# Section Visitors Program

Every MAA Section is eligible to have one Section Visitor per academic year from the Association leadership to attend and participate in a Section meeting, with all travel expenses borne by the MAA. Sections are not expected to provide the Visitor with an honorarium or stipend; the Section’s only financial obligation is to cover the registration fee and the cost of any associated social events. This popular program is a great way to find a dynamic speaker for your Section meeting, to energize your Section NExT group, to ask questions and share information with the Board of Directors.

### Why invite a Section Visitor?

The goals of this program are to:

• Provide the Association leadership with information about the unique features of the Sections they visit, with a more immediate sense of the concerns and issues facing the membership, and with a sense of the well-being of the Section, including how well it is fulfilling its mission.
• Provide the Section leadership with a perspective on trends in the Sections of the Association, with perceptions on the effectiveness of the management of the affairs of the Section, and with recognition for noteworthy Section activities and practices.
• Provide the members of the Section an opportunity to interact directly with the Association leadership though individual conversations and formal Section activities.

### What does a Section Visitor do?

To achieve these goals, each Section Visitor will participate in as much of the Section meeting as possible. In particular, the Section Visitor is expected to:

• Present at least one talk, workshop, or other activity agreed upon with the Section leadership.

These activities, and any other activities that the visitor is requested to lead, should be selected to align the experiences and talents of the Association leadership with the interests and needs of the Section.

• Attend and participate in any business meetings of the Section, meetings of the Section officers, liaison meetings, chairs’ meetings, and Section NExT activities. (Please make sure the Visitor is placed on the agenda of each of these meetings.)
• Participate in the social activities associated with the meeting.

After completing the visit, the Section Visitor will prepare a report for the MAA Board of Directors and the Committee on Sections, summarizing the activities that the visitor participated in or observed, noting those that should be shared with other Sections. The report should also reflect on the general health of the Section and areas in which the Section might improve. The Section Visitor will send a similar report to the Section officers and the Section representative.

### How to schedule a Section Visitor

Because many Section meetings are scheduled for a short "window" in the spring, Section Visitors are in high demand at that time. Therefore, Section leaders should extend an invitation as early as possible to the Section Visitor whom they want. The MAA Secretary and Chair of the Committee on Sections will assist if a Section has problems in scheduling a Section Visitor, but early planning is essential. When you invite a Visitor to your Section, please make it clear that you are inviting him/her as a Section Visitor. In order to ensure that the reimbursements are processed correctly, please notify Susan Kennedy of your section meeting speaker plans as soon as arrangements are made.

### Making your Section Visitor feel at home

Good advice for all invited guests

Each Section is asked to be a thoughtful host. In the crush of meeting details and the distribution of duties among Section officers and local arrangements folks, it is sometimes easy for responsibilities to fall through the cracks.

• Please be sure to consider your Visitor’s arrangements for travel, lodging, meals, local transportation and registration. If your Visitor arrives the night before, or stays the night after, the Section meeting, it is especially cordial that the Section consider evening dining arrangements. At least give visiting speakers options ("Do you need a ride?" or “Can we arrange for a cab?”) for airport pickups, get-togethers at meals, etc.
• Be sure to communicate fully about the schedule of events at your meeting.
• Make sure the Visitor is on the agenda for the Section business meeting, executive committee meeting, and any other appropriate events.
• Register your Visitor for the meeting! Prepare a name tag, meal tickets, and a program, and have them ready at the registration table.

### Section Visitors, Pólya Lecturers, and Section Representatives

Finally, it is important to note the distinction between the roles of the Pólya Lecturers, the Section Representatives, and the Section Visitors:

• Pólya Lecturers are leading members of the mathematical community, selected because they are outstanding speakers who are available to deliver an invited address during the Section meeting; they do not represent the leadership of the Association. Each Section may invite a Pólya Lecturer once every five years.
• The Section Representative is the Section’s official liaison with the Association; he or she reports the official actions of the Congress to the Section and communicates issues from the Section directly to the Congress. Section Representatives are provided materials by the Association to assist in this communication.
• Section Visitors are among the senior leadership of the Association and a primary purpose of their visits is to assist the Section leadership in maintaining healthy Sections by bringing to the Section leadership ideas of successful activities from other Sections and provide a means of communication between the leadership and the members.

