Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 October 11, 2017 Vol. 16, No. 3

This week's colloquium will feature student research

Title: Student research presentations
Speaker:  Russell Houpt and Sarah Seckler
Time:  Thursday, October 12 at 11:00am
Place:  VanderWerf 102

Name That Bird: Using Neural Networks to Identify Birds

Can a computer learn to identify a bird by analyzing samples of its song? This research explores how neural networks can be used to identify different birds from recordings of their songs. We explore convolutions, wavelets, and neural networks, how they work together, and what techniques were employed to teach the programs how to quickly and accurately identify birds. In earlier work, a research group at Hope College made progress on this question by using neural networks to classify bird songs on a somewhat limited scale. Our results extend this work by using similar techniques on larger data sets, improving the accuracy and speed of the analysis, and modifying the existing algorithms to take advantage of multiple core computers. 

What Bird Was That? Feature Extraction of Recorded Bird Songs for Neural Networks

In the past, researchers at Hope have worked towards identifying birds from recorded bird songs through using wavelets, image processing and neural networks. The general aim of our project is to extend this work to provide greater computational efficiency and accuracy in identification of bird songs. In this talk I will focus on taking a recorded bird song signal and extracting data from it to make it a suitable input for a neural network. This feature extraction process will involve using wavelets and related methods to create an image called a scalogram, encoding the key aspects of the sound including frequency and time. Our work focuses primarily on finding more efficient ways to extract these images, allowing us to analyze much larger data sets.

MATH Challenge

The 2017 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place on the morning of Saturday, November 4 this year. Teams of two or three students take a three-hour exam consisting of ten interesting problems dealing with topics and concepts found in the undergraduate mathematics curriculum.  Each team takes the exam at their home campus under the supervision of a faculty advisor. 

The department pays the registration fee for each team and will provide lunch to participants afterwards. A group of students may sign up as a team.  Individual students are also encourage to sign up; they will be assigned to a team on the day of the competition.  For more information, please talk with any member of the Mathematics Department or visit the MATH Challenge website
where you can also view old copies of the exam.  If you are interested in participating in the MATH Challenge, you must email Professor Cinzori at by Tuesday, October 24.

Mathematicians discover that two types of infinities have the same size 

There was in interesting article in Quanta Magazine recently about infinity. The article Mathematicians Measure Infinities and Find They're Equal discusses this recent discovery that two types of infinity that were long thought to be different sizes, do, in fact, have the same size. The article gives some history about infinities and how they can be compared.

Actuarial Career Opportunity Day

Auto-Owners invites you to their annual Information Technology & Actuarial Career Opportunity Day! The event is on Friday, October 20, 2017 from 10:30 a.m. to 4:00 p.m. IT/Actuarial Day shows students how their degree can be used in the insurance industry.
Sophomores, juniors, seniors, and recent graduates with majors in Mathematics and Computer Science are invited. Faculty is also welcome! Each faculty member who wishes to attend should fill out a registration to ensure we adequately prepare for the correct number of attendees.

More information and registration should be available soon and will hopefully be in the next newsletter.



Problem Solvers of the Fortnight

In our last problem of the Fortnight, we gave the figure shown where the blue triangle POQ is isosceles since sides OP and OQ both have length 4, theta is the angle POQ at the bottom of the triangle, and a pink semicircle sits atop the isosceles triangle.  
  • Find the area of triangle POQ as a function of theta.
  • Find the area of the semicircle as a function of theta.
  • Find the limit as theta goes to 0 of the ratio of the area of the triangle to the area of the semicircle.
let A = (a,a2) and B = (b,b2) be two points on the graph of the parabola y = x2 such that the tangent lines to the parabola through A and B are perpendicular.  Let C be the point where the tangent lines meet at a right angle.  Find the x- and y-coordinates of the point C in terms of a.

Congratulations to all those that gave correct solutions: Jacob Conroy, Matthew Dickerson, Calvin Gentry, Keri Haddrill, Karthik, Karyamapudi, Philip LaPorte, Kenneth Munyuza, Andrew Nguyen, Sarah O'Mora, Alex Osterbaan, Zheng Qu, Forest Rulison, Hugh Thiel, Jincheng Yang, and Yizhe Zhang

Problem of the Fortnight

"Well, I've come out second best in my battle with the union," said Noah van Ark.

"How so?" asked his sister Joan.

"Well, I needed to have the union workers move thousands of crates.  The exact number," said Noah, consulting his notebook, "was 69,489.  The job took nine working days.  I didn't think the union workers were putting all they had into it, but the union leaders thought otherwise.  Every day after the first day, I put six more workers on the job; and every day after the first day, each of the workers -- by arrangement -- shifted five fewer crates than was the quota for the day before.  The result was that, during the latter part of the period, the number of crates being moved actually began to go down."

What was the largest number of crates moved on any one day?

Tape your solution -- not just the answer -- to a crate of clementines, and drop it by the Problem of the Fortnight slot outside Professor Pearson's office (VWF 212) by 3:00 p.m. on Wednesday, October 18.  As always, please be sure to include your name as well as the name(s) of your math professor(s) -- e.g. Woody Kreight, Professor DeKreese -- on your solution.

One person’s constant is another person’s variable. 

Susan Gerhart

Off on a Tangent