Off on a Tangent 17.9

Next Week’s Colloquium will focus on Actuarial Science

  • Title: Actuarial Science—Overview, career pathways, and the Society of Actuaries’ Probability Exam
  • Speaker: Dr. Yew Meng Koh and students
  • When/Where: Thursday, February 21 at 11:00 am in VWF 104

Abstract: Actuarial Science is an interesting and practical field, with rewarding career outcomes. The American Society of Actuaries offers a sequence of exams, the passing of which allows certification in this field. One of these exams is the Probability Exam (P Exam), for which Hope has a MATH361/363 course sequence which helps interested students in their preparation. In this talk, a brief overview of Actuarial Science and its possible career pathways will be presented. We will then focus on the P Exam by discussing its requirements and solving three past year problems from this exam (which do not require prior knowledge of probability). We will end with comments and encouragement from some Math department seniors who passed the P Exam in its most recent Jan 2019 offering.

UPCOMING COLLOQUIA

The following colloquia are currently scheduled for this semester. More should be added as the semester goes on.

  • Feb 21 at 11:00 am, Yew Meng Koh and students, Hope College
  • April 4 at 4:00 pm, Yew Meng Koh, Tyler Gast and John McMorris

Math in the News: Bees know arithmetic

In the biggest news to hit the math world since we learned that dogs know calculus, researchers in Australia recently discovered that bees know how to add and subtract. They were trained in arithmetic by learning that blue figures meant to add and yellow figures meant to subtract. They were then tested on their arithmetic knowledge by having to make decisions as to which direction to go when walking through a maze based on these color-coded addition or subtraction problems. And the bees in the study could do it, at least better than if they just randomly guessed. You can read a short article about this in Popular Science or the full paper in Science Advances.

Problem Solvers of the Fortnight

Congratulations to Anna Carlson, Jonathan Chaffer, Adam Czeranko, Emily Dee, Holly Denouden, Christian Forester, Andrew Gilpin, Ruth Holloway, Elizabeth Inthisane, Yiwei Jiang, Fiona Johnson, Jackson Krebsbach, Abigail LaDuke, Grant Lancaster, Julia Loula, Rebekah Ludema, Cole Manilla, John McMorris, Matthew Nguyen, Eleni Persinger, Morgan Platz, Eleda Plouch, Andrew Ragains, Forest Rulison, Emma Schaefer, Bethany VanHouten, Fangtao Wang, Jonathan Washburn, Anna Wormmeester, and Samantha Yacullo — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere mathematics department fortnightly news blog.

Problem of the Fortnight

If you throw a dart at a dartboard in the shape of a regular hexagon of side length 2 feet, what is the probability that your dart lands within 1 foot of any of the six corners of the hexagon.
Write your solution — not just the answer — on a piece of paper in the shape of a regular hexagon, 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, February 22.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Chuck N. Darts, Professor Corky Board — on your solution.  Good luck and have fun!

Off on a Tangent 17.8

Help needed in pre-colloquium build

We need a few students to help build the object shown below. This object (which I’m sure we will learn the name of during the colloquium) will be used in the colloquium on symmetry (details below). We will start the build at 2:00 PM on Tuesday, February 5 in the lobby outside the lecture halls on the first floor of VanderWerf. The build will probably last until around 4:00 PM. If you can’t come at the beginning, you are still welcomed to help when you can. As a bonus you can earn a colloquium credit for helping build!

Math Colloquium on Symmetry next week

  • Title: Symmetry: A mathematical approach using group theory and linear algebra
  • Speaker: Dr. David Reimann, Albion College
  • When/Where: 4 pm on Tue, Feb 5 in VanderWerf 102
Abstract: Symmetric patterns are used in many situations to decorate an object with a repeating motif that is translated, rotated, or reflected without changing size. We will see examples of several symmetry types and look at these from the vantage point of group theory. In particular, we will study rosette patterns, frieze patterns, wallpaper patterns, and patterns on the sphere. We will then see how we can create all these pattern types with a unified framework based on the vectors and matrices of linear algebra.

Upcoming Colloquia

The following colloquia are currently scheduled for this semester. More should be added as the semester goes on.

  • Feb 5 at 4:00 pm, David Reimann, Albion College
  • Feb 21 at 11:00 am, Yew Ming Koh and students, Hope College
  • April 4 at 4:00 pm, Yew Ming Koh and Tyler Gast

Students pass Actuarial Exam

All four senior mathematics majors from the Fall 2018 Probability for Actuaries class (Calvin Gentry, Jincheng Yang, Evan Bright, and Yizhe Zhang) who took the Society of Actuaries Probability Exam (Exam P) passed it during its most recent offering in January 2019. There will be a colloquium on Thursday Feb 21 at 11am which will serve as an overview of the Exam P and provide a summary of career pathways in Actuarial Science. Prof. Koh will also solve three past exam questions (which will not need prerequisite knowledge of Probability) and some of the students who passed Exam P will be there to share their experience taking the exam and offer advice and encouragement to interested students.

