## Off on a Tangent 18.04

### Zeno’s paradox and more in next week’s colloquium

• Title: Zeno’s paradox, the harmonic series, and 1=1/2???
• Speaker: Dr. Stephanie Edwards
• When: Tuesday, October 29 @ 4:00 PM
• Where: VanderWerf 104

Abstract: Zeno’s paradox says that before one can get to position A, one must first get halfway there. Before one can get to the halfway point, one must get halfway to the halfway point, and so on.  Since this goes on forever, it seems that the distance cannot be covered. We will use geometric series to show that the distance will, indeed, be covered. We will also explore the harmonic series and show that rearrangements of the alternating harmonic series can lead to puzzling conclusions.

### Estimating areas talk coming up soon

• Title: Estimating areas
• Speaker: Dr. Paul Pearson
• When: Thursday, November 7 @ 4:00 PM
• Where: Schaap Science Center 1000

Abstract: Finding an accurate estimate for the area of an irregular shape can be hard to do.  One easy way to estimate the area is to lay a square grid over the shape and then count the squares that lie over the shape and multiply by the area of each square.  We will jazz up this method to a triangular grid and use an ingenious counting result discovered by Georg Pick to find the area of any polygonal shape with vertices on the grid.  To justify Pick’s result, we will use Euler’s formula V – E + F = 2 relating the vertices, edges, and faces of a connected planar graph.  These results are surprising because of their clever use of  basic tools from combinatorics and topology to solve the area estimation problem in geometry.  This talk is designed to be fun, interactive, and accessible to all students who have ever counted anything.  Students in math education are particularly encouraged to attend.  Please come and bring your friends (and a pencil!).

### Problem Solvers of the Fortnight

Congratulations to Meredith Bomers, Sarah Brown, Adair Cutler, Liz Cutlip, Adam Czeranko, Blake Engler, Fiona Johnson, Peter Le, David McHugh, Matthew Nguyen, McKenna Otto, Jack Radzville, Dan Romano, Bethany VanHouten, Tracy Westra, and Kamaron Wilcox — 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

Determine F(x) if, for all real x and y,

F(x)F(y) – F(xy) = x + y.

Hint:  What could F(1) be?

Affix to your solution (not just the answer) to some oddments from your Halloween celebrations, 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 1.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Hilda Brume, Professors Frank and Stein — on your solution.  Good luck and have fun!

## Off on a Tangent 18.03

### Colloquium next Thursday

• Speaker: Dr. Darin Stephenson
• Title: Modeling Data with Machine Learning
• When: Thursday, October 17, 2019 @ 4:00pm
• Where: Science Center 1000

Abstract:
The prevalence of large sets of data in our technological society has given prominence to the issues involved in processing, displaying, modeling, and making decisions from data. The subject of data science lies at the interface of computer science, statistics, and mathematics, and has applications in almost every field of study. One particular branch of data science involves “machine learning”, which is broadly defined as the process of programming computers to build predictive data models in an automatic way. Thus, a machine can “learn” a data model from a broad modeling framework by consideration of the available data, rather than having model parameters specified by a human. Often, such models have many thousands (or millions) of available parameters, and computers can sift through huge quantities of data in order to “train” model parameters in an incremental way. The availability of fast parallel computing (via GPUs or related cloud computing) often makes such models trainable in a reasonable amount of time. The goal is a model that both describes known training data well and also is effective in prediction for further data on which the model was not trained.

This talk will survey a few of the problems machine learning can address and give insight into some basic machine learning procedures. The talk will also highlight the 2-credit Math 295 course, “Machine Learning with Python”, which will be offered for the first time in the upcoming spring semester.

### Gentile lecture to feature Ira Flatow

The Natural and Applied Sciences Division is pleased to welcome Ira Flatow to campus on Tuesday, October 15, 2019, as this year’s Gentile Lectureship Series speaker.

Mr. Flatow, who is best known as the host and executive producer of Public Radio’s Science Friday and previous host of PBS’s Newton’s Apple, will deliver a presentation entitled, “Catalysts of Creativity,” which will explore the question, “Where do new ideas come from?”

The presentation will be held in the Concert Hall of the Jack H. Miller Center for Musical Arts, beginning at 7:00 pm.