### The Association leaders who are currently designated as Section Visitors

###### Jim Daniel, Treasurer
1515 Shasta Drive, #1516, Davis, CA 95616-6680
Email: daniel@math.utexas.edu
Available as a speaker: through Spring 2021

Topics include:

How much money do you (or your parents) need for retirement?
This student-oriented talk illustrates both the thinking and basic collegiate math used by actuaries in analyzing how to prepare now for future financial risk and so serves as an elementary introduction to actuarial mathematics.
Actuarial careers: what, where, who, how, and why
This student-oriented talk describes the job of an actuary, a career that has long been of interest to good problem solvers interested in applying their math skills in business.
Concave functions, Jensen's inequality, annuities, and divorce settlements".
This student-oriented 50-minute talk initially requires only pre-calculus and then basic probability. It describes functions that are concave down and some of their properties, especially Jensen's inequality that states that f(E{X]) ≥ E[f(X)] for a concave function f on an interval and a random variable X taking values in that interval. As an application, it then describes the present value of an annuity payable for life and shows that divorce settlements often overvalue the worth of the pensions of parties to the divorce and thereby treat the parties unfairly.
Community---the MAA, you, and the profession
This is a short 20-30-minute talk intended for Project NExT sessions. It describes the importance of belonging to a community and how the MAA (and other groups) provide communities of various sorts that can support and engage faculty over the years as their interests and focuses change.
###### Suzanne Dorée, Chair of Congress
Augsburg University
Email: doree@augsburg.edu
Available as a speaker: through Spring 2020

Topics include:

Writing Numbers as the Sum of Factorials

In standard decimal notation, we write each integer as the linear combination of powers of 10.  In binary, we use powers of 2.  What if we used factorials instead of exponentials?  How can we express each integer as the sum of factorials in a minimal way? This talk will explore the factorial representation of integers, including historical connections to permutations, a fast algorithm for conversion, and the secret of the “third proof by mathematical induction.”  Next we’ll extend this representation to rational and then real numbers, ending with a guest appearance by the generalized hyperbolic functions and some remaining open questions.

The Curious Case of 2s and 3s: Dynamics on Weak Compositions

The “Boltzman Game” begins with N students who each have $1. At each turn, two students are randomly selected and the first student gives$1 to the second, if possible. In the long run, how often does a student have $0,$1, $2, etc.? The answer uses Markov Chains, elementary counting, and other tools from discrete mathematics and uncovers a curious coincidence about$2s and $3s. We will also take a quick look at the state graph on these weak compositions, the induced dynamical system on partitions, and describe the Boltzman Distribution from Statistical Mechanics that motivated the game. The Graphs of Hanoi The Hanoi graphs are intricate, highly symmetric, little-known state graphs of the multi-peg versions of the famous Tower of Hanoi puzzle. In this talk, we'll tour this family of graphs, exploring what we and others have shown, and what is open for further investigation. Turning Routine Exercises into Activities that Teach Mathematical Inquiry Asking questions, checking examples, making conjectures, and constructing counterexamples are part of any mathematician's toolkit and important skills for our students to learn. The MAA CUPM curriculum guide agrees, calling us to include activities designed to promote student's progress in learning to . . . assess the correctness of solutions, create and explore examples, carry out mathematical experiments, and devise and test conjectures'' with the goal that students should develop mathematical independence and experience open-ended inquiry.'' How do we help students develop inquiry skills and ignite their curiosity about mathematics? In this professional development workshop we explore some practical strategies you can use to transform routine textbook exercises emphasizing procedural fluency and basic conceptual understanding into activities that teach inquiry. Come ready to try your hand at creating inquiry-based activities. Think-Pair-Share and Beyond: Active Learning Structures for the College Mathematics Classroom How can we create a classroom where engaged students are working hard, asking and answering each other’s questions, learning mathematics deeply, and asking for more? In this professional development workshop we will explore how active learning structures can help us create that environment in our mathematics classrooms. Whether you’re just getting started in active learning or an old pro looking for new ideas, come ready to try your hand at an array of different active learning structures. Now You're the Advisor: an Introduction to Academic Advising In this professional development workshop we explore the role of an (undergraduate) academic advisor, outlining what information an advisor needs to know, understanding the limitations on advising, and thinking about how to deal with difficult situations. Come ready to participate and with questions about the role of an advisor. ###### Michael Dorff, President Brigham Young University Email: mdorff@math.byu.edu Available as a speaker: through Spring 2022 Topics include: Workshops for Faculty and Other Teachers (50-90 minutes): How Mathematics Is Making Hollywood Movies Better What’s your favorite movie? Star Wars? Avatar? The Avengers? Frozen? What do these and all the highest earning Hollywood movies since 2000 have in common? Mathematics! You probably didn’t think about it while watching these movies, but math was used to help make them. In this presentation, we will discuss how math is being used to create better and more realistic movies. Along the way we will discuss some specific movies and the mathematics behind them. We will include examples from Disney’s 2013 movie Frozen (how to use math to create realistic looking snow) to Pixar’s 2004 movie The Incredibles (how to use math to make an animated character move faster). Come and join us and get a better appreciation of mathematics and movies The Best Jobs Last Century? – Doctor And Lawyer. The Best Jobs This Century? – Mathematician/STEM Careers! A 2014 ranking from CareerCast.com, a job search website, recently named mathematician the best job of 2014. “Mathematicians pull in a midlevel income of$101,360, according to CareerCast.com, and the field is expected to grow 23% in the next eight years,” states the Wall Street Journal blog post. Many students and professors think that teaching is the main (or only) career option for someone who studies mathematics. But there are hundreds of jobs for math students. However, just graduating with a math degree is not enough to guarantee getting one of these jobs. In this talk, we will talk about some of the exciting things mathematicians in business, industry, and government are doing in their careers. Also, we talk about the national PIC Math program that prepares students for nonacademic careers. Finally, we will reveal the three things that recruiters say every math student should do to get a job.