Statistics Showcase

The 17th annual Statistics Showcase, held Friday, January 18, recognized seven outstanding student statistics projects of the Fall 2018 semester. Congratulations go out to all of these students for their hard work and outstanding results. The following projects were presented.
  • “The Effects of Music on Memory Tasks” by Johanna Emmanuel, Sophia Kleinheksel, and Ian McNamara
  • “Accurate Portions: Shapes and Gender? by Jamie Breyfogle, Montserrat Dorantes, and Haley Russell
  • “How Do People React to Political Bias (Discrimination) Based on Party Affiliation” by Saydee Johns, Drew Schmitz, Curtis Turner, Samuel Vree, and Caleigh White
  • “Hope College and Recycling” by Franciska Loewen, Andrew Pavey, Jamie Westrate, and Andi Yost
  • “How Much Do You Remember: The Effects of Both Physical Activity and Gender on Working Memory?” by Jessica Danielle Bernal, Isaiah Hough, and William Woodhams
  • “Gender Stereotypes in the Workplace: The Next Generation?” by Rachel Hofman, Madison Kerber, Meghan Peel, and Jada Shelby
  • “Are We Dreaming of a White Christmas? A Study on Christmas Music and Feelings about Snow” by Hannah Bugg, Briar Hanlon, and Joseph Hernandez

Numberphile: How to pick the best porta-potty or soul mate

Problem Solvers of the Fortnight

Congratulations to Cal Barrett, Bradley Baysore, Meredith Bomers, Marina Budinsky, Jonathan Chaffer, Regan Corum, Adam Czeranko, Caroline Dargay, Idgie DeLoach, Holly Denouden, Christian Forester, Brandon Fuller, Graham Gould, Sydney Hines, Ruth Holloway, Elizabeth Inthisane, Yiwei Jiang, Fiona Johnson, Michael Kiley, Carson Koning, Jackson Krebsbach, Grant Lancaster, Mitchell Leonard, Dane Linsky, Julia Loula, Rebekah Ludema, James Manderville, Cole Manilla, Michelle Mathenge, Christopher McAuley, Cory McGregor, David McHugh, Marie McLaughlin, Rahja Flowers – Mitchell, Matthew Nguyen, Sarah Olen, Emma Oonk, Josh Paquin, Gina Polito, Mark Powers, Lauren Quenneville, Jack Radzville, Andrew Ragains, Keon Rick, Carmen Rodriguez, Rebecca Ruimveld, Forest Rulison, Nathan Schloff, Meghan Smith, Lydia Sprik, Riley St. Amour, Nelly Tankovo, Sean Traynor, Mary Urdaneta, Bethany VanHouten, Mike Walsh, Fangtao Wang, Jonathan Washburn, Neil Weeda, Lydia Won, Anna Wormmeester, Samantha Yacullo, Sarah Yonker– all of whom correctly solved the Problem of the Fortnight and figured out which dog received the 3.5 kg of food from the butcher.

Problem of the Fortnight

A 3 × 3 magic square is a grid of distinct numbers whose rows, columns, and diagonals all add to the same integer sum.  Sunnie creates a magic square whose sum is N, but her keyboard is broken so that when she types a number, one of the digits (0−9) always appears as a different digit (e.g. if the digit 8 always appears as 5, the number 18 will appear as 15).

The altered square is shown below. Find N.

Write up your solution (not just the answer) and drop 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, February 8.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. David Copperfield, Professors Penn and Teller– on your solution.  Good luck and have fun!

Off on a Tangent 17.7 (part b)

Help needed in pre-colloquium build

We need a few students to help build the object shown below. This object (which I’m sure we will learn the name of during the colloquium) will be used in the colloquium on symmetry (details below). We will start the build at 2:00 PM on Tuesday, January 29 February 5 in the lobby outside the lecture halls on the first floor of VanderWerf. The build will probably last until around 4:00 PM. If you can’t come at the beginning, you are still welcomed to help when you can. As a bonus you can earn a colloquium credit for helping build!

Math Colloquium on Symmetry next week

  • Title: Symmetry: A mathematical approach using group theory and linear algebra
  • Speaker: Dr. David Reimann, Albion College
  • When/Where: 4 pm on Tue, Jan 29 Feb 5 in VanderWerf 102
Abstract: Symmetric patterns are used in many situations to decorate an object with a repeating motif that is translated, rotated, or reflected without changing size. We will see examples of several symmetry types and look at these from the vantage point of group theory. In particular, we will study rosette patterns, frieze patterns, wallpaper patterns, and patterns on the sphere. We will then see how we can create all these pattern types with a unified framework based on the vectors and matrices of linear algebra.

