Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 October 9, 2015 Vol. 14, No. 3

Hope graduate returns to present at next colloquium 

Title: Using Gauss Sums to Distinguish Certain Algebraic Structures 
Speaker: Ryan Johnson, Grace College
Time:  Thursday, October 15 at 4:00 pm
Place:  Vanderwerf 102

Fusion categories are complicated algebraic structures found in diverse branches of mathematics and physics.  Quantum computing is one specific example that will be mentioned in this talk.  Classification of fusion categories is a main driving question for mathematicians in this area.  A natural method for classifying objects in mathematics is via numerical invariants.  We will consider a subclass of fusion categories and a sequence of invariants of these structures.  As it turns out, the invariants can be written as Gauss sums.  Gauss sums have a rich, well-studied history, and we can also use Gauss sums to create interesting pictures.  We use Gauss sums to prove that our invariants distinguish between different fusion categories in our subclass. 

Upcoming colloquium celebrates World Statistics Day

Title: Introduction to Statistical Data Mining
Speaker: Brad Westgate, Alma College
Time:  Tuesday, October 20 at 4:00 pm
Place:  Vanderwerf 102

Abstract:  Data mining involves extracting as much information as possible from a large dataset.  We will review different branches of data mining, including classification and clustering.  Classification refers to predicting an unknown categorical variable, using several observed variables.  For example, we might predict whether a customer will buy our product or not, using information about the customer's previous purchases.   Clustering refers to grouping a complicated dataset into smaller clusters.  For example, we might group all our customers into a few "personas," to use for marketing.  We will discuss classification and clustering methods, including Naive Bayes and the k-means algorithm, and apply these methods to real datasets.

Upcoming Colloquia

The following colloquia are currently on the schedule for the rest of the semester:
  • Tuesday , November 3, 4:00pm: Kylie Young and Cheryl Gabriel, Watkins Ross in Grand Rapids  
  • Tuesday, November 10, 11:00am: Paul Pearson, Hope College     
  • Tuesday, November 17, 4:00pm: Anil Venkatesh, Ferris State    
  • Tuesday, December 1, 4:00pm, Hope students 
  • Thursday, December 10, 11:00am, Tim Pennings, Davenport University  

Math Club

The Math Club's first game night will be Saturday, October 17 starting at 7 pm in Schaap 1118.  According to the official rules of the International Society for Math Club Game Nights: (1) you must bring yourself to game night, (2) you are encouraged to bring your friends to game night, (3) fun and interesting games must be provided by game night organizers, (4) you are allowed to bring games to share (e.g., a card game, a board game, or a math game), and (5) people must have fun at game night. 

For more info on the Hope Math Club's latest and greatest activities, visit our brand new FaceBook page, where you can also suggest future Math Club activities!

MATH Challenge

The 2015 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place on the morning (9:30am - 12:30pm) of Saturday, November 7 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. The sign-up deadline is Friday, October 23 at 4:00 p.m.  Interested students can sign up by sending Prof. Cinzori an email at

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. 

Math in the News: The abc conjecture proven?

IN 2012, mathematician Shinichi Mochizuki of Kyoto University released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers and has been called the most important unsolved problem in mathematics.  The proofs of many important theorems in number theory, such as Fermat's Last Theorem, follow immediately from the conjecture.

We reported on this in Off on a Tangent back in 2012, so why is it still in the news? Well apparently the proof isn't as easy as abc. Mathematicians are still working on understanding Mochizuki's work. He apparently invented a new branch of mathematics to complete his work. So even experts in number theory are having a hard time understanding what he is saying.

For more information see the 2012 article from Nature about the proof, visit Dr. Mochizuki's page where he lists his papers, or read the recent article in Scientific American that talks about the how the proof has been accepted in the past three years.

Hey Vsauce! Math on YouTube

Have you seen the YouTube channel  Vsauce? The videos posted there are hosted by Michael Stevens. He explores a number of scientific and philosophical topics and every now and then the topic is mathematical in nature. In an video on Zipf's Law Stevens explores that the frequency of a word's use is inversely proportional to its rank. This not only occurs in words in the English language, but in any language.

This reminds the editorial staff at Off on a Tangent of Benford's Law. This law states that the proportion of times the leading digit (d) of a large collection of numbers appears is log(1+1/d). The property of numbers is used to detect fraud since people don't make up numbers that follow Benford's Law. Another mathematical YouTube channel called Numberphile recently posted a video about Benford's Law. Check it out!

Problem Solvers of the Fortnight

In our last problem of the fortnight we told you about three students, Ann, Bob, and Cal, that competed in a series of tests.  For coming in first on any given test, one is awarded x points; for placing second, y points; and for third place, z points.  Here x, y, and z are natural numbers with x > y > z.  There were no ties on any of the tests.  Altogether, Ann accumulated 20 points; Bob scored 10 points, and Cal received 9 points.  Ann came in second on the Algebra test.  Who finished second on the Geometry test?

Congratulations to Colton Bates, Dalton Blood, TaeHyun Choi, Brooke Draggoo, Richard Edwards, Katie Finn, Russel H, Ben Hahn, Matthew Harkema, Sherah Head, Emily Kain, Cassidy Kessel, Alex Klunder, Adam Krahn, Anna Krueger, Samantha Mattingly, Maura McAfee, Aaron Micah, Anne O'Donnell, Tiffany Oken, Elizabeth Orians, Sarah Sheridan, Anna Snyder, Julia Toren, Tyler Valicevic, Kathryn Trentadue, and Landon Brower -- all of whom
correctly solved the Problem of the Fortnight in the last issue of America's leading fortnighly mathematics department electronic newsletter.

Problem of the Fortnight

Eleven Pullers (who refused to divulge whether they were Odd or Even Year) are developing a secret sticky substance to put on their hands for next year's Pull that would both give them better grip on the rope and prevent rope burn.  To keep their invention secure, they put it in a safe with a number of different locks.  Each Puller is given the same number of keys, although not necessarily the same keys.  The eleven Pullers want to be able to open the safe if and only if a majority of them are present.  What is the minimum number of locks they need to put on the safe, and how many keys does each Puller have?

Attach your solution to a string, 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, October 21.  As always, be sure to include your name as well as the name(s) of your math professor(s) -- e.g. Amber Leaf, Professor Sue Mack -- on your solution.

Even if you're on the right track, you'll get run over if you just sit there.

Will Rogers

Off on a Tangent