INDIANA
SECTION

Mathematical Association
of America

Meetings and Events
       Fall 2017
         Announcement
         Call for Papers
         Meeting Registration Form
               
        Meeting Info
            Preliminary Program
            Lodging & Directions
         
        Past Meetings
        Future Meetings
        National Events
        Other Events
        Local Checklist

Newsletters
        Current Newsletter
        Section Chair Statement
        Governor's Column
        Section News
        Columns
        Conference Pictures
        Section History
        Past Newsletters
        Submissions

Governance
        Executive Board
        Committees
        Section Bylaws
        Past Members

ICMC
        Registration Forms
        Results & Test Archive
        Past Winners

Section Awards
        Service
        Teaching
        MAA Service
Schools and Outreach
        Indiana Schools
        College Visitors Program
Indiana Project NExT
Various Links

Home


Outreach College Visitors Program


Indiana colleges have the opportunity to host one of the listed IN-MAA Visitors per year free of cost (with priority given to schools that are not currently involved in MAA activities but are interested). Each IN-MAA Visitor can speak on a topic of interest to undergraduates but also should be given an opportunity to discuss with Mathematics and other potentially interested faculty the value of membership in the MAA and participation in Indiana Section meetings and other Section activities. Interested colleges should contact the desired MAA Visitor directly to negotiate a visit date and itinerary. The MAA Visitor will then contact the IN-MAA Outreach Program Coordinator to obtain funding approval for necessary travel expenses (see here for details).

MAA Visitor Talk Titles
Kurt Bryan
Rose-Hulman Institute of Technology
kurt.bryan@rose-human.edu
The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google
Inverse Problems in Remote Sensing and Non-destructive Evaluation
The Mathematics of Cloaking and Invisibility
Picture Perfect: The Mathematics of JPEG Image Compression
Making Do With Less: The Mathematics of Compressed Sensing

Jeremy Case
Taylor University
jrcase@taylor.edu

My Favorite MAA articles for Linear Algebra
Adam Coffman
Indiana University-Purdue University Fort Wayne
CoffmanA@ipfw.edu
π/τ Debate
Generalizing Eves’ Theorem
Möbius Transformations and Ellipses
Matt DeLong
Taylor University
mtdelong@taylor.edu
An Introduction to Elliptic Curves: Taxis, Tangents and other Trails
Knot Colorability: Undergraduate Research using Crayons, Computers and Linear Algebra
David Finn
Rose-Hulman Institute of Technology
finn@rose-hulman.edu
Modeling the Shape of Baked Goods
A Stokes-vergence Theorem
Bicycle Track Constructions
Justin Gash
Franklin College
JGash@franklincollege.edu
From Buchberger to Faugere
Understanding Grobner Bases
Understanding the Advanced Encryption Standard (AES)
Rick Gillman
Valparaiso University
rick.gillman@valpo.edu
Why Do Left-Handed People Survive?
How to Find (and Keep) Neighbors
Optimizing Golf Bag Locations
Joshua Holden
Rose-Hulman Institute of Technology
holden@rose-human.edu
Braids, Cables, and Cells: Representing Art and Craft with Mathematics and Computer Science
A Tour of Public Key Cryptography (and of Number Theory)
A Good Hash Function is Hard to Find, and Vice Versa
David Housman
Goshen College
dhousman@goshen.edu
Fair Allocation
A Biological Auction
Michael Karls
Ball State University
mkarls@bsu.edu

Modeling a Diving Board
The Mathematics of Star Trek

Vesna Kilibarda
Indiana University Northwest
vkilibar@iun.edu
Groups, Generators, and Graphs
Daniel Kiteck
Indiana Wesleyan
daniel.kiteck@indwes.edu
Numberphile: Episodes from 2012
Andrew Rich
Manchester College
africh@manchester.edu
If I Were the Czar of Mathematics: Improving Mathematical Notation
The Mathematics of Spot-It
The Better Box Paradox
Leftist Numbers
A Binary Binatural Bijection
Pi is Wrong
Alain Togbe
Purdue University North Central
atogbe@pnc.edu
On Diophantine m-tuples

 