### MATH Challenge

The 2019 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place in the morning (9:30am – 12:30pm) on Saturday, November 2 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 Wednesday, October 23 at 4:00 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 encourage to sign up; they will be assigned to a team on the day of the competition.

### GVSU Statistics Career Day

Grand Valley State University’s Department of Statistics will be hosting a Statistics Career Day on Friday, November 15, 2019 at the Allendale campus in the Kirkhof Center.  This event will provide interested high school and college students an opportunity to learn about the many career options available in statistics and data analytics.

Participants will hear presentations from, and be able to speak informally with representatives from the government, health care, insurance, marketing, pharmaceutical, data analytics and other industries.  Some of the companies may have job openings or internships available.  Anyone with an interest in statistics or data analytics is welcome.

This event is designed to attract promising students to the field of statistics and to give students a chance to meet with corporate representatives to discuss job opportunities.

Registration is up – please go to gvsu.edu/stat and look for career day.

### Auto-Owners Insurance’s IT/Actuarial Day

Auto-Owners invites you to their annual IT/Actuarial Day, which shows students how their degree can be used in the insurance industry.

The event is on Friday, October 18, 2019 from 10:30 a.m. to 4:00 p.m. in Lansing, MI. Sophomores, juniors, seniors, and recent graduates with majors in Computer Science and Mathematics are invited. Faculty and staff are also welcome! Anyone who wishes to attend should fill out a registration to ensure we adequately prepare for the correct number of attendees.

Register online from now until end of day Monday, October 14th.

### 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 9, 2019. 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, visit their website (where you can also register).

### Problem Solvers of the Fortnight

Congratulations to Blake Harlow, Kamaron Wilcox, Hugh Thiel, Josiah Brett, Maddy Eppard, and Adam Heisler — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department news blog.

### Problem of the Fortnight

“Well, I’ve come out second best in my battle with the union,” said Noah van Ark.

“How so?” asked his sister Joan.

“Well, I needed to have the union workers move thousands of crates.  The exact number,” said Noah, consulting his notebook, “was 69,489.  The job took nine working days.  I didn’t think the union workers were putting all they had into it, but the union leaders thought otherwise.  Every day after the first day, I put six more workers on the job; and every day after the first day, each of the workers — by arrangement — shifted five fewer crates than was the quota for the day before.  The result was that, during the latter part of the period, the number of crates being moved actually began to go down.”

What was the largest number of crates moved on any one day?

Tape your solution — not just the answer — to a crate of clementines, and drop it by the Problem of the Fortnight slot outside Professor Pearson’s office (VWF 212) by 3:00 p.m. on Friday, October 18.  As always, please be sure to include your name as well as the name(s) of your math professor(s) — e.g. Woody Kreight, Professor DeKreese — on your solution.

## Off on a Tangent 18.02

### Problem-solving colloquium coming soon

• Title: Math Puzzles and Challenges
• Speaker: Dr. Tim Pennings, Davenport University
• Time/Location: Tuesday, October 1, 2019 at 11:00 AM in VanderWerf 102

Abstract: Polya, or was it Rudin, said that the heart of mathematics is solving problems. So put away your text books filled with useless definitions and theorems, put on your game face, and come get ready to be stumped by – and perhaps solve – some surprising math puzzles and challenges. Not for the weak of spirit.

### Mathematics students enjoy the fall social

Students and professors enjoyed the recent mathematics fall social. Ice cream sundaes were served and everyone participated in the game “Would you rather…” Once the participants figured out their answers, they had to find others with matching answers. Below are some of the groups of “matchers” that were formed.

### Problem Solvers of the Fortnight

Congratulations to Meredith Bomers, Josiah Brett, Anna Carlson, Jonathan Chaffer, Adair Cutler, Adam Czeranko, Kara Dahlenburg, Ryan DeWitt, Emily Dee, Liam Diephuis, Eli Edwards-Parker, Blake Engler, Reilly Herman, Jackson Krebsbach, Peter Le, Cory McGregor, Kyle Magennis, James Mandeville, Matthew Nguyen, Liam Orndorff, Eleni Persinger, Danielle Reiber, Peter Ruffolo, Hugh Thiel, Shane Vaara, Bethany VanHouten, Danni VanIwaarden, Fangtao Wang, and Kamaron Wilcox — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department news blog.

