Off on a Tangent 17.11

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.

Time to sign up for a math class!

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).

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