MAA Visitors

Kurt Bryan, Rose-Hulman Institute of Technology, kurt.bryan@rose-human.edu

Kurt Bryan (Ph.D., 1990, University of Washington) is Professor of Mathematics at the Rose-Hulman Institute of Technology. He has held a post-doctoral position at the Institute for Computer Applications in Science and Engineering (ICASE) at NASA's Langley Research Center, worked in industry from 1984 to 1990 as a mathematician and statistician at Blount Industries, been a visiting faculty member at Rutgers University, the US Air Force Academy, and has done much consulting for industry. His research interests lie mainly in partial differential equations, especially inverse problems. He is particularly interested in teaching applied mathematics to undergraduates, and has involved many students in his research and consulting. He was IN-MAA Treasurer (2012-2014) and is a regular contributor to the "Media Highlights" column in the College Math Journal..

The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google
When Google went online in the late 1990's, one thing that set it apart from other search engines was that its search result listings always seemed to deliver the "good stuff" up front. With other search engines, one often had to wade through screen after screen of links to irrelevant web pages that just happened to match the search text. Part of the magic behind Google is its PageRank algorithm, which quantitatively rates the importance of each page on the web, allowing Google to rank the pages and thereby present to the user the more important (and typically most relevant and helpful) pages first. In this talk, we explore the wonderful linear algebra that lies behind the traditional PageRank algorithm.

Inverse Problems in Remote Sensing and Non-destructive Evaluation
What do medical diagnosis, oil exploration, and airport security all have in common? Answer: The need to see inside an object---a human body, the earth, a suitcase. In each case we apply energy (mechanical, electromagnetic, even thermal) to the object, observe the response, and try to infer internal structure. We'd prefer to do this without damaging the object! This process frequently gives rise to mathematical "inverse problems." Inverse problems are sometimes summarized as the mathematics of "deducing cause from effect." In this talk I'll discuss the mathematical formulation of some common inverse problems, and techniques for solving them, with plenty of examples drawn from applications. This includes some sophisticated work done by undergraduates in Rose-Hulman's summer REU program.

The Mathematics of Cloaking and Invisibility
Cloaking and invisibility are staples of popular fiction, especially science fiction. The pseudo-explanation usually given is that "the selective bending of light rays" (to quote Mr. Spock) around the object to be cloaked can render the object invisible. But with the laws of physics in the real world, is this really possible, even in theory? Scientists and mathematicians have recently found that the answer to this question is a qualified "yes." In this talk I'll give a quantitative, but accessible account of the essential mathematical idea behind one approach to cloaking, in the context of an electromagnetic imaging technique called "impedance imaging.''

Picture Perfect: The Mathematics of JPEG Image Compression
Without effective image compression, the "www" in a web URL would probably stand for "World-Wide Wait." In this talk, I'll discuss the mathematics behind JPEG compression. JPEG compression is a wonderful application of elementary Fourier analysis and linear algebra, which I'll illustrate with plenty of audio and visual demonstrations. I'll then show how some of the shortcomings of traditional JPEG compression are addressed by the new wavelet-based JPEG 2000 standard.

Making Do With Less: The Mathematics of Compressed Sensing
Suppose a bag contains 100 marbles, each with mass 10 grams, except for one defective off-mass marble. Given an accurate electronic balance that can accommodate anywhere from one to 100 marbles at a time, how would you find the defective marble with the fewest number of weighings? You've probably thought about this kind of problem and know the answer. But what if there are two bad marbles, each of unknown mass? Or three or more? An efficient scheme isn't so easy to figure out now, is it? Is there a strategy that's both efficient and generalizable? The answer is "yes," at least if the number of defective marbles is sufficiently small. Surprisingly, the procedure involves a strong dose of randomness. It's a nice example of a new and very active topic called "compressed sensing" (CS), that spans mathematics, signal processing, statistics, and computer science. In this talk I'll explain the central ideas, which require nothing more than simple matrix algebra and elementary probability. I'll then show some applications, including how one can use this to build a high-resolution one-pixel camera.

 


Jeremy Case, Taylor University, jrcase@taylor.edu

Jeremy Case is a Professor and chair of the Mathematics Department at Taylor University in Upland, Indiana. He received his Ph.D. from the University of Minnesota in 1995, and his interests include linear algebra and undergraduate research. He was chair of the Indiana MAA section in 2006-07 and served on the board of the Dolciani series which produces mathematical books aimed for a broad audience. Professor Case was a Project NExT fellow in 1996, and he has been a consultant for several Indiana NExT fellows.

