Off on a Tangent 17.4

A colloquium for the dogs

  • Title: Do Dogs Know Calculus?
  • Speaker: Dr. Tim Pennings, Davenport University
  • When/Where: 11:00 AM on Thursday, November 8 in VanderWerf 102

A standard calculus problem is to find the quickest path from a point on shore to a point in the lake, given that running speed is greater than swimming speed. Elvis, my Welsh Corgi, never had a calculus course. But when we played “fetch” at Lake Michigan, he appeared to choose paths close to the calculus answer. In this talk we form a mathematical model and reveal what was found when we experimentally tested this ability.

What’s going on with this graph?

What’s Going On in This Graph? is a fairly new weekly activity from the American Statistical Association and The New York Times. Each week an interesting graph is shown and students are asked questions like “What do you notice?” and “What do you wonder?”

On the Friday following the release, The New York Times Learning Network publishes a “reveal”—a follow-up that includes the original article, summary of student responses, additional questions students may want to answer, and stat nuggets.

This week’s graph in involves red states and blue states and various voting rights issues. Check it out here.

Problem Solvers of the Fortnight

We had a large escargatoire of snails and huge bale of turtles work on our last problem of the fortnight. Congratulations to Camen Andrews, Barry Bait, Cal Barrett, Meredith Bomers, Josiah Brett, Evan Bright, Dominick Byrne, Jeremiah Casterline, Grace Charnesky, Adair Cutler, Liz Cutlip, Annie Dankovich, Emily Dee, Ford Fishman, Ce Gao, Timothy Hwang, Elizabeth Inthisane, Jackson Krebsbach, Jiangcheng Lu, James Mandeville, Michelle Mathenge, Kianna Novak, Jacob Nurenberg, Megan O’Donnell, Zheng Qu, Karen Quay, Theo Roffey, Hugh Thiel, Hans Veldman, Thomas Vongphrachanh, Fangtao Wang, Tracy Westra, Kamaron Wilcox, Yizhe Zhang, and Jacob Zoerhof – all of whom correctly solved the Problem of the Fortnight in the last issue of America’s preeminent fortnightly mathematics department news blog.

Problem of the Fortnight

Autumn walked into the Peanut Store last week to buy some jelly beans for Halloween. “I’d like a hundred jelly beans,” she told the manager. “I’m sorry. I can’t do that,” he said. “What do you mean?” asked Autumn. “I can’t sell you a hundred jelly beans,” he said, “because my scoops have been bewitched. You see, the purple scoop only scoops to the next largest multiple of 30, the green scoop only scoops to the next largest multiple of 70, and my orange scoop only scoops to the next largest multiple of 110.” “I don’t understand,” said Autumn. “Well, for instance,” the manager explained, “let’s say you had 70 jelly beans. I could increase your jelly bean count to 90 with the purple scoop, or to 110 with the orange scoop, or to 140 with the green scoop.” After musing about this curious situation for a moment, Autumn said, “Okay. If you can’t give me 100 jelly beans, then please give me the smallest number of jelly beans that you could scoop out for me in more than 100 ways.” After thinking for a few moments and scribbling a few calculations on the back of a salt water taffy wrapper, the manager gave her a bag with that many jelly beans in it.

How many jelly beans were in Autumn’s bag?

Write your solution on a scrap of paper and affix to it (by staple, paperclip or glue) a piece of your favorite Halloween candy, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson’s office – room 212 in The Werf – by 3:00 p.m. on Friday, November 2. As always, be sure to include your name and the name(s) of your math professor(s) – e.g. Reese S. P. Sess, Professor Lemonhead – on your solution. Good luck and have fun!

Just one more thing …

We will leave you with a picture of Prof. Vance and her family taken last weekend during Hope’s Homecoming Donut Run. The staff at Off on a Tangent thinks the run should be renamed Run Torus!, Run!

They just felt like runnin’.

Off on a Tangent 17.3

The intricacies of card shuffling will be explored in the next colloquium

  • Title: Card Shuffling 101
  • Speaker: Dr. Darin Stephenson, Hope College Mathematics Department
  • When/Where: 4:00 pm, Thur. Oct 25 in Schaap 1000

Abstract: We discuss the physical process of card shuffling (by various methods) and ways in which these processes can be modeled mathematically. Interesting mathematical questions include “How many shuffles are required to sufficiently ‘mix up’ a deck of cards?” and “How many shuffles will it take to return a deck of cards to its original ordering?” We will also discuss ways various people have exploited the mathematics of card shuffling to cheat at cards or perform card tricks. We will develop the necessary mathematical background relating to permutations and randomness, and explain some other real-world applications of these mathematical notions.

MATH Challenge

The 2018 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place on the morning (9:30am – 12:30pm) of Saturday, November 3 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 Monday, October 22 at 5:00 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 encouraged 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.

U of M Biostatistics Prospective Student Day

The Department of Biostatistics at the University of Michigan will hold a Prospective Student Information Day on Saturday, November 10, 2018. The purpose of this event is to provide information to students who may be interested in graduate study in biostatistics. They expect attendees to be undergraduate and masters students who have identified biostatistics as their interest area, as well as students who are completing an undergraduate degree in math, statistics, biology, or some related discipline, and have not yet decided on their future plans.

At the event, presentations by students and faculty will focus on what biostatistics is and what biostatisticians do, on the job opportunities in biostatistics, and on the admissions and financial support opportunities at the University.

For more information, take a look at their flyer or visit their website (where you can also register).

Problem Solvers of the Fortnight

Congratulations to Holly Denouden, Ce Gao, Zheng Qu, Cole Persch, Hugh Thiel, and Yizhe Zhang – all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department blogosphere news post.

Problem of the Fortnight

Tommy Turtle and a Sammy Snail are at the corner of a cubical aquarium with side length 3 ft.  “Wanna race to the opposite corner?” asks Tommy.  “Well . . . I . . . suppose . . . some  . . . exercise . . . might . . . be . . . nice,” Sammy replies.  Tommy can swim through the interior of the cube at a rate of 6 ft/min, while Sammy has to stick to the sides but can slide along at a rate of 2 ft/min.  If they take off at the same time, how long, to the nearest tenth of a second, does Tommy have to wait for Sammy at the opposite corner (assuming, of course, they both go on their respective shortest routes)?

Write your solution on a cubical aquarium (of any size) and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson’s office, room 212 in The Werf, by 3:00 p.m. on Friday, October 19.  As always, be sure to include your name and the name(s) of your math professor(s) – e.g. Ellie DeLuits, Professor N. Candessent – on your solution.  Good luck and have fun!