Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 November 20, 2015 Vol. 14, No. 6

 Colloquium after Thanksgiving will feature students

Title: Research by Hope College Mathematics Majors
Speakers: Jiyi Jiang, Tae Hyun Choi, Aaron Green & Cole Watson     
Time: Tuesday, December 1 at 7:00-7:50 pm
Place:  VanderWerf 102

Jiyi Jiang: Classifying Handwritten Digits Without Seeing an Image

Digital images of handwritten digits are high dimensional and vary with writing style. This work presents a method to perform classification on one of handwritten digits database, MNIST, and enable visualization in low dimensional space. To address the handwritten digit variation issue, the edges of each digit in an image are firstly highlighted by gradient feature extraction. Then, the curse of high dimension is broken by t-SNE algorithm, which constructs a certain “lens” so that one can visualize MNIST on two or three coordinates. The “lens” also helps trace from low dimension back to the high dimension in which clustering is applied  to assigned level sets and form a more explicit visible structure among all data points. The last process is done by Mapper algorithm.

Tae Hyun Choi: Examining the effects of heavily-censored survival data on quantile estimation and precision

The analysis of survival data (time to event data) is frequently complicated due the occurrence of right-censored observations. Many methods for dealing with this have been proposed, encompassing non-, semi- and parametric models for the data. In this talk, we explore the effects heavily-censored data have on quantile estimation as well as estimation precision. Comparisons will be made across methods and differences, advantages as well as disadvantages of these methods will be discussed.

 Aaron Green & Cole Watson: Graph Pebbling and Graham’s Conjecture

Graph pebbling is a game on a connected graph G in which pebbles are placed on the vertices of G. A pebbling move consists of removing two pebbles from vertex and adding one to an adjacent vertex. A configuration of pebbles is r-solvable if for a given target vertex r, there is a sequence of pebbling moves so that at least one pebble can be placed on r. The pebbling number of a graph G is the smallest integer π(G) such that any configuration that uses π(G) pebbles is r-solvable for any r in V (G). A long standing conjecture in graph pebbling is Graham’s Conjecture. It states that given any two graphs G and H, π(G□H) ≤ π(G)π(H), where G□H is the Cartesian product of graphs. A graph G satisfies the two-pebbling property if two pebbles can be placed on any vertex v in V(G) given any configuration of 2π(G)-q+1 pebbles, where q is the number of vertices that have at least one pebble. The smallest known graph that does not satisfy the two-pebbling property is called the Lemke graph (L). We will show that Graham’s conjecture holds for such families as L□Kn and several others.

Upcoming Colloquium

After the next fortnight, there is only one colloquium currently on the schedule for the semester.
  • Thursday, December 10, 11:00am, Tim Pennings, Davenport University  

Math Club News

Math Club invites you and your friends to "A Brilliant Young Mind" at the Knickerbocker Theater (downtown Holland) on Friday, December 4. We plan to meet in the lobby at approximately 7:20 pm Friday and then find seats. Bring your Hope student ID for free admission. The movie has both math and romance, so it must be good!

Movie description (from the Knickerbocker website):

In a world difficult to comprehend, Nathan struggles to connect with those around him - most of all his loving mother - but finds comfort in numbers. When Nathan is taken under the wing of unconventional and anarchic teacher, Mr. Humphreys, the pair forge an unusual friendship and Nathan's talents win him a place on the UK team at the International Mathematics Olympiad. From suburban England to bustling Taipei and back again, Nathan builds complex relationships as he is confronted by the irrational nature of love.

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).

Hope students participate in the MATH Challenge

Hope again had a great turnout of students participating in the Michigan Autumn Take-Home Challenge on November 7 this year.
Students competed with other students around the state (as well as other states) working in groups on ten interesting problems. We look forward to hearing the results in the near future.

The following students competed (grouped by team):
  • Elizabeth Orians, Russell Houpt, Andrew Shay
  • Kimberly DeGlopper, Tiffany Oken, Kathryn Trentadue
  • Justin Richardson, Brennan Heidema, Cordell Engbers
  • Sarah Sheridan, Molly Meyer, Daria Solomon
  • Emily Joosse, Jacob Jansen, Benjamin Pederson
  • Jason Gombas, Mark Powers, Mark VanderStoep
  • Eric Krzak, Jake Verschueren
  • Nathan Rock, Rachel Alfond, Denver Stevens
  • Baylie Moony, Carrie Ritter
  • Cole Watson, Zac Geschwendt, Evan Vogel
  • Megan Klintworth, Kristen Pogats
  • Melissa Kindinger, Richard Kish, Tom Ritzman

Math in the News: Sports outcomes are quite predictable

A few weeks ago Michigan State's football team beat Indiana in what could be described as a close game with a final score of 52 to 26. How is a 52-26 game close? While most of the game was very close, MSU scored 21 points in the last five minutes while Indiana mostly stood there and watched.

Apparently this is not an unusual event in sports. Researchers at the University of Colorado and the Santa Fe Institute recently published a paper on the scoring patterns that occur in different sports with most of their research done by looking at basketball games. They found that the highest leads tend to occur fairly early or fairly late in games. While scoring in these times tend to be more erratic, most of the game is similar to watching ten players flip coins. Speaking more mathematically, they found that scoring during the most of the game conforms to a "random walk process."

For more information, read an article at

Problem Solvers of the Fortnight

In our last problem of the fortnight we showed square ABCD with 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?

Congratulations to Robert Abbaduska, George Baker, Michaela Biegner, Page Bleicher, Dalton Blood, Tae Hyun Choi, Brooke Draggoo, Richard Edwards, Kate Finn, Tyler Gast, Zach Geschwendt, Lindsey Gryniewicz, Ben Hahn, Justin Hanselman, Russell Houpt, Lara Iaderosa, Jesse Ickes, Jiyi Jiang, Erik Johnson, Tom Johnson, Cassidy Kessel, Anna Krueger, Eric Krzak, Nolan Ladd, Noah Lihviller, Elizabeth Orians, Christian Otteman, Kim Palmer, Ivy Peterson, Katie Reed, Megan Shibley, Daria Solomon, Jack Thompson, Kathryn Trentadue, Tyler  Valicevic, Joey Watson, and Grace Wiesner -- all of whom correctly solved the Problem of the Fortnight in the last issue of America's leading fortnightly electronic mathematics department newsletter.

Problem of the Fortnight

After Thanksgiving dinner, sit back, relax, and let your mind chew on the following problem. Find all real values of x, with x greater than or equal to 3, that satisfy the following equation:

Write your solution on a napkin from your Thanksgiving feast, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Wednesday, December 2.  As always, be sure to include your name and the name(s) of your math professor(s) -- e.g. Tofer Key, Professor Tor Dokken --  on your solution.

The length of your education is less important than its breadth, and the length of your life is less important than its depth.

Marilyn Vos Savant

Off on a Tangent