My Favorite MAA articles for Linear Algebra
Linear Algebra has many wonderful applications which are not always found in textbooks. Linear algebra applications can be found in computer science, games, and politics. This talk will sample articles from the journals of the Mathematical Association of America illustrating novel ideas. Furthermore, I will provide strategies for reading these articles as an entry into more advanced mathematics.

 


Adam Coffman, Indiana University-Purdue University Fort Wayne, CoffmanA@ipfw.edu

Adam Coffman is a Professor of Mathematics at Indiana University - Purdue University Fort Wayne. He received his Ph.D. from the University of Chicago in 1997 and his research interests are in geometry and complex analysis. Professor Coffman was the Public Information Officer for the Indiana MAA from 2008 to 2014 and he has given several talks at Indiana Section Meetings and the MAA MathFests.

π/τ Debate
Which is better, π = τ/2 ≈ 3.14 or τ = 2π ≈ 6.28? Are you a pi-rate or a tau-ist? This debate might help you decide whether to celebrate Pi Day (March 14) or Tau Day (June 28)! This debate was originally held with Andy Rich, but either speaker is willing to take on any other contestant!

Generalizing Eves’ Theorem
The cross-ratio is an interesting quantity in geometry, with many applications. A 2011 article by Marc Frantz in Mathematics Magazine discusses Eves’ Theorem, which states that certain ratios of Euclidean distance are invariant under projective transformations (a non-Euclidean notion) of the plane, generalizing a property of the crossratio. The theorem can be generalized to higher dimensions, and some of the results on invariant ratios of areas pre-date Eves.

Möbius Transformations and Ellipses
The image of an ellipse under a Möbius transformation of the plane is not necessarily an ellipse. I will show some pictures that demonstrate Möbius transformations, and how they distort the shape of an ellipse.


Matt DeLong, Taylor University, mtdelong@taylor.edu

Matt DeLong received his Ph.D. in Mathematics from the University of Michigan in 1998. He teaches all levels of the mathematics curriculum using a variety of active learning strategies, and he co-teaches the freshman seminar on the foundations of the liberal arts taken by all Taylor first-year students. He is a Fellow of the Bedi Center for Teaching and Learning Excellence, and co-coaches Taylor's highly successful mathematics competition team. His MAA activities include Indiana Section Treasurer (2006-2009), Associate Director of Project NExT (2012-2016), Alder Award Committee Member (2010-2013), and Hedrick Lecture Committee Member (2015-2017). Matt was awarded the 2005 Alder Award and the 2012 Haimo Award for distinguished teaching from the MAA.

An Introduction to Elliptic Curves: Taxis, Tangents and other Trails
Elliptic curves are beautiful mathematical objects that have connections to many areas of mathematics and applications to areas as diverse as string theory and internet security. This talk will focus on what an elliptic curve is and why it is "elliptic." How does a simple geometric construction yield the interesting and useful arithmetic structure on elliptic curves? Finally, there will be some applications of elliptic curves, including their role in the proof of Fermat's Last Theorem.

Knot Colorability: Undergraduate Research using Crayons, Computers and Linear Algebra
Knot theory is the mathematical branch of topology that studies mathematical knots. Knot Theory is an active field of mathematical research with many important applications in physics, chemistry and biology. Knot Theory is also unusually accessible (for modern mathematics) to research by undergraduates. In this talk, I will first give a non-technical overview of knot theory. I will then discuss knot colorability, which can sometimes be used to distinguish knots, and report on some results from undergraduate research that used methods requiring only a little bit of linear algebra.

 


David Finn, Rose-Hulman Institute of Technology, finn@rose-hulman.edu

David Finn received his PhD from Northeastern University in partial differential equations and geometric analysis in 1995. He was active in the Rose-Hulman REU from 2006-2013 mentoring 24 students, and continues to mentor senior theses and independent studies. His research centers on the application of differential equations to geometry and physics, and teaches courses in analysis, geometry and applied mathematics. His MAA activities include Project NExT 1995-1996, INMAA Newsletter Editor (2004-2008), Member of Mathematics Across the Disciplines Committee (2007-2013).

