Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
February 3, 2017 Vol. 15, No. 8
http://www.math.hope.edu/newsletter.html


Hope grad returns to present at next week's colloquium



Title: Swarms of fireflies to restarting the heart: modeling the onset of synchrony
Speaker: Dr. Mark Panaggio ’09, Assistant Professor of Mathematics, Hillsdale College
Time:  Tuesday, February 7 at 4 pm 
Place:  VanderWerf 104

Many natural and engineered systems are made up of components that exhibit oscillatory behavior. When these components interact, they often spontaneously begin to oscillate in unison, a phenomenon that has been observed in swarms of fireflies and pedestrians on bridges. Synchronization has a critical role in the transportation of blood throughout the human body, electricity on the power grid, and information between telecommunication devices and a breakdown of synchrony can be detrimental to the efficient operation of these systems.  In this talk, I will discuss the Kuramoto model, a mathematical model that describes the dynamics of a network of coupled oscillators. Analysis of this idealized model will reveal a variety of interesting and unexpected behaviors including phase transitions and the formation of asynchronous patterns and can shed light on both the emergence and collapse of synchronization in nature.


Upcoming Colloquia


We have the following additional math colloquia on the schedule for this semester. More will most likely be added.
  • Fri, Feb 24 at 3:00 PM in VWF 102: Dr. Seth Guikema - University of Michigan
  • Tue, Mar 14 at 11:00 AM in VWF 102: Dr. Dave Kung - St. Mary's College of Maryland 
  • Tue, Mar 14 at 4:00 PM in VWF 102: Dr. Dave Kung - St. Mary's College of Maryland 
  • Thur, Apr, 20 at 4:00 PM in VWF 102: Dr. Lauren Keough - GVSU



Lower Michigan Mathematics Competition


The 41st Annual Lower Michigan Mathematics Competition (LMMC) will be held at UM-Flint this year on Saturday, April 8.  Students from colleges and universities in Michigan will gather to challenge themselves on ten interesting problems, working together in teams of up to three people. The competition takes place in the morning and after lunch there is a discussion of the solutions. 

If you want to participate, you must sign up by Wednesday, March 15 (right before spring break) by sending Prof. Cinzori's an email at cinzori@hope.edu.  You may register as a team (of two or three) or individually (and you will be placed on a team).

The picture shown with Hope Students holding the Klein Bottle Trophy for winning the LMMC is getting a bit old. It would be nice to have a victorious team so this picture could be updated!


Summer workshop on big data available to undergraduates

The University of Michigan Biostatistics, Statistics and Electrical Engineering & Computer Science departments are running a six-week workshop this June and July in Ann Arbor on big data, targeted specifically at undergraduates. There is no cost to attend, and accepted applicants will receive a stipend to cover living expenses.

Lectures will be led by a diverse group of stellar biostatistics, statistics, electrical engineering, and computer science faculty at the University of Michigan. Working in teams, students will participate in mentored big data research projects.

Application closes March 1, 2017. For more information about the workshop and an application visit https://sph.umich.edu/bdsi/


 Statistics Showcase


The 15th annual Statistics Showcase, held on Friday, January 20, recognized six outstanding student statistics projects of the Fall 2016 semester. Congratulations go out to all of these students for their hard work and outstanding results. The following projects were presented.
  • “Cell Phone Use and Studying” by Lauren DeYoung, Kelly O’cock, Victoria Swift, and Carolyn Williams
  • “Gender and Charity” by Travis Alderman, Noah Mellifont, Riley Schmitz, and Peter Smith
  • “Health Awareness and How it Affects Eating Behavior” by Leah Asen, Alexis Cutler*, Justin Folkert, and Abby Whitwam
  • “Modern Biases of Grading Tests” by Annah Duffey, Catherine Dustrude, Bryanna Pratt, and Hanna Town-Bowen 
  • “Money and Politics Research” by Grace Commire, Annie Dokter, and Harley Schultz
  • “The Effects of a Dominantly Left Brain” by Jordan Benjamin, Micah Manthei, and Matthew Orr



Euclidea is an app for geometric constructions

 
If you miss doing straightedge and compass drawings from your high school geometry class, we found an app for you and you don't even need a straightedge or compass.  The site is called Euclidea and it can be accessed on a computer or you can download a free app for your phone.

The authors state, "With Euclidea you don’t need to think about cleanness or accuracy of your drawing — Euclidea will do it for you. But it’s also a game. A game that values simplicity and mathematical beauty. Find the most elegant solution — the one, which is built in the least possible moves, — and you’ll get the highest score."


Math in Action

Math in Action presents lively and informative discussions of current issues in mathematics education while providing an opportunity for practicing PreK – 12 teachers, prospective teachers, curriculum directors, and college and university faculty to share ideas, concerns, and resources. The conference consists of six hour-long sessions with eight separate interactive presentations during each. 

Last year the Math Department was able to fund the registration costs and provide transportation to the conference for interested Math Ed majors.  We are making the trip this year and again the department will cover costs for our majors.

