MAA  Mathematical Association of America

Seaway Section

Location: Siena Hall 105

Note: James Park's talk, originally scheduled for 2:50 - 3:15 in this session has been cancelled. You may find his paper in the arXiv, arXiv.2104.09449.

1. Time:

   12:20 pm – 12:45 pm

   Title:

   Publishing LaTeX documents on the web

   Speaker:

   Cesar Aguilar (SUNY Geneseo)

   Abstract

   In this talk, we will discuss some of the limitations of using PDF files to publish mathematically rich documents on the world wide web and demo currently available tools for publishing LaTeX documents in HTML.

2. Time:

   12:50 pm – 1:15 pm

   Title:

   A Game Changer: Engaging Mathematics with the Lean Theorem Prover

   Speaker:

   Jon Bannon (Siena College)

   Abstract

   Computer proof assistants allow you to reinterpret theorems and their proofs as levels of a video game. Level design is the construction of the theorem statement, and "beating" the level amounts to constructing the (interactive) proof. In this session, we will play with the Lean Proof Assistant, and then discuss how the mathematics community is engaging with it and how to get involved.

3. Time:

   1:20 pm – 1:45 pm

   Title:

   Victims of Higher Space: Science Fiction for the Mathematics Classroom

   Speaker:

   Daniel Look (St. Lawrence University)

   Abstract

   The late 1800s and early 1900s saw a flourish of activity in mathematics and physics with mathematicians laying the groundwork for non-Euclidean geometry and mathematical models for higher dimensions. These ideas were picked up by pseudo-scientists and occultists as explanations for spiritual and supernatural events, eventually making their way into popular culture fiction in the early 20th century via stories appearing in so-called pulp publications. We will examine examples of uses of higher dimensions, mathematics, and physics in these stories and discuss the veracity of the usage. We’ll end with a brief discussion of how these stories and concepts can be folded into an upper level undergraduate course on popular culture and mathematics.

4. Time:

   1:50 pm – 2:15 pm

   Title:

   How I Learned to Stop Worrying and Love Online Exams (Continued)

   Speaker:

   Jeff Suzuki (Brooklyn College)

   Abstract

   During AY 2021-2022, we gave all our college algebra midterm exams online, but had an in-person final exam. To our surprise, student performance on the unmonitored midterm exams generally matched their performance on the in-person finals. This suggests that properly designed online exams can provide authentic and reliable measures of student understanding. We'll provide an overview of our approach.

5. Time:

   2:20 pm – 2:45 pm

   Title:

   A short proof of Fermat's two-square theorem

   Speaker:

   Sam Northshield (SUNY Plattsburgh)

   Abstract

   In 1990, Zagier proved, in one sentence, that every prime congruent to 1 modulo 4 is a sum of two squares. While attempting to understand Zagier's proof, I came up with my own short proof. A consequence is an easily implemented algorithm for finding the two numbers whose squares sum to a given prime.

Location: Siena Hall 106

Note: This is our special session on the History of Mathematics and its use in teaching. This session has been organized by Toke Knudsen from SUNY Oneonta and Elizabeth Wilcox from SUNY Oswego.

1. Time:

   12:20 pm – 12:45 pm

   Title:

   The Langlands Program a Few Centuries Back

   Speaker:

   Gary Towsley (SUNY Geneseo)

   Abstract

   I have been attempting to understand the Langlands Program for awhile now. I have noticed similarities between the modern work and the problems of the solution of the quintic and of Fermat's efforts to generate primes. It is this similarity I wish to present.

2. Time:

   12:50 pm – 1:15 pm

   Title:

   Poisson's exploration of complex line integrals

   Speaker:

   Jeff Johannes (SUNY Geneseo)

   Abstract

   In a 1820 paper published in the Journal de l'Ecole Polytechnique, Poisson wrote about complex line integrals. In one of the first hesitant steps in history, Poisson struggles with how to interpret line integrals in the complex plane, thinking that they potentially give rise to different values for associated real integrals. In this talk we will look at the details of the first complex line integrals and Poisson's early considerations of the results.

3. Time:

   1:20 pm – 1:45 pm

   Title:

   Multiplication in Ethiopian Marketplaces and Russian Peasant Schools

   Speaker:

   Mark McKinzie (St. John Fisher University)

   Abstract

   In 1896, an account of an interesting multiplication technique appeared in a French journal: this method, which was described as being used by Russian peasants, combined doubling ("duplation"), halving ("mediation") and a bit of addition. Thirty-five years later this same method was observed by Leo Roberts in an Ethiopian marketplace. This talk will described the method, compare it to a similar multiplication algorithm found in ancient Egypt, and trace the history of how this method was introduced to people in the United States.