Soap Bubbles and Mathematics

In high school geometry we learn that the shortest path between two points is a line. In this talk we explore this idea in several different settings. First, we apply this idea to finding the shortest path connecting four points. Then we move this idea up a dimension and look at a few equivalent ideas in terms of surfaces in 3-dimensional space. Surprisingly, these first two settings are connected through soap films that result when a wire frame is dipped into soap solution. We use a hands-on approach to look at the geometry of some specific soap films and "minimal surfaces".

Successfully Mentoring Undergraduates in Research: A How to Guide for Mathematicians

Students engaged in undergraduate research are more successful during and after college in terms of: problem solving, critical thinking, independent thinking, creativity, intellectual curiosity, disciplinary excitement, and communication skills. Also, undergraduate research is a “high-impact practice” that is positively correlated with student higher GPAs, retention esp. during 1st to 2nd year, graduation rates, satisfaction with college, and pursuit of graduate degrees. In this presentation, we will discuss some of the nuts and bolts of successfully mentoring undergraduate student in mathematics research. Topics include picking an appropriate research problem, recruiting and selecting students to mentor, setting expectations and dealing with group dynamics, starting the research and moving it forward, helping students develop communication skills, and preparing for the future.

###### Deanna Haunsperger, Past-President
Carleton College
Email: dhaunspe@carleton.edu
Available as a speaker: through Spring 2020

Topics include:

Does Your Vote Count?
Are you frustrated that your candidate never wins? Does it seem like your vote doesn’t count? Maybe it doesn’t. Or at least not as much as the voting method with which you choose to tally the votes. Together we’ll take a glimpse into the important, interesting, paradoxical world of the mathematics behind tallying elections.
It is a problem as old as humanity: given a resource to be shared (water, land, cake) how can it be shared fairly between several people? The answer, in the case of two claimants, is simple and ancient and known to every five-year-old with a sibling: I cut,You choose. Things get much more interesting, and challenging, if one has more than one sibling. We are forced to ask ourselves exactly what “fairly” means in the question; “fair” from whose point of view and by what criteria?
Bright Lights on the Horizon
Math Horizons, the MAA undergraduate magazine, is now over twenty years old. In those two decades many fabulous articles have appeared. In this talk we will survey some of the speaker’s favorites, that list includes pieces on square-wheeled bicycles, Egyptian arithmetic, non-transitive dice, magic tricks, jokes, and mathematical paintings, theater and sculpture. An idiosyncratic tour of the best of Math Horizons.
###### Rachel Levy, Deputy Executive Director
Mathematical Association of America
Email: levy@maa.org

Topics include:

How to Prepare for a Job in Business, Industry and Government

Mathematical Modeling from Kindergarten to Industry

How to Communicate about Math so People Will Want to Listen

Mathematacal Adventures in Fluid Dynamics

###### Lisa Marano, Chair, Committee on Sections
West Chester University
Email: lmarano@wcupa.edu
Available as a speaker: through Spring 2021

Topic: Mathematics and Service Learning

###### Michael Pearson, Executive Director

Mathematical Association of America, 1529 18th Street NW, Washington DC 20036
Email: pearson@maa.org

###### Carol S. Schumacher, Vice President

Kenyon College, Gambier, OH 43022
Email: Schumacherc@kenyon.edu

Available as a speaker: through Spring 2020

Topics include:

All Tangled Up: Toys have inspired a lot of interesting mathematics. The SpirographTM helps children create lovely curves by rolling a small circle around the inside or the outside of a larger circle. These curves are called hypotrochoids and epitrochoids and are special cases of mathematical curves called roulettes. A roulette is created by following a point attached to one curve as that curve “rolls” along another curve. Another children’s toy, the TangleTM, inspired some students and me to investigate roulettes that we get by rolling a circle around the inside of a “tangle curve,” which is made up of quarter circles. The resulting roulettes we named “tangloids.” In this talk, we will look at many pretty pictures and animations of these curves and discuss some of their interesting properties. As a bonus, I will discuss the nature of generalization, which is very important in mathematics.

