Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
September 23, 2016 Vol. 15, No. 2

Student summer research will be the topic of next week's colloquium

Title: Student Summer Research Reports
Speakers: Sarah Petersen, Allison VanderStoep, Taylor Rink, Hope College Students
Time: Tuesday, September 27 at 4 pm
Place: VanderWerf 102

Modeling Pioneer Plant Populations found in Monteverde, Costa Rica (Sarah Petersen)

Within the context of an ongoing project studying the consequences of avarian seed dispersal on gap-dependent plants, mathematical questions such as “How does gap area data collected along a transect, or line, relate to forest area as a whole?” and “Is it likely that the probability of an adult plant reproducing depends on gap area?” arise.  We explore these questions, their answers, and some of the classical geometric probability problems to which they are related.

One bird, two bird? Red bird, blue bird? Analyzing bird songs using wavelets, image processing, and neural networks.
(Allison VanderStoep and Taylor Rink)
Biologists, ecologists, and bird enthusiasts want to estimate bird population trends in order to monitor changes in ecosystems. Recently, time-consuming field observations of birds have been augmented by audio recordings of birds. In the lab, we deciphered the types of birds singing in these recordings. We used wavelet transforms to convert audio signals into images called scalograms. These scalograms display bird songs in a format similar to sheet music; they show how the pitch and volume of a bird’s song change over time. After applying denoising methods to the images, we trained a neural network to identify the birds from the processed images. Although wavelet transforms, image processing, and neural networks are all vital components to analyzing birds calls, this talk will specifically be focused on neural networks.

Upcoming Colloquia

The  following additional colloquia are on the schedule for this semester, but more will be added.
  • October 20 and 21, Andrew Christlieb, Michigan State University (The Gentile Lectures)
  • Thursday, November 17, Victor Piercey, Ferris State University

Math Club  Game Night!

Do you like to play games?  Or, maybe you've never been to a game night, but would like to try it out. 

We've got some awesome games (party games, strategy games, skill games, card games, etc.) for you and your friends to play and we would love it if you to bring your own games and your friends to the first Math Club game night on Friday, September 30 at 7 pm in Schaap 1116. 

The first and only rule of Math Club Game Night is that everyone should have fun!  Please come!

Interview with Dr. Martha Precup, Mathematics Postdoctoral Researcher at Northwestern University

Martha Precup is a 2008 Hope College graduate and mathematics major. After Hope she earned a Ph.D. in mathematics at the University of Notre Dame. She then spent two years as a postdoctural associate at Baylor University and is now in her second year in a postdoctural lecture position at Northwestern University. The following interview was conducted last week.

Martha, you were a math major when you went to Hope College.  What were your favorite math memories and experiences at Hope?

During the summer after my sophomore year, I got to participate in a research experience for undergraduates (REU) on a project with Dr. Aaron Cinzori.  It was one of my favorite summers!  I learned a lot about math research, and I really enjoyed thinking carefully about the problem and trying out different methods.  My group was actually able to publish a paper on our results.  I’m still in touch with some of the other students I met at the REU that summer, and see them regularly at conferences!  We had a great time working—but we also enjoyed the beach.

So by your sophomore year you obviously had an interest in math, but when did your interest in math begin and what has sustained that interest?  Are there particular things that you love about math?

My interest in math began after taking my first proof writing course at Hope.  I find it very satisfying to fully understand and dissect a problem.  (I mean, how do you really know that the sum of two even numbers is even?)  In fact, as I soon discovered, this is what math research is all about!  Although it can be frustrating, it is amazing how mathematics can be used to connect different ideas and simple truths.  In some ways, math is more like art than science.  The challenge of solving a problem and trying to see it from all different angles is what I find so satisfying about what I do. 

I understand for your research you study Lie theory.  Is Lie theory about lies?  Please tell us what Lie theory is about and how you became interested in it.

