## Focus on Math: Dana Richards

The vast majority of mathematical puzzles ask for the existence of a solution. It is merely an exercise when the method is known and it is more of a puzzle when the method is not clear. An algorithmic puzzle takes this further by only asking for the method itself or a property of the method.  It is in this sense that much of computer science is puzzle solving. We discuss the theory behind this in the context of material taken from Martin Gardner’s Scientific American column. The answer to the following puzzle will be given:

There are five pirates dividing up 100 gold coins. Pirates are strictly ordered by seniority, are very logical and wish to live. The rule pirates use to divide gold is: (1) the most senior pirate suggests a division, (2) all pirates vote on it, (3) if at least half vote for it then it is done, otherwise the senior pirate is killed and the process starts over.  What happens?

Dana Richards is an associate professor of Computer Science at George Mason University. His research is on theoretical and algorithmic topics.  He has been a friend of Martin Gardner for nearly four decades and has edited Gardner’s book

The Colossal Book of Short Puzzles and Problems.

Join us at 4:00 on March 22nd to hear from Dana in 1170 TMCB.

## Focus on Math: Alissa S. Crans

Date:  April 12th, 2018 4:00 PM 1170 TMCB

Title:  Frosting Fairness, Finally!

Abstract:  Many of us are familiar with how to slice a cake ensuring equal sized slices for all.  But what about those of us who want an equal amount of frosting as well?!  This question is a classic with the problem solvers amongst us.  In 1975, Martin Gardner considered a square cake cut into 7 pieces in his Scientific American column.  More than a decade earlier, H.S.M. Coxeter posed the problem for a square cake sliced into 9 pieces as an exercise in his book, Introduction to Geometry.  Together, we will solve this problem for a square cake cut into 5 pieces, and investigate the other cake shapes for which the same procedure will produce slices with equal cake and frosting.

Bio:  Alissa S. Crans has been recognized nationally for her enthusiastic ability to share and communicate mathematics, having been honored by the MAA with the Hasse Prize and Alder Award. Her research lies in the field of higher-dimensional algebra and is currently supported by a Simons Foundation Collaboration Grant. Alissa is known for her active mentoring of women and underrepresented students, as well as of junior faculty as a member of the MAA Project NExT leadership team. When not enticing students with the beauty of mathematics at Loyola Marymount University or sharing her enthusiasm for math in settings ranging from “Nerd Night Los Angeles” to public school classrooms, you can find her rehearsing with the Santa Monica College Wind Ensemble or on her quest to find the spiciest salsa in LA.

## Focus on Math: Ross Curtis

Title: From Science to Product at AncestryDNA

Abstract: Converting cutting-edge research into everyday consumer products is exciting and challenging. In this talk I will discuss recent groundbreaking research (published in Nature Communications) that identifies recent populations using genetic data from our direct to consumer DNA business. Then, I will highlight some of the process that went into turning that research into a product that helps users connect with recent populations their ancestors may have come from.

Biography: Ross Curtis joined the AncestryDNA team in January of 2012. He is a computational biologist specializing in genetics and visual analytics and loves applying his expertise to family history and genealogy. Before AncestryDNA, Dr. Curtis focused on using visualization and statistics to discover genetic mutations that contribute to disease. Dr. Curtis received his B.S. from Brigham Young University and his Ph.D. in Computational Biology from Carnegie Mellon University.

Join us Thursday, November 16 at 4:30 in TMCB 1170 to hear about Ross’ experience on the AncestryDNA team.

## Focus on Math: Pamela Harris – Professor

Thursday, October 19, 2017 at 4:30:pm in 1170 TMCB

Title: Invisible Lattice Points

Abstract: This talk is about the invisibility of points on the integer lattice ℤ ✕ ℤ, where we think of these points as (infinitely thin) trees. Standing at the origin one may notice that the tree at the integer lattice point (1, 1) blocks from view the trees at (2, 2), (3, 3), and, more generally, at (n, n) for any n ∈ ℤ≥0. In fact any tree at (ℓ, m) will be invisible from the origin whenever ? and m share any divisor d, since the tree at (ℓ/D, m/D), where D = gcd(ℓ, m) blocks (ℓ, m) from view. With this fact at hand, we will investigate the following questions. If the lines of sight are straight lines through the origin, then what is the probability that the tree at (ℓ, m) is visible? Meaning, that the tree (ℓ, m) is not blocked from view by a tree in front of it. Is possible for us to find forests of trees (rectangular regions of adjacent lattice points) in which all trees are invisible? If it is possible to find such forests, how large can those forests be? What happens if the lines of sight are no longer straight lines through the origin, i.e. functions of the form f(x) = ax with , but instead are functions of the form f(x) = axb with b a positive integer and a ∈ ℚ? Along this mathematical journey, I will also discuss invisibility as it deals with the underrepresentation of women and minorities in the mathematical sciences and I will share the work I have done to help bring more visibility to the mathematical contributions of Latinx and Hispanic Mathematicians.

