Off on a Tangent 19.02

Time to sign up for a math or stats class!

Since registration for spring 2021 classes starts soon, we thought you might want to see some details of the upper-level mathematics classes that will be offered.

Math 280: Bridge to Higher Mathematics is designed to help students transition from computational mathematics to problem solving, generalization and abstraction, and writing solutions clearly.  Course topics may include functions and sets, recursion, induction, counting techniques, equivalence relations, an introduction to group theory, and an introduction to real analysis.  The course will be taught via inquiry-based learning and you will work with other students to solve problems together.

MATH 311: Statistical Methods. In this first-half-semester course we will explore statistical inference for one and two variables, starting with simulation-based approaches and then transitioning to traditional theory-based techniques all while aiming to develop a deep conceptual understanding of inferential statistics. Throughout we will explore real research studies through active-learning. This course has the same content and learning objectives as Math 210, but the material is covered in half the time. So it is designed for students who have a significant prior experience with statistics (e.g., high school statistics course) or calculus. (Students cannot receive credit for both Math 210 and Math 311.)

MATH 312: Applied Statistical Models picks up where MATH 311 (or MATH 210) leaves off. In this second-half-semester course we take a deeper look at sources of variation in data and use statistical models to predict values of response variables. These models will now allow for the inclusion of multiple explanatory variables (categorical, quantitative, or a mix), and not just a single explanatory variable as we use in MATH 311. We will again aim at developing a deep conceptual understanding of statistics. Students will also carry out a research project at the end of the semester.

Math 362: Mathematical Statistics. If you enjoyed Math 365 and/or are thinking of pursuing an interest in probability, statistics, or actuarial sciences, consider taking Math 362 this Spring.  We will start the course with the Central Limit Theorem and other results involving long term behavior of random processes.  We will see how these results inform estimation and hypothesis testing in statistics. The class will be an upper-level math course but we will get our hands dirty with a couple of real-world data sets.   

Math 360: Combinatorics and Graph Theory. I encourage you to think about taking Combinatorics and Graph Theory this spring.  Both of these fields provide lots of examples that are both easy to understand and filled with complexity.  It is a good setting for practicing your mathematical thinking and proof writing skills.  We will practice proof by induction, proof of bijections, combinatorial proofs, and proofs using the pigeonhole principle.  If practicing math skills isn’t enough motivation, take the course to learn to count cards and evaluate your odds in games of chance. 

MATH 370. Advanced Differential Equations picks up where we set differential equations aside in Math 232.  We’ll start by looking at series solutions for solving linear ODEs, a technique that is flexible and broadly applicable.  Then we’ll move into work on partial differential equations.  We’ll do some theoretical and some applied work on the PDEs including separation of variables and Green’s functions.  If there is interest, we’ll also do an introduction to numerical solutions to PDEs via the finite element method.

Fall social(ly distanced)

Despite having to remain socially distant, we still managed to hold our annual fall social with ice cream treats and some fun games. Below are two pictures from this year’s event and one from a few years ago. Can you tell which is which?

Problem of the Fortnight

A long hallway has 20,000 LED lights.  Each is operated by a switch that turns the LED light either red or green.  As coincidence would have it, 20,000 people form a line at one end of the hallway (six feet apart and wearing masks, of course).  Initially all the lights are green.  The first person walks through the hallway and turns each light red.  The second person walks through the hallway and hits the switch on every second light, thereby turning all the even-numbered LEDs green.  The third person walks through the hallway and hits the switch on every third LED, turning some red and others green.  The fourth person hits the switch on every fourth LED, and so on.

Which LEDs are red after the 20,000th person has passed through the hallway? You can find the solution here. (But don’t peek unless you’ve got an answer to check!)

Midstates Consortium’s Undergraduate Research Symposia

If you’ve completed research recently, you may be able to present your results at one of the two Midstates Consortium’s Undergraduate Research Symposia online hosted at University of Chicago and Washington University in St. Louis.  

Students who have done research in Psychology, Biology, Chemistry, Physics, Engineering, Math, Computer Science, Neuroscience, and related fields are encouraged to apply.  
The abstract submission deadline is October 5, 2020.  For more information, please see https://mathsciconsortium.org/

West Michigan Regional Undergraduate Science (WMRUGS) Research Conference

The 2020 West Michigan Regional Undergraduate Science (WMRUGS) Research Conference held on Friday, November 6, 2020, and Saturday, November 7, 2020.