### Problem of the Fortnight

Find positive numbers n and a1a2 , . . ., an  such that  a1a2 + . . . +  an = 1000 and the product (a1)(a2). . . (an) is as large as possible.  (Hint: Try replacing 1,000 in turn by 2, 3, 4, 5, 6, 7, 8, 9, … and search for patterns that emerge.)

Drop your solution 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, September 27.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Stew Dios, Professor Tott — on your solution.  Good luck and have fun!

## Off on a Tangent 18.01

#### Mathematics students attend MathFest and win an award

MathFest is an annual meeting of the Mathematics Association of America and this past summer the conference was held in Cincinnati, Ohio. Three Hope students presented papers during the conference. Jackson Krebsbach’s presented “Dunes and Drones: A Machine Learning Approach to Mapping Dune Vegetation Using Small Unmanned Aerial Systems and Ground-Based Photography,” Dane Linsky presented “A Model of Animal Movement with an Absorbing Interface,” and Eric Leu presented “Remote Identification of Cloud Forest Landslides: A Machine Learning Approach.”

Eric Leu won the Janet L. Andersen Award for Outstanding Student Presentation in Mathematical Biology during the conference. Eric’s win continues a tradition of Hope students earning this award and as well as others at MathFest.

#### Mathematics professor wins best paper award

Dr. Brian Yurk is co-author of a scholarly paper that has been named the best of 2017 and 2018 by the Journal of Biological Dynamics.

The article, which Dr. Yurk wrote with Dr. Christina Cobbold of the University of Glasgow in Scotland and was published in the Journal in December 2017, presents equations to help ecological researchers better understand the population patterns of animals.  The article received the journal’s Robert May Prize, awarded every other year for the best paper in the journal during a two-year period.

Titled “Homogenization techniques for population dynamics in strongly heterogeneous landscapes,” the paper provides a way to model how long-term dispersal patterns of animal populations are shaped by how individuals respond to the variability they encounter in their environments from day to day.

#### Statistics students win national award

A Hope College student research paper won third place in a biannual national statistics competition, continuing a tradition of strong finishes in the event by Hope’s statistics students. Sally Hakim and Aidan Piwnicki earned the award in the Spring 2019 Undergraduate Statistics Project Competition sponsored by the Consortium for the Advancement of Undergraduate Statistics Education and the American Statistical Association.

Hakim and Piwnicki were honored for their project “A Study on the Immediate Impacts of Product Placement on Consumer Choices,” which they pursued during the spring 2019 Introductory Statistics class taught by Prof. Todd Swanson.  The students examined whether or not seeing a product in a television segment had an immediate impact on individuals’ preference for that product.  While their study did not find a significant effect, they note in their paper that a larger and more random sample (they surveyed 34 students in one location) would be necessary to accurately determine what would likely be a small difference.

Hope students have been honored in the national competition eight times in the past three years.  In addition to Hakim’s and Piwnicki’s third-place award, past Hope groups earned three first-place awards, a second-place award, another third-place award and two honorable mentions.

#### Statistics professors win best paper award

The simulation-based approach to statistics instruction that was first piloted at Hope College has once again earned national recognition.

The Journal of Statistics Education presented its 2018 “Best Paper” award to Hope mathematics professors Todd Swanson and Jill VanderStoep and six colleagues from other institutions for a paper they co-authored that examines — and affirms — the effectiveness of a simulation-based curriculum for introductory statistics.  It is the fourth time that Swanson, VanderStoep and other co-authors have received national recognition for publications related to their work.

This latest award, named the “Jackie Dietz Best ‘Journal of Statistics Education’ Paper Award” in honor of the journal’s founder, is for the paper “Assessing the Association Between Precourse Metrics of Student Preparation and Student Performance in Introductory Statistics: Results from Early Data on Simulation-based Inference vs. Nonsimulation-based Inference,” published by the journal in August 2018.  It was presented during the Joint Statistics Meetings conference held in Denver, Colorado, on July 27-Aug. 1.

Read more about the research as well as some background on their work here.

#### Students attend the Joint Statistical Meetings

(The following was written by John McMorris and Tyler Gast on their experiences at JSM 2019.)