Modeling the Shape of Baked Goods
Such a talk covers a mathematical description for how heat and material properties affect the shape of baked goods such as bread, cookies and cake.

A Stokes-vergence Theorem
What happens when a student asks about integrating a vector field dotted with a spatial curve’s normal in an attempt to generalize the divergence form of Green’s theorem? You get a Stokes’-vergence theorem.

Bicycle Track Constructions
Talks based off the author’s Polya Award winning article: “Can you construct a unicycle track with a bicycle?”

 


Justin Gash, Franklin College, JGash@franklincollege.edu

Justin Gash is a graduate of Indiana University--Bloomington, earning his M.S. in computer science in 2007 and a Ph.D. in mathematics in 2008. He earned his B.A. in 2001 from DePauw University. Justin is an Associate Professor at Franklin College in Franklin, IN. His research interests are Grobner basis algorithms, undergraduate research, and mathematics education. Dr. Gash began serving on the Executive Board of the IN-MAA in 2010 as the Student Activities Coordinator. In that capacity he has supervised five ICMC competitions and helped to organize five workshops for undergraduates attending the IN-MAA spring conferences. He also served as the Indiana Section NExT Coordinator from 2010 through 2012. He currently resides in Franklin, IN with his wife, Andrea, and their Miniature Schnauzer, Phoebe.

From Buchberger to Faugere
A introductory history lesson in Grobner Bases theory, this talk starts with the basic definitions of a term order and a Grobner Basis of a polynomial ideal. Using illustrative examples, we review Buchberger's Algorithm. Finally, we introduce a variant of Buchberger's Algorithm, F5, introduced by Faugere early this century. (Note: This talk is suited to students who have had a modern algebra course and have been exposed to Grobner Bases before.)

Understanding Grobner Bases
This talk focuses on a basic problem that faces cryptologists and algebraists alike: solving large systems of equations with many unknowns. Starting from this motivation, Grobner bases are introduced. There is an emphasis on examples to demonstrate to the audience how interesting cancellations of terms not only make the calculations of a Grobner basis non-trivial, but also how these patterns are captured through Buchberger's Algorithm: the original method for computing Grobner Bases. The talk concludes with a brief discussion about why cryptographers/cryptologists care about Grobner bases and some progress that has been made in the field. (Note: This talk can be given at a freshman/sophomore-level or a senior-level.)

Understanding the Advanced Encryption Standard (AES)
This talk provides an outline for AES, including a step-by-step breakdown of the properties that make it "tick." Special attention is paid to invertibility and computability, which may be of particular interest to students interested in computing and mathematics. The talk is book-ended with an explanation of private key cryptography and some strategies for attacking the encryption. (Note: This talk is best-suited to students who've had some modern algebra, but can be given in a slightly altered version to sophomore-level-and-above students.)

 


Rick Gillman, Valparaiso University, rick.gillman@valpo.edu

Rick Gillman completed his undergraduate work at Ball State University and earned his Doctorate of Arts at Idaho State University in 1986. He has worked at Valparaiso University since then, rising to the rank of Professor and is currently Associate Provost for Faculty Affairs. Along the way he served as Assistant Dean for Sponsored Research and Faculty Development, was the founding director of VU’s Celebration of Undergraduate Scholarship, and was chair of his department. Rick has edited to two volumes published by the Mathematical Association of America (MAA), A Friendly Competition and Current Practices in Quantitative Literacy, and recently served as chair of the MAA’s Problem Series Editorial Board, and is Chair of the MAA Committee on Sections. He has been active in the Indiana section for many years, having served as secretary-treasurer, chair, and governor. Rick co-authored Models of Conflict and Cooperation, jointly with David Housman, from Goshen College.

Why Do Left-Handed People Survive?
This talk explores the question of why people are predominately right-handed, a trait shared by no other species. It answers the title question by considering the cultural, biological, and genetic explanations for our left-handedness. Two evolutionary game theoretic models are offered to explain why it may have been advantageous (from an evolutionary perspective) to have a fraction of the population be left-handed.