Via virtual platform, students will share the story of their research project with other college students, faculty, research scientists and other college students, as well as build their network of peers with similar interests and experiences. Attendees will also hear stimulating talks on current topics in biology, biochemistry, bioinformatics, chemistry, computer science, engineering, geology, neuroscience, physics, and more. Graduate school, professional school and medical school recruiters will be on hand to discuss educational opportunities with their institutions. Internship and employment recruiters also will be available to discuss opportunities with their organizations.

The deadline to register is Monday, October 26, 2020. For more detailed information on the upcoming virtual research conference, visit: https://vaigs.vai.org/undergrad-research/wmrugs/.

Off on a Tangent 19.01

Welcome!

Welcome to the first issue of Off on a Tangent for the year. This is the official newsletter for Hope College’s Department of Mathematics and Statistics. In the past, we published every fortnight (i.e. every two weeks). This year, being a bit (by a bit I mean A LOT) different than past years, we will publish a little more sporadically. We will try to keep you updated on what is going on in the department as well as some current interesting mathematical and statistical happenings around the world. We also plan to include a problem of the fortnight in each issue. However, this year you will not turn them in for colloquium credit, but work them for fun.

MATH Challenge

The 2020 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place in the morning (9:30am – 12:30pm) on Saturday, November 7. 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. 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 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. 

Follow us on Social Media

Now you can follow the Hope College Department of Mathematics and Statistics on Instagram and Twitter! Follow @hopemathstat on either Instagram or Twitter for information on faculty members and students in our department, jobs in mathematics, mathematical facts, fun problems to try, and happenings in the world of mathematics.

A few weeks ago, Pi Man, not only made an appearance on Instagram but has also been spotted around campus!

Incognito and irrational? “Sometimes I am 3.14159+…other times not.” —Alfred Bester, The Pi Man

Fall Ice Cream Social

Join the Mathematics and Statistics faculty and fellow math students for our traditional Fall Social on Friday, September 18 from 3:14 to 4:14 PM. The event will take place on the Van Andel Plaza located in front of the A. Paul Schaap Science Center under the tent. We will have ice cream treats and fun games. (All COVID-19 appropriate.) This is a great way to get to know your fellow math students and faculty. Remember to wear your favorite face mask to the event! (Rumor has it that there may be a few giveaways of some face masks like Pi Man is wearing!)

Vanderboards!

Have you seen the chalkboards that were recently installed outside VanderWerf Hall? Has the physics that is on them in this picture been replaced by mathematics yet? I hope so. These boards, which we are calling the Vanderboards, will be used during outside classes. They are also available for individual student use. However, during this COVID time, chalk for sharing can’t be provided. (Geometer’s Note: Notice the nice one-point perspective in this picture.)

Actuary Internship Opportunity

Jackson National Life Insurance Company has internship opportunities available within their Actuarial Department in Lansing, Michigan for the Summer 2021.

Jackson is one of the largest life insurance companies in the United States. It has been providing advisors with products to help their clients achieve financial security for over 50 years. 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 using this link no later than October 1st, as selections for the 2021 intern class will likely be made before this year’s end.

For more information contact Ivan Parker at ivan.parker@jackson.com.

Problem of the Fortnight

The carousel on Windmill Island here in Holland has been around a long time and is starting to show signs of wear. In fact, the deck of the carousel has needed a paint job for a couple years now. However before it could be painted, Herm VanderVeedenVanderMeen (the carousel master) wanted to know exactly how much paint would be needed to do the job. The problem was, though, he couldn’t figure out how to determine the area of the carousel deck, which is an annular ring, because the motor and gears in the middle of the merry-go-round prevented him from measuring the radii of the inner and outer circles. If he could have measured those, his job would have been easy!

One day, he was talking to a group of Hope College students, who had taken their parents to Windmill Island, and he told them about his dilemma. One of the students, who had taken some really great math courses at Hope, said to him, “I think I can help you out,” and she took his tape measure, walked over to the carousel and made a single measurement along a straight line. Her measurement was 30 feet, and after making a few quick calculations in her head, she told Herm the area of the carousel deck.

The question is, What measurement did she make (and how did she use it to calculate the area of the carousel deck), and what is the area of the carousel deck?