In order to get the transportation request submitted in time, and to get the early bird registration rate, if you are interested in attending please let Dr. Mann know by Feb 7th.  As payment is required when you register, Dr. Mann will be happy to do that for you and charge it to the department.  The GVSU folks ask that you list a first and second choice for each session so that they can have a sense of rooms and resource needed.  The brochure describes the choices for each session.  What worked well last year was to have you fill out the first part of the registration form at the Math in Action website, print it and give it to Dr. Mann and he will take care of completing your registration. 

The keynote speaker is Tracy Zager who has a new book out, Becoming the Math Teacher you Wish You'd Had. You can preview the book here



Problem Solvers of the Fortnight


In our last problem of the fortnight we saw the following exchange between Math Man and Vectoria:

"Hi, Vectoria!"
Looking up from her table at Van Wylen, Vectoria says, "Oh, hi, Double M.  You seem chipper."
"Well, I had a great Christmas break.  I got caught up on some sleep over the holidays, and I'm feeling rejuvenated at the start of this new semester."
"Hey, that's great. . . ."  Vectoria's voice trails off as she turns her attention back to the papers strewn out on the table before her.

"What are you looking at, Vectoria?"
"Oh, it's this problem I've been thinking about off and on for the past day or two.  The other day as I was sitting in the chapel, I looked up at a stained glass window, and an interesting shape caught my attention.  It was a square, probably 2-ft on each side.  Two quarter circles, centered at the lower vertices of the square, intersected each other to form something like this," said Vectoria, as she showed Math Man the picture she had drawn:

"Wow, you draw really neat pictures, Vectoria!"
"Thanks, M's.  What I was wondering," Vectoria continued, "was whether I could find the areas of the smaller regions in the square."
"Hmmm. . . .  Which region in particular?"
"Oh, I don't know.  Any of them, I suppose.  I think once you found one, you could probably get the others."
"Yeah, maybe you're right. . . .  It's kind of a cool problem.  Can I work on it with you?"
"Sure!  Which region should we tackle first, Double M?"
"How about ABE?"

Congratulations to Brandon Brown, Owen Donahoe, Richard Edwards, Jeffrey Engle, Jason Gombas, Keri Haddrill, Philip LaPorte, Alex Osterbaan, Babu Bhatt, Zheng Qu, Hugh Thiel, Joey Watson, Elizabeth Woodford, Jincheng Yang, and YungChul Yoon -- all of whom correctly solved the first P. Fort of the new year!




Problem of the Fortnight


On her way through Van Wylen Library, Vectoria spots Math Man sitting on a table, deep in thought.

"Hey, M's.  What'cha doin'?"
"Well, I was trying to figure out this math problem: If r1 and r2 are the roots of x2 + bx + c = 0, then the sum of the roots is -b and the product of the roots is c.  Why is that?"
"Oh, well, if
r1 and r2 are the roots of the x2 + bx + c, then it must factor as (x - r1)(x - r2), which multiplies out to
x2 - (r1 + r2)x + r1r2,
and since this has to be equal to x2 + bx + c, we need -(r1 + r2) = b and r1r2 = c."

"Oh, that's cool!  I didn't know that."
"Yeah, it's kind of interesting, I guess.  But why did you want to know that, Double M?"
"Oh, I don't really.  It's just a hint that Professor Airat Bekmetjev gave me for the problem I'm really interested in."
"Airat Bekmetjev. . . .  What kind of a name is that?"
"I don't know.  I think maybe it's Dutch."
"Hmmm. . . .  Anyway, what's the other problem you're working on?"

"Oh, it's kind of cool.  A line intersects the hyperbola xy = 1 at points P and Q  and the x-axis at A and the y-axis at B.  The problem is to prove that AP = BQ"
"Wait!  Any line?"
"Yeah, I guess so.  It just says 'a line,' so I'm assuming it means any line that intersects the curve in two points and also the x- and y-axes."
"And what about P and Q?  Do they have to be in any particular positions?"
"No, I don't think so.  It just says they are points where the line intersects the hyperbola.  I think they could be either like this . . . or like this," Math Man says, showing Vectoria the figures he's drawn.


"Hmmm. . . .  That is kind of a cool problem.  But how does Dr. B's hint help?"
"I don't know.   That's what I'm trying to figure out."

Help Math Man and Vectoria by proving that AP = BQ, explaining your reasoning clearly and carefully.  Submit your solution to the Problem of the Fortnight slot outside Professor Mark Pearson's office by 3:00 p.m. on Friday, February 10.  As always, be sure to include your name, as well as the name(s) of your math professor(s) -- e.g. Noah Dia, Professors Les Schur and Rhea Lee -- on your solution.  Good luck and have fun!  




You'll get mixed up, of course,
as you already know.
You'll get mixed up
with many strange birds as you go.
So be sure when you step.
Step with care and great tact
and remember that Life's
a Great Balancing Act.
Just never forget to be dexterous and deft.
And never mix up your right foot with your left.

And will you succeed?
Yes! You will, indeed!
(98 and 3/4 percent guaranteed.)

from
Oh the Places You'll Go
by Dr. Suess


Off on a Tangent