During the final week of July 2019, we flew to Denver for the Joint Statistical Meetings of 2019 to present on the research conducted during summer 2018. Upon arrival, we were greeted by the hot, dry climate the city is known for. Denver was perfect for such an event. Streets and public transportation were readily available across the city, allowing us easy access to the eateries nearby the convention center.

I [John] flew in on Sunday to settle in before presenting the following morning. The presentation followed by a poster session on Monday was a great experience for speaking in a professional setting and presenting to people working in statistics. I spent the rest of the day around the convention center attending multiple other oral presentations and poster sessions and learning about more advances in statistics.

Monday, the first day I [Tyler] arrived, was filled with travel and preparation for my stay and presentation. Tuesday allowed us the full experience of the convention. We walked the grounds and listened in on hours of presentations and lectures regarding all the uses and results made from statistical research. It was an enjoyable experience to say the least and we used every bit of time we had to absorb the experiences the PhD’s and graduate students had as they presented on their life’s work.

My final day was my presentation day and I am proud to say that I did meet the fifteen minute mark on the presentation with ease, allowing myself the experience of presenting in a professional environment. Overall, the experience was a huge benefit in the ways of experience in travel, professionalism with others, and presenting in a serious and semi-formal manner.

#### Interested in being a tutor?

Hope’s mathematics department often gets requests from external people who are interested in hiring tutors (typically for a middle or high school student). As a service to the community, we collect names of students that are interested in being a tutor. If you would like your name added to the list of potential tutors please complete the following form located here. Note: If you want to be added to a tutoring list, your Hope College email will be given out to those that request it.

#### Internship opportunities in actuarial science

The Jackson National Life Insurance Company has internship opportunities available within their Actuarial Department in Lansing, Michigan for the Summer 2020.

An internship with Jackson’s Actuarial Department offers practical, hands-on work experience that enhances students’ academic, career, and personal development, while helping the company identify talented individuals.

Students who are interested in applying for an internship are strongly encouraged to apply at on their website. Students are encouraged to submit applications no later than October 1st, as selections for the 2020 intern class will likely be made before this year’s end.

#### Problem of the Fortnight

Two adjacent vertices of a regular 100-gon are labeled as P and Q. Line segments are drawn to join P and Q to each of the other 98 remaining vertices. How many bounded regions does this figure have? (The regular 7-gon in the figure below illustrates the idea of the problem and shows the 19 bounded regions formed by the process.)

Write your solution (not just the answer) on a regular n-gon of your own choosing, 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, September 13. As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Ben Wundering, Professor Les Unh — on your solution. Good luck and have fun!

## The Last Colloquium

Join us on Tuesday, April 16 at 7:00 p.m. in Room 102 of The Werf (aka VanderWerf) for the last colloquium of the semester.  Professor Pearson will be presenting Euler’s solution to the Basel Problem, which asks the question, “What is the sum 1 + 1/4 + 1/9 + 1/16 + … ?”  Professor Pearson will attempt to do justice to Euler’s remarkable genius in explaining his clever solution to this problem, and he will also discuss how this problem gave rise to one of the most important unsolved problems in mathematics today . . . and what all of this has to do with internet security.  Students in Calc 2 or above will have studied the important background material for this talk, but students at all levels of math are invited to come and learn about this interesting story in the history of mathematics.

## Math Spring Social

On April 1, the Math Department had its annual game and pizza night. A number of new games made an appearance—one of them had players depicting increasingly complicated scenarios, another required the players to shut their eyes and listen to instructions from a phone app. Someone also introduced a campfire game which involved the transmission of hand signals.
Since the proportion of people who do not enjoy games and/or pizza is rather low, there’s a high probability that all those who attended had a good time. Pictures are below.

## Stanford Pre-Collegiate Summer Institutes

Eleni Persinger, a high school student from Saugatuck and Hope College mathematics student, has been accepted into the Stanford Pre-Collegiate Summer Institutes. This is a three-week summer residential program where students engage in single-subject intensive study. Eleni will be studying discrete mathematics.

Besides discrete math, the institute also offers the mathematics of symmetry, number theory, cryptography, and knot theory as well as other science and non-science classes.