Click here for the solution. But don’t click until you have given the problem the old college try!!!!

Gömböc—The Shape That Shouldn’t Exist

Off on a Tangent 18.10

Statistics colloquium set for Monday

  • Title: Statistics is not an easy bake oven
  • Speaker: Dr. Phil Boonstra, University of Michigan
  • When/Where: Monday, March 2 at 4:00 PM in VanderWerf 104

Abstract: Statistics is sometimes viewed—and taught—as if it were an easy bake oven: add some data, choose the right settings, and await your (scrumptious?) answer. As it turns out, this is not actually how statisticians typically describe their thought process. One way that this gap between external and internal perceptions manifests is in terms of understanding that any statistically derived answer will be couched in uncertainty. I will talk about this specifically in the context of early phase clinical trials of anti-cancer drugs. After giving a brief introduction about the history, basic design, and current success rates of such trials, I will present some of my work as a cancer biostatistician helping to design these trials. My goal is to bridge this gap in perception and understanding. Well-designed clinical trials are about making the best decision (e.g. which dose to choose, whether to stop the trial early, or whether to declare that our drug is a ‘success’) *and* also properly quantifying our uncertainty about that decision. Most of this talk will be accessible to non-statisticians.

Computer Science Colloquium (with enough math to make it a math colloquium) coming up

  • Title: An Interesting Talk about Uninteresting Numbers
  • Speaker: Dr. Herb Dershem, Hope College
  • When/Where: Thursday, March 12 at 11:00 AM in VanderWerf 102

Abstract: What does it mean for a number to be random? This talk will explore this question in a manner that will expand your understanding of the concept of randomness and its role in computer science using a recently discovered concept called algorithmic complexity. Along the way, we will discover that all numbers can be divided into those that are interesting and those that are uninteresting. Also, you will be introduce to the only known uninteresting number in the universe, know as Chaitin’s Omega.

Michigan Section of the Mathematics Association of American Meeting

Grand Valley State University Mathematics Department is hosting this year’s Annual Meeting of the Michigan Section of the Mathematical Association of America. The meeting will take place Friday-Saturday, April 3-4. 

This is not only a great nearby mathematics conference to attend, but student’s are also encourage to present. The deadline to submit a talk or poster is Friday, March 13. More information about the conference and directions on how to submit a presentation are located on their website linked above.

Leap day?

Is tomorrow February 29 or March 1. You could certainly look at your calendar to find out, but that’s too easy. We provide the flow chart below to help you decide.

Problem Solvers of the Fortnight

Congratulations to Camen Andrews, Aerin Baker, Jeff Bikus, Collin Bradley, Josiah Brett, Colin Brown, Sarah Brown, Josh Brummel, Anna Carlson, Miguel Castelan, Ethan Cramer, Adam Czeranko, Calleb Diekema, Liam Diephuis, Cameron Dunn, Blake Harlow, Kyle Hydorn, Britta Johnson, Tyler Koran, Ted Lockett, Tahvanh Lucero, Anna Molloy, Brendan Murphy, Matthew Nguyen, Eleni Persinger, Cedric Porter, Forest Rulison, Charlie Stafford, Shane Vaara, Bethany Van Houten, Jason Veldman, Ben Walters, Kamaron Wilcox, Ashley Zardus, and Will Zywicki — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics and statistics department newsblog.

Problem of the Fortnight

Three boys, Alex, Bart and Chuck, and their sisters Delilah, Eunice and Frances (not necessarily in that order), had chickens for pets.  Last week was unusual.  Each chicken laid as many eggs as its owner owned chickens.  Bart had three times as many chickens as his own sister, and had eight more chickens than Chuck’s sister.  Further, by the end of the week, Bart had collected 56 more eggs than Alex; Chuck had collected 52 more than Delilah; and Alex had collected as many eggs as Delilah and Eunice together.

How many chickens did each of the six people own?  Who was whose sister?  What came first, the chicken or the egg?

Submit your solution inside an egg 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, March 6.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Sonny Sideup, Professor Chris P. Bacon — on your solution.  Good luck and have fun! 


This Mazda 3 just got an upgrade!