How to Find (and Keep) Neighbors
This talk explores the implications of our natural instinct to be around other people ‘like ourselves.’ In a major work, Schelling (1971) investigated the equilibrium states possible in bi-cultural housing environments. Young (2001) extended this work by identifying those equilibrium states which are also stochastically stable. Undergraduate students at Valparaiso University (2009, 2011) extended these results to multi-cultural environments. The new results have applications from describing the formation of high school cliques, to the American political landscape, to the stability of post-civil war Libya.

Optimizing Golf Bag Locations
We model the behavior of a walking golfer who must decide where to leave his or her golf bag when approaching a green to putt. The goal is to minimize the amount of walking (and hence the amount of time) necessary to finish the hole and move on to the next tee.

 


Joshua Holden, Rose-Hulman Institute of Technology, holden@rose-human.edu

Joshua Holden is a Professor of Mathematics at the Rose-Hulman Institute of Technology. He received his Ph.D. from Brown University in 1998 and his professional interests are in number theory, cryptography, mathematical fiber arts, and the use of cognitive theories in teaching. He has also been active in the Rose-Hulman REU and has mentored many undergraduate research projects. His MAA activities include being a Project-NExT consultant (2010-present), and INMAA Principal Information Officer (2014-present). He has also given several talks at INMAA Section Meetings, MAA MathFests, and MAA Sessions at the Joint Meetings.

Braids, Cables, and Cells: Representing Art and Craft with Mathematics and Computer Science
The mathematical study of braids combines aspects of topology and group theory to study mathematical representations of one-dimensional strands in three-dimensional space. These strands are also sometimes viewed as representing the movement through a time dimension of points in two-dimensional space. On the other hand, the study of cellular automata usually involves a one- or two-dimensional grid of cells which evolve through a time dimension according to specified rules. This time dimension is often represented as an extra spatial dimension. The ideas of representing both strands in space and cellular automata have also been explored in many artistic media, including drawing, sculpture, knitting, crochet, and weaving. This talk will present a system which captures the behavior of strands in certain of these media. Some theorems about what can and cannot be represented with these cellular automata will be presented.

A Tour of Public Key Cryptography (and of Number Theory)
Like other branches of mathematics, number theory has seen many surprising developments in recent years. One of the most surprising is the fact that number theory, long considered the most "useless" of any field of mathematics, has become vital to the development of modern codes and ciphers. We will take a tour of some of these ciphers, focusing on the "public key" ciphers --- ciphers which answer the question "Can two persons who have never had a secret in common, by a public discussion agree upon a common secret?" (Beutelspacher) For perhaps the first time in history, the answer is yes in practical terms. The ideas are very easy to understand, and yet underlie large portions of both modern number theory and modern cryptography.

A Good Hash Function is Hard to Find, and Vice Versa
Secure hash functions are the unsung heroes of modern cryptography. Introductory courses in cryptography often leave them out --- since they don't have a secret key, it is difficult to use hash functions by themselves for cryptography. In addition, most theoretical discussions of cryptographic systems can get by without mentioning them. However, for secure practical implementations of public-key ciphers, digital signatures, and many other systems they are indispensable. In this talk I will discuss the requirements for a secure hash function, the current state of the art in hash functions, and my attempts to come up with a "toy" system which is both reasonably secure and also suitable to work with by hand.

 


David Housman, Goshen College, dhousman@goshen.edu

David Housman received his Ph.D. in Applied Mathematics from Cornell University in 1983. He teaches courses in applied mathematics and computer science using interactive lectures, projects, self-discovery, cooperative groups, and a process orientation. He has mentored over seventy students in undergraduate research through summer programs, independent studies, and senior theses. His research interests are in game theory with applications to biology, economics, and political science. His MAA activities include Indiana Section Secretary (2001-2008), Indiana Section Governor (2008-2011), Contributed Paper Sessions Committee Member (2009-2012), and Contributed Paper Sessions Committee Chair (2012-2015).

Fair Allocation
One to four problems involving the distribution of resources such as money, people, voting power, and jobs is examined.  For each problem, audience members will act as negotiators or arbitrators and then learn about some of the relevant mathematics.  

A Biological Auction
The audience will participate in an auction with a somewhat unusual rule. We will explain why this auction models certain biological
phenomena. Finally, techniques from calculus will be used to determine the biologically optimal strategy.

