The Math Club had a successful game night last Saturday and will be hosting another movie night soon. (Look for an announcement in the next edition of Off on a Tangent.)

For more info on the Hope Math Club's latest and greatest activities, visit their brand new FaceBook page (and request to join the group).

Statistics Career Day at GVSU

Interested in a career in statistics? If so, head on over to Statistics Career Day that will be held at Grand Valley State University on Friday, November 20, 2015 in the Kirkhof Center on the Allendale Campus. The intended audience includes high school and college students from West Michigan.

This event will provide students an opportunity to learn about the many career options available in statistics by meeting corporate representatives to discuss job opportunities and university faculty to discuss graduate study. The keynote speaker is David Morganstein, Vice-President and Director of Statistical Staff at Westat, Inc., and president of the American Statistical Association.
Registration is free unless you want a lunch provided for $5. For more information about the event and to register click here.

Math in the News: How to show your work

Maybe this isn't real math in the news, but it was too funny to pass up.  The picture on the left, of a student's response to a test question, showed up on Reddit a couple of days ago. The question asked, "Bobby has four dimes. Amy has 30 pennies. Which child has more money?"

A fairly easy question and the student answered Bobby. The second part of the question  asks, "How do you know? Show your thinking." By looking at the drawing the student made for the answer, it looks like it was spot on. Though I do wonder why the face is so sad. Perhaps it's a picture of Amy.

Problem Solvers of the Fortnight

In our last problem of the fortnight we said, let P(x) be a monic polynomial of degree 2015 (that is, a polynomial whose leading term is x^(2015)).  Suppose you know that P(n) = n for n = 1, 2, 3, 4, ..., 2015.  Is it possible to determine P(2016)?  If so, what is it?  If not, why not?

Congratulations to Aleah Hahn, Colton Bates, and Zac Geschwendt -- all of whom correctly determined P(2016) in the last Problem of the Fortnight.

Problem of the Fortnight

Square ABCD has sides of length 1.  Square PQRS has the same center as square ABCD and has PR parallel to BC and QS parallel to AB as shown.  Dotted segments AS, AP, BP, BQ, CQ, CR, DR, and DS are drawn.  The figure is cut along the dotted lines, and then then triangular faces are folded up so that A,B,C, and D meet above the center of the squares to form a right pyramid with square base.  What is the maximum possible volume of this pyramid?

Write your solution on the base of such a right pyramid, and submit it to the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Wednesday, November 18.  As always, be sure to include your name and the name(s) of your math professors -- e.g. Gene Yuss, Professor Bryll Yant -- on your solution.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.  

John Louis von Neumann

Off on a Tangent