Sarah Petersen, a 2017 Hope College graduate in mathematics and current graduate student at the University of Notre Dame received an honorable mention in this year’s prestigious National Science Foundation’s Graduate Research Fellowship Program. This program recognizes and supports outstanding graduate students in NSF-supported science, technology, engineering, and mathematics disciplines who are pursuing research-based graduate degrees. Sarah is working in the mathematics field of topology.

## When is Easter?

Easter Sunday is still more than a week away, almost the end of the semester. Three years ago it was on March 27. Did you ever wonder how the date is determined? The easy answer is that Easter is the first Sunday after the first full moon on or after March 21. However, there is a more difficult mathematical answer to that question. In an old article written by Ian Stewart, Easter is a Quasicrystal, you can see the 10 steps needed to calculate the date of Easter for any given year.

## Problem Solvers of the Fortnight

Congratulations to James Bird, Evan Bright, Anna Carlson, Jeremiah Casterline, Carolyn Coopker, Johnny DeMaagd, Christian Forester, Keegan Frisbie, Reilly Herman, Jacob Kowalski, Leah Krudy, Grant Lancaster, Peter Le, Libby McCormick, Gina Polito, Jack Radzville, Keon Rick, Jordyn Rioux, Rebecca Ruimveld, Mikaelah Snoap, Sean Traynor, Allison VanDam, Bethany VanHouten, Kimberly VanHouten, Kameron Wilcox, and Sunnie Zou — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department news blog.

## Problem of the Fortnight

Find the area of quadrilateral ABCD, given that the vertical lines are perpendicular to the base and the distances are as given in the figure.

Write your solution on a quadrilateral piece of paper of the same shape as ABCD 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, April 19.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Stew Dent, Dr. Dokter — on your solution.  Good luck and have fun!

## A statistical look at mass shootings will be presented in next week’s colloquium

• Title: Examining U.S. mass shooting incidents – trends, commonalities, and intensities
• Speaker: Dr. Yew-Meng Koh, Tyler Gast and John McMorris
• When/Where: 4:00 pm on Tuesday, April 2 in 102 VanderWerf

Abstract: Mass shootings in the U.S. appear to be random and unpredictable events. However, a closer examination of these events reveals certain trends and commonalities between them. In this study, we classify mass shootings using Principal Component Analysis as well as Factor Analysis. We compare the clustering performance of these two methods and provide conclusions regarding similarities and distinct features between mass shooting incidents which arise from the different clusters of incidents are discussed. Salient variables that help with clustering shooting incidents and their determination are highlighted as well. To address the question on whether shooting incidents are occurring with a significantly different intensity in recent times, we model US mass shooting incidents as a non-homogeneous Poisson process (NHPP). We also utilize the NHPP model for variable selection. Relevant conclusions from various NHPP models will be presented and discussed.

## Statistics students win national awards

Statistics research projects conducted by two teams of Hope College students have earned first place and honorable mention in a national competition. Both have been honored in the Fall 2018 Undergraduate Statistics Project Competition.

Johanna Emmanuel, Sophia Kleinheksel and Ian McNamara won first place for  their project “The Effect of Music on Memory Tasks” and  Christopher Belica, Kendall Collins-Riley, and Safia Hattab received honorable mention for their project “The Effects of Positivity and Negativity on Response Length”
The two papers were written in fall 2018 introductory statistics classes taught by Dr. Yew Meng Koh. This makes a total of seven student papers from Hope College students in the past two years that have won awards in this national competition.

## New scholars are inducted into Pi Mu Epsilon

Sixteen students were recently inducted into the Michigan Delta chapter of Pi Mu Epsilon.  Founded on in 1914 at Syracuse University, Pi Mu Epsilon currently has over 350 chapters at colleges and universities throughout the United States.  Hope College has had a chapter since 1974, the fourth in Michigan.

The purpose of the society is to promote scholarly activity in mathematics among the students in academic institutions.  Students were invited to join based on their GPA in their mathematics courses as well as their overall GPA.  The induction ceremony was held on April 15 at 6:28 p.m. (or two pi o’clock).  After the short ceremony everyone enjoyed our tradition of eating pie.

The students inducted this year are:  Meredith Bomers, Marcus A. Brinks, Anna J. Carlson, Lauren A. Cutler, Kara Dahlenburg, Camille M. Fogg, Yechan Hwang, Scott D. Joffre, Jacob M. Kelley, Danielle P. Reiber, Kyra D. Ross, Forest D. Rulison, Bethany M. VanHouten, Hans J. Veldman, Roger D. Veldman, and Micaela M. Wells.