Off on a Tangent 18.09

Department Changes

Three big changes have happened in the mathematics department in the past couple months. First of all, we have been approved to provide a minor in Statistics. This minor includes taking the following courses: Calculus 2 (132), Introductory Statistics (311 or 210), Applied Statistical Methods (312), Applied Statistical Methods 2 (313) or Mathematical Statistics (362), Probability (365), and six additional credits (most likely including Calculus 1 (131) and two additional credits).

We have also added a Statistics Emphasis for Mathematics Majors. Students earning a mathematics major with emphasis in statistics must include Introductory Statistics (311), Applied Statistical Methods (312), Applied Statistical Methods 2 (313) or Mathematical Statistics (362), and Probability (365) as part of their elective mathematics courses.

Finally, we have officially changed our name to the Department of Mathematics and Statistics!

Pizza and Game Night

The Mathematics and Statistics Department is hosting a pizza and game night on Monday, February 17 from 6:28 to 8:28 PM. (To a mathematician that is 2π time to 2π + 2 time. Perhaps it’s time we told the mathematicians that the statisticians use π for something completely different than a particular irrational number.) Come join your fellow students and professors for pizza and fun board games. All of this takes place in VanZoeren 247.

Nebraska Conference for Undergraduate Women in Mathematics

Professors Stephanie Edwards and Dyana Harrelson, along with 11 undergraduate students and 3 other professors, traveled in a caravan across the Midwest to the Nebraska Conference for Undergraduate Women in Mathematics a couple weeks ago. The pictures shown below are Hope students Meredith Bomers, Fiona Johnson, and Emily Dee in the frame and Meredith presenting her talk, “Developing a General Compton Scattering Cross-Section in Strong Magnetic Fields.”  

Tutors needed

Hope College often gets requests from external people who are interested in hiring tutors and so, as a service to the community, we collect that information. If you would like your name to be added to a tutoring list, click here and fill out the form.

Professor Yurk’s work highlighted in SPERA

Hope College’s latest edition of SPERA includes an article about Dr. Brian Yurk. The article highlights his research in the dunes of Michigan and the rain forests of Costa Rica as well as his love for outdoor activities.

Hope grad Russell Houpt profiled

Russell Houpt, a 2018 graduate who majored in Psychology and Mathematics, is featured on the American Psychological Association (APA) Careers blog. They are doing an interview series on Psychology graduates who are using their undergraduate degrees in Psychology in their careers. Read about what Russell is doing now and how his Hope College education prepared him for his career.

Budapest Semesters in Mathematics Education

Interested in studying mathematics abroad? The Budapest Semesters in Mathematics Education has influenced many students, some who are pursuing a teaching certificate in mathematics and others who are mathematics majors curious about the Hungarian pedagogy based on guided discovery. Application deadlines are as follows:

  • Summer 2020 term is April 1
  • Fall 2020 semester is May 1
  • Spring 2021 semester is Nov. 1

Applications are accepted on a rolling basis so students are encouraged to start their applications now at bsmeducation.com/application/. Recent graduates are also encouraged to apply, as well as current seniors and in-service teachers.

Problem Solvers of the Fortnight

Congratulations to Sarah Brown, Ethan Cramer, Gabe DeYoung, Liam Diephuis, Cameron Dunn, Evan Nickel, Matthew Nguyen, Liam Orndorff, Eleni Persinger, Peter Ruffolo, Shane Vaara, Bethany VanHouten, Ben Walters, 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-thing.

Problem of the Fortnight

Imagine, if you will, a flat-bottomed pot with a circular cross-section of radius 4 inches.  What is the radius of the marble (with radius less than or equal to 4 inches) which when placed in the bottom of the pot, requires the largest amount of water to be completely covered?

Affix your solution to a marble (with radius less than or equal to 4 inches), 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 21.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Ray Diaz, Professor Aggie Marbull — on your solution.  Good luck and have fun! 

Happy Valentines Day from the Department of Mathematics and Statistics

Off on a Tangent 18.08

Two colloquiums scheduled in the next fortnight

  • Title: The Numerical Range of the Product of a Composition Operator and an Adjoint of a Composition Operator
  • Speaker: Dr. Michael Dabkowski, University of Michigan-Dearborn
  • Time/Location: Thur, Feb 6 @ 4:00 PM in VWF 104

Abstract: Composition operators take a function and compose it with another function (called an inducing map) to form a new function. When we allow the functions considered to be complex-valued, we uncover a trove of mathematical connections. In this talk we will consider functions which are elements of the Hardy space and compose them with the monomials zk. When this composition operator is multiplied by an adjoint of a composition operator of the same form we see the structure of a weighted shift operator. We will define the numerical range of this operator, investigate its convexity, and show that by inputting collection of lacunary polynomials we can foliate the numerical range.