Off on a Tangent 17.7

Was that test too easy?

Did you ever take a class where you (and most everyone else in the class) received an A without really working that hard? Well that class was too easy. Or maybe you took a class that was a little out of your comfort zone and despite working really hard you ended up with a D. Sounds like that class was too hard.

Just like Goldilocks, you need a class that is just right. But what is just right?  According to researcher Robert Wilson, a test that is just right (or one that leads to optimal learning) is one in which you score 85%. He calls this the 85% rule for optimal learning. For more information on this, you can read the entire research article here or read a shorter report on the article in Scientific American here.

[Editor’s Note: The average score on my statistics quiz this week was 85% as was Prof. Cinzori’s Multi 2 quiz—just right!]

A most unexpected answer to a counting puzzle

Christian Forester alerted us to this video that gives a very surprising answer to a physics/math problem.

Problem of the Fortnight

In honor of the newly redefined kilogram, we give you the following problem to begin the semester.

Anna Berington, one of the 2018 Iditarod mushers, has five dogs — Abby, Betsy, Charlie, Danny, and Ebeneezer — who have peculiar dietary constraints. Each must consume a whole number of kilograms of food every day, and Betsy needs one more kilogram than Annie, Charlie needs one more kilogram than Betsy, Danny needs one more kilogram than Charlie, and Ebeneezer (the lead dog) needs one more kilogram than Danny.  The butcher gives Anna 12 packages of scraps whose weights are: 2, 2, 2, 2.5, 2.5, 3, 3, 3, 3, 3.5, 4, and 4.5 kg.  The butcher wrote “Ebeneezer” on one of the 2-kg packages and “Betsy” on one of the 3-kg packages, so Anna gave those packages to those dogs.

Given the Anna satisfies the peculiar dietary constraints of her dogs, as well as the butcher’s wishes for the two specially marked packages, which dog got the 3.5-kg package?

Write your solution (not just the answer) on a sheet of butcher paper and drop 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, January 25.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Thu Nome, Professors Balto and Togo– on your solution.  Good luck and have fun!

Off on a Tangent 17.6

Mathematical gift ideas

It is that time of year. No, not final exams, Christmas shopping. But what do you get the math geek on your Christmas list this year? To help you out, Business Insider made a list of some awesome gifts that include a Klein Bottle bottle opener, a telescope for your iPhone, chocolate gaming dice, and math joke t-shirts.

Esty also has a site devoted to gifts for math lovers that includes a Merry X-Math sweatshirt, pi ornaments, and some object that contains a hippopotenuse. (I guess that one is for those where only a hippopotenuse will do!) Head over to Zazzle for prime number mugs, math clocks, and lots of things that say something about math being importanter. (I’m not sure who would buy something like that!) Finally, if you take a trip over to Mathnasium you will find a cutie pi onesie, a hypercube paperweight, and pi cookie cutters.

Remember it is only (the smallest square that can be written as the sum of two squares)-days until Christmas!

Problem Solvers of the Fortnight

Congratulations to Adair Cutler, Alyssa O’Donahue, Britta Johnson, Calvin Gentry, Camryn Zeller, Ce Gao, Chris McAuley, Christian Erickson, Dane Linsky, Dylan Burke, Ford Fishman, Hugh Thiel, Jacob Zoerhof, Jordan Corstange, Julia Loula, Kachikwu Nwike, Kam Wilcox, Karen Quay, Keegan Frisbie, Lydia Meinhard, Mackenzie Green, Mark Powers, Meredith Bomers, Micaela Wells, Mikaelah Snoap, Thomas Kouwe, Valerie Dien, Yizhe Zhang, Zach Wylie, Jonathan Washburn and Zheng Qu – all of whom correctly solved the Problem of the Fortnight in the last issue of America’s preeminent fortnightly mathematics department newsblog.

Problem of the Fortnight

Positive integer n has the property that n – 64 is a perfect cube. Suppose that n is divisible by 37. What is the smallest possible value of n?

Write your solution (not just the answer) on a Christmas decoration of your own making, 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, December 7. As always, be sure to include your name and the name(s) of your math professor(s) – e.g. Carrie A. Toone, Professor Carol Ling – on your solution. Good luck and have fun!

 

Off on a Tangent 17.5 (part b)

Graph Pebbling colloquium this week!