Hahaha.  No lie, Lie theory is named for the work of mathematician Sophus Lie.  He showed that certain groups could be studied more easily by considering a special kind of vector space instead.  All that last sentence means is that the goal of Lie theory to take difficult problems from abstract algebra and turn them into easier ones in linear algebra.  In my research, I usually take a hard problem and turn it into an easier one about matrices—the kind you learn about in the first few weeks of a linear algebra class.  Since linear algebra was one of my favorite classes (hat tip to Drs. Mark Pearson and Airat Bekmetjev for teaching me linear algebra), I decided that this was the research for me!

So you enjoyed summer research and linear algebra while at Hope, could you share something else interesting with us, either about yourself or something else interesting about math while you were a Hope student?.

When I started school at Hope, I had no background in Calculus!  Lots of students think that if they do not take calculus in high school then they are already behind, and math probably isn’t for them.  If you didn’t take calculus or other math classes (or even if you did) I encourage you to try them out at college!  I actually got a D on my first Calculus 1 exam at Hope!  After that, I realized I didn’t really understand the class.  I doubled down in my studying efforts, and it turned out the this class was much more interesting than I had originally thought. 

Stephanie Harper receives a Mathematics Education Scholarship

Stephie Harper recently received word that she has been awarded a $2,500 Miriam B. Schaefer Scholarship from the Michigan Council of Mathematics Teachers. Stephie is a senior, dual major (Mathematics, Elementary Education and Integrated Science Group, Elementary Education) and is currently student teaching.  She is the fifth recipient of this award at Hope. Prof. Kate Vance was our first winner in the scholarship’s inaugural year and Melanie Leonard was Hope's most recent recipient in 2013.
Stephie worked with Prof. Eric Mann as a teaching assistant for his Mathematics for Elementary Teachers courses as well as helped him restructure these courses during the summer to help better meet the needs of the students. In describing Stephie's work, Prof Mann said, "Her work was exceptional; comparable to that of experienced teachers I have had as graduate students at other universities. I have enjoyed (and learned from) our long conversations exploring ways to teach mathematics and science to meet students’ needs at all levels of readiness."

Congratulations Prof. Stephanie Edwards!

A big congratulations to Prof. Stephanie Edwards on her marriage to Shawn Teegardin last Friday. Professors Chuck Cusack and Brian Yurk served as witnesses. After the ceremony the wedding party returned to the mathematics department's Ice Cream and Fun event to celebrate with the mathematics students and faculty.

Prof. Chuck Cusack's mathematical art is now on display at ArtPrize

Prof. Chuck Cusack, a member of both the Mathematics Department and Computer Science Department at Hope College, is currently competing in ArtPrize, the world's largest art prize competition.  He creates mathematical art out of Lego bricks.  His entry this year, Increasing Asquareness, a Fibonacci Rectangle made out of Latin squares, is currently on display at the Fifth Third Bank Plaza located at 111 Lyon Street in downtown Grand Rapids.

You can vote for this this piece of art by registering at the Artprize website, downloading the app, and visiting ArtPrize. Round one voting continues through October 1. The number of this piece is 62580 and Chuck says to vote early and often so he has increasing avoteness.

Math Man posts inspirational signs

Todd Swanson, OOAT News Desk Correspondent: Hi, Math Man!  Some students took a picture of you posting "Learn Like a Champion Today" signs in the math hallways and classrooms.  Why did you do that?

Math Man: I went to the Notre Dame vs. Michigan State football game last weekend, and the people near me said that the Notre Dame football players have a "Play Like a Champion Today" sign on the tunnel leading from the locker room to the field that players touch on their way out to play the game.

TS: So, what do you hope to accomplish by posting the "Learn Like a Champion Today" signs?

MM: Well, I want students to be fired up to learn!  I want students to enjoy what they're doing and to "play hard on the math plane" just like the footballers play hard on the field.  I want students to do homework problems together so that they spend less time on answer-checking algebra, more time learning concepts, and more time giving and getting the immediate feedback to and from others that's so critical for learning.  Plus, working with others is fun!  When studying alone, I want students to use active studying techniques, such as working through an example in the textbook by writing down the problem statement, closing the book, writing as much of the solution as possible, and then going back to the example in the book when stuck or finished to get feedback.  Do students know that half of the homework questions in the book have answers in the back?  Isn't that great?  I also want to encourage students to get the help they need on a regular basis from the free Math Lab and from visiting their professors' office hours!