 


Michael Karls, Ball State University, mkarels@bsu.edu

Michael Karls is a Professor in the Department of Mathematical Sciences at Ball State University, where he has been a faculty member, since completing his Ph.D. in Mathematics at the University of Wisconsin – Milwaukee in 1993. His expertise is in applied mathematics, with a specialization in PDE. His recent research, published jointly with undergraduates, has been focused on simple ways to experimentally verify that models based on classic equations actually do model reality. Michael’s professional service to the MAA includes nine years as a member of the INMAA Executive Board – comprised of two terms as Newsletter Editor, as well as Vice Chair, Chair, and Past Chair. In addition, he has served at the national level on the MAA Committee on Sections, MAA CUPM Subcommittee on Undergraduate Research, and MAA Board of Governors. In 2007, he was awarded the INMAA Distinguished Service Award.

Modeling a Diving Board
The beam equation is a classic partial differential equation that one may encounter in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating beam. A diving board can be thought of as a cantilever beam, which is a bar with one end fixed and the other free to move. Using a video camera and physics demonstration software to record displacement data from a vibrating cantilever beam, we verify a modified version of the beam equation that incorporates damping and a forcing term.

The Mathematics of Star Trek
We look at the challenges of designing a physics-based mathematics course for a general audience composed of both math and non-math majors. This course, “The Mathematics of Star Trek”, is designed “from scratch” and based on popular culture and historical topics. We will outline the topics chosen and give examples of homework and discussion questions used.

 


Vesna Kilibarda, Indiana University Northwest, vkilibar@iun.edu

Dr. Vesna Kilibarda received her bachelors and master's degrees in mathematics at the University of Belgrade, Yugoslavia, and her second master's and Ph.D. in mathematics with minor in computer science in 1994 from University of Nebraska, Lincoln. She was a Fulbright scholar at University of Nebraska, Lincoln in the 1987/1988 academic year. Her research interests are in algebraic semigroup theory and scholarship of teaching and learning mathematics. She published 11 journal articles and presented her work at regional, national, and international conferences, many times with her students. She is a winner of numerous teaching awards and grants and a member of FACET - Indiana University Faculty Colloquium of Excellence in Teaching since 2005. She is very active in Indiana Section of Mathematical Association of America (MAA) where she served as a chair, vice-chair, and past chair 2009-2012. Her latest position is Associate Professor of Mathematics in the Department of Mathematics and Actuarial Science of Indiana University Northwest. Currently she is a Co-Principal Investigator for NSF Grant Scholarships in Science, Technology, Engineering, and Mathematics (S-STEM) for project "Advancing Indiana Math and Science."

Groups, Generators, and Graphs
Groups are first introduced in undergraduate curriculum as a primarily algebraic concept - a set equipped with an algebraic operation (group multiplication) obeying a number of rules of algebra. One important way to enrich the structure of a group is to give it some geometry. One way to provide a geometric structure is to specify a list of generators S of the group G and build its, so called, Cayley graph with respect to that generating set. This way we can encode information about a group in a graph. On the other hand we can understand graphs by studying their groups of symmetry. In the talk we will present several such results about groups and their Cayley graphs: 1) Every finitely generated group acts on its Cayley graph; 2) A group G is free if and only if G acts freely on a tree; and 3) Every subgroup of a free group is free.

 


Daniel Kiteck, Indiana Wesleyan University, daniel.kiteck@indwes.edu

Daniel Kiteck received his PhD in Mathematics from the University of Kentucky in an area of Algebra (His PhD Adviser is in Relative Homological Algebra). He started at Indiana Wesleyan University in 2008 and enjoys teaching a number of classes (some favorites: Abstract Algebra, Senior Seminar, History of Mathematics, Mathematics for Future Elementary Teachers), as well as doing undergraduate mathematics research. He has enjoyed many IN-MAA meetings over the years, and he will serve as chair 2016-2017. He has given a number of talks at IN-MAA meetings and served the IN-MAA section of Project NExT. He is also a Project NExT fellow.