4. Time:

   1:50 pm – 2:15 pm

   Title:

   The early history of compactness and its use in pedagogical design.

   Speaker:

   Naveen Somasunderam (SUNY, Plattsburgh)

   Abstract

   The concept of compactness is arguably one of the most abstract and difficult concepts to grasp in undergraduate mathematics. It involves two seemingly disparate ideas, sequences and open covers, that nevertheless unify under some mild constraints of the underlying set. In this talk, we examine the works of Dirichlet, Borel, and Lebesgue from the mid to late 1800s. These pioneers were influential in the further development of this concept by Frechet and Hausdorff in the 1900s. We shall also discuss how the historical development could be useful in pedagogical design of an advanced calculus course for undergraduates.

5. Time:

   2:20 pm – 2:45 pm

   Title:

   My Summer Vacation in Perspective.

   Speaker:

   Olympia Nicodemi (SUNY Geneseo)

   Abstract

   My summer travels had a theme: to follow the artists of the early renaissance in their development of perspective. My tour guide was the wonderful Danish historian, Kirsti Andersen. In this talk, I will follow her on a side trip that explores a sequence of diagrams found in the work of the early Renaissance artist and mathematician, Piero della Francesca (c. 1415-1492). In his De prospectiva pingendi (“On Perspective in Painting”), he presents an unusual approach to drawing a simple cube in perspective. His diagrams are not milestones in either art or mathematics, but they do provide an interesting look at how a pre-Cartesian artist/mathematician coordinated without coordinates.

6. Time:

   2:50 pm – 3:15 pm

   Title:

   Writing and Teaching the History of Polish Mathematics

   Speaker:

   Emelie Kenney (Siena College)

   Abstract

   An area of the history of mathematics that is lesser known, both in the general population and in the community of mathematicians, is the history of Polish mathematics, particularly in the Interbellum, during World War II, and immediately after that war. This history is rich with accomplishments, however, especially those of women who earned degrees and taught while in hiding from the Nazis, and deserves attention from a wider audience. Why is this history so little known? There are numerous reasons. In this talk, we discuss some of the issues and achievements of Polish women mathematicians, as well as reasons for their relative obscurity.

Location: Siena Hall 120

1. Time:

   12:20 pm – 12:45 pm

   Title:

   Playing with Continued Radicals and Iterated Exponents

   Speaker:

   Hossein Behforooz (Utica University)

   Abstract

   In real analysis and number theory courses, the study of the Continued Radicals and Continued Fractions and Iterated Exponents are very popular and interesting subjects. In this talk we will present some notes on the calculation of the continued radicals and iterated exponents with integer elements and integer values by using splitting of the integers under radicals in a certain way which are very bizarre and interesting approaches. Since the time of the lecture is short I promise to state the theorems without proofs. That will change my presentation from theoretical approach lecture to a fun and amusement type of lecture. Yes, this talk is understandable to undergraduate students. Come and join us. MATH is FUN.

2. Time:

   12:50 pm – 1:15 pm

   Title:

   An Impartial Combinatorial Game on a 3×3 Board with Magic Square Constraints

   Speaker:

   Matthew Coppenbarger (Rochester Institute of Technology)

   Abstract

   An impartial combinatorial game on a 3×3 array with constraints used for magic squares is defined. Entries for the game are nonnegative integers from 0 to n. We show that Bob has a winning strategy for n = 1 and Alice has the winning strategy for all other values of n. A winning strategy for each case is provided.

3. Time:

   1:20 pm – 1:45 pm

   Title:

   Distributing Points on the Sphere

   Speaker:

   Jack Graver (Syracuse University)

   Abstract

   In the the 1920s A Dutch botanist P.M.L. Tammes was interested in the distribution of the pores on pollen grains: they seemed to be ``evenly distributed." In 1906 a physicist, J.J. Thompson, was also interested in this problem: negatively charged particles are attracted to the surface of a positively charged sphere - but repel each other and seem to be ``evenly distributed." The joints of Buckminster Fuller's geodesic dome also seem to be ``evenly distributed." For computer scientists, the coordinates of a finite set of points on the sphere are the code words of a spherical code: the further apart the words are from one another the more accurately one can decode a message that includes some transmission errors. Finally, the golfball manufacturers distribute the dimples on their golfballs evenly! Exactly what do we mean by ``evenly distributed"? Is it the same in all cases? How would we find/construct such distributions? One point is clearly ``evenly distributed" on the sphere as are two antipodal points. Three points evenly distributed around an equator? The four vertices of an inscribed regular tetrahedron is pretty clearly the solution for four. Should we be able to use the inscribed platonic solids to get the solutions for 6 (octahedron), 8 (cube), 12 (icosahedron) and 20 (dodecahedron). But what about 5?, 7?, 9?, $\dots$. Come and we'll talk about it.