  • Title: Recidivism, Risk scores, and Race: An overview of potential biases and notions of fairness in statistical models for predicting recidivism in the U.S.
  • Speaker: Dr. Yew-Meng Koh, Hope College
  • Time/Location: Thur, Feb 13 @ 11:00 AM in the Fried-Hemenway Auditorium (MMC 135).

Abstract: Predicting recidivism with defendants’ recidivism risk scores has become increasingly widespread in the U.S., with these scores influencing consequential decisions in trials. Concern has been raised in some quarters about the equity of these predictions across racial groups and the estimation of the risk scores themselves. This talk focuses on various reasonable notions of statistical parity, how they relate to each other, and the impossibility of simultaneously satisfying all definitions of statistical parity. The trade-offs from adopting one notion of fairness over another are also discussed, and suggestions are made for a reasonable compromise between several competing definitions.

Statistics Showcase

The 18th annual Statistics Showcase, held Friday, January 17, recognized ten outstanding student statistics projects of the Fall 2019 semester. Congratulations go out to all of these students for their hard work and outstanding results. The following projects were presented.

  • “The Effect of Energy Drinks” by Scott Corman, Abigail Dieffenbach and Erica Hofman
  • “How Do You Retain Information Better?” by Nic Larson, Abby Rakus and Kylie Slavik
  • “Reaction Times” by Jo Cook, MeKenna VanKoevering and Paige Wilmer
  • “A Toy Story: Factors that Affect Children’s Toy Prices” by Yuki Kojima, Emily Smith and Yung Yue Tneh
  • “Comparing Analytical Methods: Intramurals and Grade Point Average” by Michael Boynton, Mason Fritz and Nicholas Hoffman
  • “Effects of Background Music on Short-Term Memorization Ability” by Lindsey Heidema, Grace Kennedy, Claire Leikert and Megan McCarthy
  • “The Jelly Bean Test” by Julia Hopkins, Terry Nguyen, Caiti Warne and Leyang Xu
  • “The Difference of Preference Between Coke and Pepsi” by Lindsey Badger and Kendall Bouma
  • “Gamers vs. Non-Gamers: Tests of Cognitive Skills” by TJ Abraham, Seth Piersma and Caleb Schoon
  • “Influence of Brand Name on Preference” by Elly Deneef
Participants in the 18th Annual Statistics Showcase

Joint Mathematics Meetings

Here are some more pictures from this year’s Joint Mathematics Meetings in Denver. Three Hope students, Cole Persch, Jack Krebsbach, and Eric Leu, are shown presenting their posters.

Also shown enjoying a lovely buffet at Mint India in Denver are Hope’s student presenters along with Dr. Yurk and Dr. Edwards, as well as former Hope students Nathan Graber, Jessalyn Bolkema, and David McMorris (and wife Marla Williams).

Buttons!

Have you seen any of these cool math buttons around? Do you have any? The mathematics department started making buttons this year and are giving them out to those that take mathematics classes; a different button for each class. Which classes do you think the buttons in the picture represent?

U of M Big Data Summer Institute

Are you interested in big data? The University of Michigan conducts an annual Big Data Summer Institute and it will be held June 15 to July 24 this coming summer. You can find more information on the flyer or on their website.

Hope students that have attended this program in the past have found it to be a great experience. We just received a note from the University of Michigan professor that runs the program and he said, “I am in the process of reviewing applications for the Big Data Summer Institute. Unfortunately there were no applications from Hope College, which is a bummer because we seemed to have great Hope students virtually every year at the Big Data Summer Institute. We make a particular effort to grab great in-state students.”

So if you are interested, check it out. They are waiting for your application.

Your Health Lecture Series

Michigan State University’s College of Human Medicine provides for an annual lecture series co-sponsored by Hope, MSU, and Holland Hospital. This year’s talk is titled, “Millions of Lives Saved: The Incredible Impact of Immunizations.” It will be presented by Dr. Keith English, a pediatric infectious disease specialist at Michigan State. The talk will be held at 7:00 PM on Tuesday, February 4 in Graves Auditorium.