## Spring Social

It’s no joke! The Mathematics Department is hosing a Spring Social on Monday, April 1 starting at 6:28 pm in VanZoeren 247. There will be a number of different games and puzzles to play as well as some pizza and soda pop to consume. Word has it that there will even be some pizza that doesn’t contain pineapple.

Since registration for fall 2019 classes starts soon, we thought you might want to see some details of the upper-level mathematics classes that will be offered.

• Math 321: History of Math is a great course because we get to look at the whole scope of mathematics and pick out some of the most fun parts to study more closely.  You’ll learn interesting new things about math you thought you knew and new interesting things about some of the people that made that math—from the quadratic formula to the Riemann Hypothesis and lots of stuff in between.
• Math 331: Real analysis is a course that many math students have been waiting for since the day they started their first calculus class. This course explains why and how everything in calculus works and what can go wrong if some things don’t work. Together we will see the importance of mathematical proofs and how to write them. We will talk about real numbers and sets. You will see functions, derivatives, series and integrals in a new light.   We will discuss and solve many interesting  problems together. In many ways, real analysis is one of the courses that helps you to become experts and creators of mathematical knowledge.
• Math 334: Complex Analysis is Calculus + imaginary numbers = SO MUCH FUN!  Why constrain ourselves to the real line when we can jump into the complex world, solve cool and interesting problems, and then bring them back into the real world?   We will also learn a bit about the Mandelbrot set, chaos, and fractals!  Keep iterating:)
• Math 341: Algebraic Structures I. When you think about algebra, you probably recall solving equations that involve symbols from your days in middle school and high school.  Algebra is actually about much more than just solving equations.  It’s about the study of structure and symmetry of real objects (e.g., a Rubik’s cube or a wallpaper pattern), how to relate the structure and symmetry of one object to a seemingly different object, how to ask good questions and solve problems, and about learning to write clear solutions (i.e., proofs).  We will learn about groups, rings, integral domains, and (time permitting) a bit about fields.  In this course there will be a moderate amount of lecture.  A lot of time in and out of class will be spent exploring and discussing interesting problems with your peers.  Reading mathematics outside of class, active learning, participation in discussion, and willingness to investigate will be expected.  I guarantee that we will have fun learning math together!
• Math 351: In College Geometry, we’ll take another look at the Euclidean geometry that you studied in high school, but we’ll also get to find out about and explore several other geometries—finite, affine, hyperbolic, neutral, projective.  The thing that made Euclid’s Elements required reading for educated people for 2,000 years is still true:  doing geometry is a very effective way to sharpen your ability to reason, argue, and communicate.
• Math 395: Statistical Methods III begins where MATH312 ends. MATH312 introduces statistical models for predicting response variables which could be quantitative or could be categorical (binary). These models allow for the inclusion of multiple explanatory variables, which are potentially a mix of categorical, and quantitative variables. Statistical Methods III builds on these foundations, where more advanced prediction methods and models will be introduced. The intuition and rationale behind these methods, as well as the conclusions they allow us to make will be emphasized throughout the course, so that the overall objectives of the analyses would not be obscured by the methodologies themselves. Part of the course would involve implementing these methods on multivariate data sets, and iteratively tweaking them for improved predictive performance.

## Problem solvers of the fortnight

Congratulations to Brandon Fuller, Elizabeth Inthisane, Sean Traynor, Fantao Wang, Kameron Wilcox, and Sunnie Zou — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department news blog.

## Problem of the fortnight

Suppose that f is a differentiable and invertible function on the interval [0,1] such that f(x) ≥ x with equality holding at the endpoints.  Given that the region bounded by y = 0, x = 1, and y = f(x) has area A, what is the area of the region bounded by y = f(x) and y = f –1(x)?

Write your solution — not just the answer — on a square piece inside a region bounded by a function and its inverse, 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, April 5.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Shirley Wright, Professor Mae B. Soh — on your solution.  Good luck and have fun!

## XKCD

A recent xkcd comic explained the difference between differentiation and integration (or maybe Calc 1 and Calc 2).

## 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!

## 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

## 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!

## 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.

## 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!