4. Time:

   1:50 pm – 2:15 pm

   Title:

   What Ate the Eight Root?

   Speaker:

   Hossein Shahmohamad (R I T)

   Abstract

   This talk establishes a family of root reduction identities. In particular, radical expressions whose root is a power of two are reduced to radical expressions whose root is equal to two; i.e., a square root. One particular reduction identity is used to provide a solution to a problem posed in the 56th Putnam exam.

5. Time:

   2:20 pm – 2:45 pm

   Title:

   A Covering Property

   Speaker:

   Gabriel Prajitura (SUNY Brockport)

   Abstract

   We will discuss the possible size of certain union of balls centered ar the rationals and of radiae the harmonic numbers. This is joint work with Gabriela Ileana Sebe from Polytechnic University of Bucharest & The Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy.

6. Time:

   2:50 pm – 3:15 pm

   Title:

   An Unexpected Expected Value

   Speaker:

   John Peter (Utica University)

   Abstract

   We investigate what happens if we roll a die along an infinite gameboard with roll again spaces. We look at some special cases for certain board configurations, and for dice of various size.

Location: Siena Hall 121

1. Time:

   12:20 pm – 12:45 pm

   Title:

   Quaternions - Navigating in Space or inside the Human Body

   Speaker:

   Jue Wang (Union College)

   Abstract

   Quaternions are four dimensional extension of complex numbers. They are now widely used in computer graphics and video games to represent orientations in 3D. Although less intuitive than Euler angles for visualizing roll, pitch, and yaw, quaternions have proven to be a more robust and efficient tool for tracking rotational motions. Quaternion development is attributed to William R. Hamilton in 1843. His work became the first non-commutative algebra to be studied. I will demonstrate how a gimbal lock can occur with Euler angles. A well-known gimbal lock incident happened in the Apollo 11 Moon mission. I will show orientation tracking with quaternions applied to ultrasound imaging. 3D printing, inertial measurement unit, Arduino microprocessor, and ultrasound system are integrated for reconstructing 3D volumetric views of the inside of the human body.

2. Time:

   12:50 pm – 1:15 pm

   Title:

   Well-Posedness and higher regularity of an inverse source problem for a parabolic equation

   Speaker:

   Sedar Ngoma (SUNY Geneseo)

   Abstract

   We consider an inverse time-dependent source problem for a parabolic partial differential equation with Neumann boundary conditions and subject to an integral constraint in a domain of $\mathbb{R}^n$, $n\ge 1$. We show the well-posedness and higher regularity of solutions in Hölder spaces. We then develop and implement an algorithm that we employed to approximate solutions of the inverse problem using a finite element discretization in space and the backward Euler scheme in time. The numerical experiments show that the proposed scheme is an accurate approach to approximate solutions of this inverse problem.

3. Time:

   1:20 pm – 1:45 pm

   Title:

   Linear Functions (modulo n) and Associated Algebraic Structure

   Speaker:

   Robert Sulman (SUNY Oneonta)

   Abstract

   We consider linear maps f(x) = ax+b (mod n) and explore the variety of “cycle graphs” produced by iteration. When gcd(a, n)=1, one additional condition enables us the determine the complete cycle structure without making any x/f(x) calculations. When gcd(a,n)≠1, “whiskers” will be present in the cycle graphs. We will also see symmetry in the distribution of inverse-pairs (in cycle graphs) among the units of the ring (Zn, +n, ●n). Finally, we examine the groups whose elements are linear maps (mod n). Several of the initial ideas have been introduced in this author’s Liberal Arts Mathematics classes.

4. Time:

   1:50 pm – 2:15 pm

   Title:

   Algorithms for Sustainability Optimization

   Speaker:

   Ahmad Almomani (SUNY Geneseo)

   Abstract

   Recently, many researchers have developed different types of optimization algorithms in various areas of sustainability and sustainable development. Many Optimization models for optimum efficiency in sustainability are established in environmental, economic, energy resources sustainability, and more. In this talk, I will introduce many examples of using optimization algorithms for various sustainability issues.