Problem of the Fortnight

Sally leaves Scooteroplis on her scooter at the same time Billy leaves Bikeville on his motorozed bike.  They meet at a point 24 miles closer to Scooteropolis than to Bikeville.  At this point, they swapped vehicles and returned to their home towns.  Sally completed her trip 9 hours after the switch, and Billy returned to Bikeville 16 hours after the switch.  Assuming the scooter and motorized bike maintained constant (but different speeds), what is the distance between Scooteropolis and Bikeville.

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, February 7.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Phil N. deBlank, Professor S.A. Antser — on your solution.  Good luck and have fun!

Problem Solvers of the Fortnight

Congratulations to Camen Andrews, Colin Brown, Josh Brown, Sarah Brown, Anna Carlson, Liam Diephuis, Cameron Dunn, Ryan Miller, Matthew Nguyen, Cole Persch, Eleni Persinger, Forest Rulison, Shane Vaara, Bethany VanHouten, Kamaron Wilcox, Tom Yonker, and William Zywicki—all of whom correctly solved the problem in the last issue of America’s premiere fortnightly mathematics department news blog.

Off on a Tangent 18.07

Joint Mathematics Meetings

Professor Edwards sent in a couple of pictures from the Joint Mathematics Meetings in Denver, Colorado. One is the obligatory ABS (awkward boarding selfie) of herself, Prof. Yurk, Cole Persch, Eric Leu, and Jack Krebsbach as they embarked on their journey. (And no, that is not Prof. Cusack’s head in the background.)

The other picture is of Nathan Graber (2012 Hope graduate) presenting at the meetings. Nathan is finishing his PhD at University of Colorado at Denver.

Problem of the Fortnight

The Van De Lay pharmaceutical company has developed two new drugs (call them A and B) for the treatment of uromycytisis.  In the first clinical trial, drug A cures 20% of the cases, and drug B cures 15% of the cases.  In the second clinical trial, drug A cures 85% of the cases and drug B cures 75% of the cases.  And yet, taken over both clinical trials, drug A has a 41.7% cure rate and drug B has a 55.0% cure rate.

Determine (i) the relationship between the number of people receiving drug A in the two trials and (ii) the relationship between the number of people receiving drug B in the two trials that would explain these figures.

Put your solution in an old medicine bottle and drop it in the Problem of the Forntight slot outside Professor Mark Pearson’s office, room 212 in The Werf, by 3:00 p.m. on Friday, January 24.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. H.E. Pennypacker, Dr. Martin Van Nostrand — on your solution.     

Off on a Tangent 18.06

Problem solvers of the fortnight

Congratulations to Pablo Bejarano, Josiah Brett, Griffin Bruso, Anna Carlson, Luke Christensen, Austin Cortes, Adair Cutler, Liz Cutlip, Adam Czeranko, Eli Edwards-Parker, Liam Faber, Mackenzie Green, Blake Harlow, Jacob Harrelson, Rebekah Harrelson, Adam Heisler, Fiona Johnson, Tyler Koran, Jacob Kowalski, Peter Le, Rebekah Ludema, James Mandeville, Matthew Nguyen, Josie Surel, Hugh Thiel, Karsten VanFossen, Bethany VanHouten, Nolan Vandegrift, Joseph Weber, Tracy Westra, Kamaron Wilcox, and William Zywicki — all of whom correctly solved the problem in the last issue of our fortnightly rag.

Problem of the fortnight

A circular disk of radius r < 1 rolls along the interior of a 1 × 1 square, always tangent to at least one of the sides.  (The picture below shows two sample locations of the circle.) What value of r maximizes the total area covered by the disk, and what is the total area the circle sweeps out as it rolls along the interior of the square?

Write your solution on a square of paper, 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 6.  As always, be sure to include your name and the name(s) of your math professor(s) — for example, Ray D. Oss, Professors C. Cant and Cy Kloyd — on your solution.  Good luck and have fun!  

Off on a Tangent 18.05

Student Research Colloquium

  • Title: Student Research
  • Speaker: Hope Students
  • When: 11:00 AM on Tuesday, November 19
  • Where: VanderWerf 102

Abstract: Hope mathematics students will talk about the research they have been conducting over the past year.