Numberphile: Episodes from 2012
Numberphile is a YouTube series focusing on interesting math aimed at a general audience. I will give highlights from the first year of numberphile, which are primarily episodes from 2012. I just finished these (around 100 episodes around 5-10 minues each), and I will continue to watch them. Topics include Heegner numbers, a special modern magic square, Brown numbers, and more.

 


Andrew Rich, Manchester College, africh@manchester.edu

Andrew Rich graduated from Bethel College in Kansas with a mathematics major in 1977, and received a Ph.D. in mathematics from University of Chicago in 1989. He taught at Kansas State University 1989-1992 and has been at Manchester University, and a member of the Indiana MAA, since 1992. He served as Secretary of the Indiana section 2008-2013. Has also lived and taught in Indonesia, Korea, Scotland, and Nicaragua.

If I Were the Czar of Mathematics: Improving Mathematical Notation
If you had complete power to redesign mathematical notation, what changes would you make?

The Mathematics of Spot-It
Spot-It is a game with 55 cards, each having 8 symbols. Any two cards have a unique symbol in common. What is the mathematics underlying this game? (Hint: projective geometry.)

The Better Box Paradox
The game show host shows you two boxes with hidden amounts of money inside. You choose one and open it. No matter what you see in the box, a simple probability calculation shows that the expected value of the other box is better. What should you do and how can we resolve this paradox?

Leftist Numbers
Suppose numbers were represented with decimal digits arranged in strings to the left, instead of to the right as we are accustomed to. The resulting number system includes all rational numbers but has many surprising features. This is a simple way to introduce p-adic numbers.

A Binary Binatural Bijection
Count the number of base 2 representations of a natural number, allowing digits 0, 1, and 2. This sequence leads, via the Euclidean algorithm and continued fractions, to a bijection between the integers and the rational numbers. Flipping the bijection "across the decimal point" leads to a continuous function with wonderful set-theoretic, analytic, and fractal properties.

Pi is Wrong
The Gospel according to Tau. One side (the right one) of a debate between π and τ. Which circle constant is better? (Note: Adam Coffman represented the π side in a debate at the Spring 2015 Indiana Section MAA meeting. This talk could be a debate with Adam Coffman, a debate with a local π supporter, or a one-sided talk.)

 


Alain Togbe, Purdue University North Central, atogbe@pnc.edu

Alain Togbe received his Ph.D. in Mathematics from Université Laval, Québec, Canada in 1997. He has published extensively in number theory and is an editor for the International Journal of Applied Mathematics & Statistics and the International Journal of Mathematics and Statistics. He has served as Indiana Section Vice Chair (2014-15) and Chair (2015-16).

On Diophantine m-tuples
A set of m distinct positive integers {a1, ..., am} is called a Diophantine m-tuple if ai aj +1 is a perfect square. In general, let n be an integer, a set of m positive integers {a1, ..., am} is called a Diophantine m-tuple with the property D(n) or a D(n)-m-tuple (or a Pn-set of size m), if ai aj +n is a perfect square. Diophantus studied sets of positive rational numbers with the same property, particularly he found the set of four positive rational numbers {1/16, 33/16, 17/4, 105/16}. But the first Diophantine quadruple was found by Fermat. That is the set {1, 3, 8, 120}. Moreover, Baker and Davenport proved that the set {1, 3, 8, 120} cannot be extended to a Diophantine quintuple. The problem of the extendibility of Diophantine m-tuples is of a big interest. During this talk, we will give a very quick history of Diophantine m-tuples, discuss of the conjectures and the recent progress to solve these conjectures.

 


Funding Process Details

After agreeing upon a visit date and itinerary with a host school, the MAA Visitor will email the IN-MAA Outreach Program Coordinator (David Housman, dhousman@goshen.edu) to obtain funding approval for necessary travel expenses. The email should include (1) the visit date and itinerary, (2) host school name and faculty contact name and email address, and (3) projected travel expenses. Travel expenses will be limited to round trip mileage based on the IRS rate (53.5 cents per mile as of January, 2017) and up to one night lodging. There will be a maximum reimbursement of $300 per visit. Annually, no more than $1,500 will be spent on this program. Funding will generally be approved on a first-come, first-served basis within budget constraints. When possible, priority will be given to schools that are not currently involved in MAA activities.

---
Comments? Email the Public Information Officer.
MAA online Disclaimer