  • Title: Graph Pebbling
  • Speaker: Dr. Airat Bekmetjev, Hope College
  • When/Where: 11 am on Thur, Nov 29 in VanderWerf 104
AbstractPebbling is a process defined on a connected graph. Pebbles are configured on vertices of the graph and are moved along the edges. A pebbling move consists of taking two pebbles from a vertex, placing one on an adjacent vertex, and discarding the other. The objective of pebbling is to put at least one pebble on a designated vertex, called the root. A configuration is called solvable if any vertex can get at least one pebble through a sequence of moves. Pebbling can be used in transportation and communication networks and optimal resource allocation.
Some interesting questions arise: How many pebbles are enough to guarantee that any configuration is solvable ? What are the optimal ways to move pebbles? Can we construct an algorithm that determines if a given pebbling configuration is solvable? In this colloquium we will try to answer some of these questions along with the discussion about the existence of the threshold phenomenon in pebbling. We will see how the solvability of a random pebbling configuration dramatically changes after the number of pebbles reaches a certain value called the pebbling threshold. We will also discuss new results in pebbling related to the two-pebbling property and Graham’s Conjecture on the product of graphs.

Off on a Tangent 17.5

The irrationality of pi will be presented in next week’s colloquium

  • Title: Niven’s Proof of the Irrationality of Pi
  • Speaker: Dr. Aaron Cinzori, Hope College
  • When/Where: Tuesday, November 13, at 11:00 a.m. in VWF 102

Abstract:  Approximations of the value of pi are known to a ridiculous number of digits.  But to actually establish that pi is not a rational number requires not just approximations, but proof.  The first proof that pi is irrational was given by Lambert in 1761, and it required some sophisticated analysis, but in 1947, Ivan Niven gave a remarkably short and clear proof that pi is irrational using only ideas from calculus. (So it is as easy as pi!) We’ll take a detailed look at Niven’s proof as well as peeks at some of  the history of pi in mathematics.  And of course there will be poetry.

 Students participate in MATH Challenge

Hope again had a nice turnout of students participating in the Michigan Autumn Take-Home Challenge this past Saturday. Students competed with other students around the state (as well as other states) working in groups on ten interesting problems. Apparently this test was more difficult than usual (or not as easy as pi), so while we look forward to hearing the results in the near future we may not expect them to be very high scores. The following students competed (grouped by team):

  • Chris McAuley, Quentin Couvelaire, Evan Bright
  • Matt Edkins, Adam Czeranko, Mackenzie Green
  • Evan Mulshine, Ruth Holloway, Trevor Hile
  • Eric Leu, Jackson Krebsbach

Memphis Teacher Residency

David Montague, the Director of the Memphis Teacher Residency (MTR), will be on campus next Wednesday, November 14th to speak in Chapel and recruit for MTR. He is also hosting an Information Session on that same day from 6:30-7:30pm in VNZ 247.

MTR provides a full year residency program preparing teachers for work in low-performing public schools in Memphis.  They offer a Master’s degree in Urban Education (tuition free), a full year internship co-teaching with a mentor teacher, free housing and a monthly living stipend.  Their mission is Christian love expressed in equal education.

Problem Solvers of the Fortnight

Congratulations to Cole Persch, Evan Bright, Holly Denouden, and Caleb Stuckey– all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department newsblog.

Problem of the Fortnight

Consider the sequence a1 = 2, a2 = 3, a3 = 6, a4 = 18, . . . , where an = an-1 . an-2.  What is the largest k such that 3k divides a11?

Write your solution on a paper plate turkey (paper hand turkeys will also be accepted) 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 16. We are hoping for a rafter of turkeys to appear in the Problem of the Fortnight slot next week! As always, be sure to include your name and the name(s) of your math professor(s) – e.g. Tom Gobbler, Professor Herb Stuffing – on your solution.  Good luck and have fun!

Elvis was in the building during this week’s colloquium

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 cinzori@hope.edu.

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!

Off on a Tangent 17.2 (part b)

Colloquium Next Week Tuesday

  • Title: The P+ P’ problem and George Polya
  • Speaker: Dr. Stephanie Edwards, Hope College
  • When/Where: Tuesday, October 2, 2018 at 11:00 am in VWF 102

Many open problems in entire function theory, specifically, the distribution of zeros of real entire functions, can be tracked back to work by George Polya.  One of these such problems was stated in a Polya and Szego text from the early 1900’s: If P is a real polynomial with only real zeros, find the number of non-real zeros of P^2+P’.  If one removes the hypothesis that P has only real zeros, the problem becomes quite difficult and was not solved until the 1980’s. We will discuss a simple solution to the problem, look at natural questions that arise from the problem and discuss some open questions which have their roots in Polya.

Colloquium Schedule

The following other colloquia are on the schedule this semester. More should be added as the semester goes along.
  • Thursday October 25, 2018 at 4:00 pm, Darin Stephenson, Hope College
  • Thursday, November 8 at 11:00 am, Tim Pennings, Davenport University