TS: Thanks for caring about our students, Math Man!  You'll always be our favorite super hero! (Though based on the outcome of the football game, the team from my alma mater, MSU, played a bit more like champions than the Fighting Irish. Maybe Notre Dame needs a bigger sign!)

IT & Actuarial Career Opportunity Day

Auto-Owners invites you to their annual Information Technology & Actuarial Career Opportunity Day! The event is on Friday, October 14, 2016 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.

Register online here from now until end of day Monday, October 10th. If you have any questions, please email Erin McLaughlin at or call 517-886-1855.

Problem Solvers of the Fortnight

In our last Problem of the Fortnight we presented the following conversation between Math Man and Prof. Cinzori:

"Hey, Professor Cinzori.  What's that?"

"Oh, hey, Math Man.  This thing?  It's a die."
"No, I know it's a dice -- or, I mean, die -- I always get those words mixed up.  Mostly because they don't make sense to me, I think.  I mean, if we have two dice and one die, shouldn't we have two mice and one mie? . . .  Anyway, what I was asking was what shape is that?"
"Oh, it's an icosahedron.  I always carry an icosahedral die in my pocket.  You never know when such a thing will be useful."
"How many sides does it have?"
"Twenty.  Each side is an equilateral triangle."
"How long are the sides of the triangles?"
"One centimeter."
"So what's its diameter?"
"Well, Math Man, I have to run to class.  But you have enough information now to figure it out for yourself."

Congratulations to Brandon Brown, Michaela Jurewicz, Jenna King, Philip LaPorte, Chris Manquen, Jacquelyn Schwark, Daria Solomon, Ashley Trojniak, Alli VanderStoep, and Brittney Weickel -- all of whom came to Math Man's assistance by correctly solving the Problem of the Fortnight in the last issue of America's premiere fortnightly electronic mathematics department newsletter.

Problem of the Fortnight

Hi, Professor Vance!
Oh, hi, Math Man.  How are you?
Just fine, thanks.  But I'm a little puzzled at the moment.  I found this diagram on a piece of paper outside your office door.  I think one of your students must have dropped it.
Well, puzzle no longer, Math Man.  I can tell you whose that is!  It's actually mine -- and I need it for my class today.  So, I'm really glad you found it.  Thanks, Math Man!
Well, sure.  Happy to help.  But I wasn't really puzzled about whose paper it was.  I was puzzled about what the diagram is supposed to be showing.
I can help you there, too!  It's a proof of the law of cosines.
Really?!?  That's neat! . . . .  Just one question: what's the law of cosines, and how does this picture prove it?"
I think that was two questions.
Well, I wasn't sure how to count that compound sentence.  I mean, there are two questions, but they're joined by a conjunction to make a single sentence. . . .  Well, whatever.  Can you help me understand this?
Sorry, Math Man, I can't right now.  I have to run to class.  Thanks for finding this diagram, though!
But wait!  Could you just tell me what the law of cosines is?

On her way out the door, Professor Vance says, "Not right now, Math Man.  Sorry.  I'm running late as it is.  You can Google it, though."
"Yeah, I suppose.  That will tell me what the law of cosines is, but how in the world is this diagram supposed to prove anything?"
Walking down the hall, Professor Vance turns and, walking backwards, says, "That's a good puzzle for you.  You figure it out!"

Help Math Man with his latest mathematical conundrum by explaining how this diagram proves the law of cosines.  Write your solution on a triangular piece of paper, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Friday, September 30.  As always, be sure to include your name and the name(s) of your math professor(s) -- e.g. Noah Dia, Professors I.M. Lost and Bea Wildered -- on your solution.  Good luck and have fun!    

Off on a Tangent bonus: Furbonacci Cats

The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

Charles Caleb Colton

Off on a Tangent