Math work is joint with Bethany Kubik, Edray Goins, and Aba Mbirika. Diversity work with Alexander Diaz-Lopez, Alicia Prieto Langarica, and Gabriel Sosa.

Biography: Pamela E. Harris is a Mexican-American Assistant Professor in the department of Mathematics and Statistics at Williams College. She received her B.S. from Marquette University, and M.S. and Ph.D. in mathematics from the University of Wisconsin-Milwaukee. Her research interests are in algebra and combinatorics, particularly as these subjects relate to the representation theory of Lie algebras. Her recent research on vector partition functions and projects in graph theory has been supported through awards from the National Science Foundation and the Center for Undergraduate Research in Mathematics. Harris co-organizes research symposia and professional development sessions for the national conference of the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science, was a Mathematical Association of America’s Project NExT (New Experiences in Teaching) Fellow from 2012-2013, and is an editor of the e-Mentoring Network blog of the American Mathematical Society. In 2016, she co-founded www.Lathisms.org an online platform that features prominently the extent of the research and mentoring contributions of Latins and Hispanics in the Mathematical Sciences. She is also the lead editor for the Special Issue on Motherhood and Mathematics of the Journal of Humanistic Mathematics.

## Robert J. Lang, Focus on Math

Date: Thursday, September 28, 2017

Time: 4:30PM

Room: 1170 TMCB

Title: From Flapping Birds to Space Telescopes: The Mathematics of Origami

Abstract: The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami and its underlying math has enabled safer airbags, Brobdingnagian space telescopes, and more.

Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over100 papers and 50 patents in lasers and optoelectronics as well as authoring, co-authoring, or editing 25 refereed papers, 17 books, and a CD-ROM on origami. Since 2001, he has been a full-time artist and consultant on origami and its applications to engineering problems. He received Caltech’s Distinguished Alumni Award, in 2009 and was elected a Fellow of the American Mathematical Society in 2013.

## Focus on Math

Have you ever been in a math class and asked yourself in a blurt of frustration, “When will I ever use this!?!” If so, your answer is here! BYU Department of Mathematics is excited to announce its “Focus-In-Math” speakers for Winter Semester 2017. Professional lecturers with careers in mathematics from across the country will be visiting our school throughout the semester to teach us how they use math. Our three guest speakers this semester are Dr. Gwen Spencer, Dr. Nick Trefethen, and Dr. Robert Bradshaw. This is an extremely beneficial opportunity for anyone going into careers involving math.

Our first speaker, Dr. Gwen Spencer, graduated from Harvey Mudd College with her bachelor’s degree in mathematics and went on to attain a PhD in Operations Research, as well as Postdoctoral Fellowships in Environmental Studies, Computer Science, and Economics. She is a successful mathematician and specializes in Approximation Algorithms, Stochastic Optimization, and Graph Theory. With her unique background and experience, Dr. Spencer can help us see math from an innovative viewpoint.

Dr. Nick Trefethen is a renowned mathematician with a bachelor’s degree from Harvard, his master’s from Stanford, and a Ph.D. on “Wave Propagation and Stability for finite Difference Schemes.” He has experience working at the Courant Institute of Mathematical Sciences, the Massachusetts Institute of Technology, and Cornell University. He is now an appointed chair at the University of Oxford, and a Fellowship of Balliol College, Oxford. Dr. Trefethen brings with him an extraordinary understanding of mathematics, and we are extremely excited to learn from such a prominent mathematician.

Dr. Robert Bradshaw is one of our very own BYU Alumni! After graduating BYU with double degrees in mathematics and linguistics he went on to get his Doctor of Philosophy (Ph.D.) in mathematics from the University of Washington. He has worked the past seven years as a Software Engineer for Google, and after meeting students last year as they toured Google’s Offices in Seattle, BYU invited him to share with students who share the same cougar pride.

Anticipate a powerful lineup of speakers and lectures this semester. Do not forget to mark your calendars:

• Thursday, February 23 – Dr. Gwen Spencer
• Thursday, March 23 – Dr. Nick Trefethen
• Thursday, April 13 – Dr. Robert Bradshaw

Join us for “Focus in Math Lectures” in room 1170 TMCB at 4 PM on the listed dates. See math from a new perspective – Learn the real answers to why and to what depth we use math.