Joint Mathematics and Computer Science Colloquium

  • Title: Scalable Algorithms and Hybrid Parallelization Strategies for Multivariate Integration with ParAdapt and CUDA
  • Speaker: Omofolakunmi (Fola) Olagbemi, Western Michigan University
  • When: 11:00 AM on Thursday, November 21
  • Where: VanderWerf 102

Abstract: The evaluation of numerical integrals finds applications in fields such as High Energy Physics, Bayesian Statistics, Stochastic Geometry, Molecular Modeling and Medical Physics. The erratic behavior of some integrands due to singularities, peaks, or ridges in the integration region suggests the need for reliable algorithms and software that not only provide an estimation of the integral with a level of accuracy acceptable to the user, but also perform this task in a timely manner. We developed ParAdapt, a numerical integration software based on a classic global adaptive strategy, which employs Graphical Processing Units (GPUs) in providing integral evaluations. Specifically, ParAdapt applies adaptive region partitioning strategies developed for efficient integration and mapping to GPUs. The resulting methods render the framework of the classic global adaptive scheme suitable for general functions in moderate dimensions, say 10 to 25. The algorithms presented have been determined to be scalable as evidenced by speedup values in the double and triple digits up to very large numbers of subdivisions. An analysis of the various partitioning and parallelization strategies is given.

MATH Challenge

Hope again had a great turnout of students participating in the Michigan Autumn Take-Home Challenge on Saturday, November 3. Students competed with other students around the state (as well as other states) working in groups on ten interesting problems. This year’s problems included one where cats chased each other inside a regular polygon and another involving flipping coins to complete an NCAA bracket. You can see all of this year’s questions and solutions here.

The following students competed in this year’s MATH Challenge (grouped by team):

  • Eleni Persinger, Josiah Peterson, Julion Figueroa
  • Ted Eppinga, Evan Maday, Hans Veldman
  • Eric Leu, Jack Krebsbach, Emily Dee
  • Carolyn Atkinson, Alyssa O’Donohue, Lydia Meinhard
  • Kara Dahlenburg, Danielle Reiber
  • Matthew McAllister, Seth Almquist, Ivan Vanderkolk
  • Hayla Johnson, Reganne Diener
  • Kachikwu Nwike, Brandon Fuller, Askaree Crawford

Flatland: The Film

You are invited to a viewing of Flatland, a 2007 computer-generated film by Ladd Ehlinger, on Wednesday, November 13, at 9:00 p.m. in 102 VanderWerf. 

The movie is based on a novel of the same name, written in 1884 by Edwin Abbott Abbott.  The book is both a satire on Victorian society and an attempt to explain higher dimensions.  The movie retains some of those characteristics but adds some modern twists.

You can view a trailer for the film here.

Problem Solvers of the Fortnight

Congratulations to Tucker Babb, Jeff Bikus, Colin Brown, Griffin Bruso, Caroline Burkhardt, Austin Cortes, Adam Czeranko, Jason Deans, Brett Dyer, Blake Engler, Blake Fuller, Graham Gould, Brennan Hendrikson, Tyler Koran, Jacob Kowalski, Peter Le, Rebekah Ludema, James Mandeville, Cory McGregor, David McHugh, Matthew Nguyen, Kachikwu Nwike, Liam Orndorff, Madelyn Orndorff, Jack Radzville, Eric Salisbury, David Slakes, Shane Vaara, Bethany VanHouten, Nolan Vandegrift, Hans Veldman, Kamaron Wilcox, and William Zywicki — all of whom correctly solved the Problem of the Forntight in the last issue of The Blogosphere’s premiere fortnightly mathematics department news blog.

Problem of the Fortnight

Alexa has a collection of identical Amazon boxes.  She stacks 11 of them, end to end, to form one longer rectangular prism and is surprised when her assistant soothingly yet mechanically informs her that this rectangular prism has three times the surface area as one of the individual boxes.  “Three times?!” Alexa exclaims.  “Is there an ‘Echo’ in the room?,” her assistant wittily replies.  “Okay, assistant,” says Alexa.  “How many do I need to join end to end in order to form a rectangular prism with nine times the surface area?”

Write your solution on a cardboard box, 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 15.  As always, be sure to write your name and the name(s) of your math professor(s) — e.g. Ray Diennes, Professor D. Gries — on your solution.  Good luck and have fun!

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.