Fast forward, slow motion: A graphical link between fast and slow time scales: The world is shaped by interactions between things that develop slowly over time and things that happen very rapidly. Picture a garden. A bud takes hours to open up into a flower. A bee takes seconds to fly in, pollinate the flower and then depart. It can be difficult to fully consider both fast and slow time scales at the same time---yet it is the interaction between these events that makes the garden work. Mathematicians have developed a number of techniques for analyzing systems that include both fast and slow time scales. We will consider a graphical method for predicting what happens when fast and slow interact.

Zeroing in on the Implicit Function Theorem: In mathematics, it often happens that baroque, highly technical results disguise beautiful underlying principles. This talk traces the path from the elegant contraction mapping principle to the rather inscrutable implicit function theorem---a path that passes through Newton’s method for finding roots, linear algebra and linear approximation, and the geometry of multidimensional surfaces.

What is the definition of definition? and other mathematical cultural conundrums: Helping our students think like mathematicians should be at the center of every class we teach. The goal of every math class should be to turn out students who can bring mathematical reasoning to bear in the context of the material taught in the course. In order to help our students do this, we teachers must think deeply about what is going on in their heads. This can be devilishly difficult. In particular, it requires a great deal of self-reflection. How do we think about mathematics? Why is it that so many things are obvious in retrospect but hard to fathom at first? And how do we help our students past these barriers? As a teacher, I have learned a lot about this from my students. During a recent sabbatical leave, I became a student myself, taking courses for the first time in over three decades. This also helped me think about teaching and learning in new ways. The talk will be filled with illustrative examples of activities that can be used in different courses to help students engage the mathematical ideas of the course as mathematicians do every day

###### James Sellers, Secretary
University of Minnesota - Duluth
Email: jsellers@d.umn.edu
Available as a speaker: through Spring 2022

Revisiting What Euler and the Bernoullis Knew About Convergent Infinite Series

All too often in first-year calculus classes, conversations about infinite series stop with discussions about convergence or divergence. Such interactions are, unfortunately, not often illuminating or intriguing. Interestingly enough, Jacob and Johann Bernoulli and Leonhard Euler (and their contemporaries in the early 18th century) knew quite a bit about how to find the *exact* values of numerous families of convergent infinite series. In this talk, I will show two sets of *exact* results in this vein. The talk will be accessible to anyone interested in mathematics.

On Euler’s Partition Theorem Relating Odd-Part Partitions and Distinct-Part Partitions

In the mid-18th century, Leonhard Euler single-handedly began the serious study of integer partitions and made fundamental contributions to the area for the next few decades. In particular, he proved a remarkable result which says that the number of partitions of the integer n into distinct parts equals the number of partitions of n into odd parts. My goal in this talk is to discuss Euler's impressive work on partitions, including snapshots of historical (original) publications of Euler, and then to describe numerous 20th and 21st century results which spring from Euler's original result. The talk will be self-contained and geared for both students and faculty alike.

Cool Results Involving Fibonacci Numbers and Compositions

Compositions provide a wonderful backdrop for a number of well-known families of numbers, especially the Fibonacci numbers. In this talk, we will gently introduce the idea of a composition of an integer (which is just an ordered sum of integers), and then discuss how various families of compositions give rise to the Fibonacci numbers, Jacobsthal numbers, and a host of generalizations. The talk will be completely self-contained and understandable by all, especially undergraduate students interested in mathematics. Conjectures and opportunities for possible undergraduate research will be discussed at the end of the talk.

Advising Mathematics Students Academically and Professionally (suitable as a Section NExT workshop)

Mathematics Research With Undergraduates: Stories of Personal Success (suitable as a Section NExT workshop)

For the past several years of my career, I have enjoyed working with undergraduates on mathematical research projects of various types, from senior capstone experiences and research-intensive independent study courses to full-fledged research projects. I have found each of these experiences truly enriching, especially those endeavors which ended with refereed publications. (I have been privileged to write at least half a dozen papers with undergraduate co-authors!) In this talk I will share many of the details of these experiences. I will strive to answer the "why" and "how" of doing mathematical research with undergraduate students, from my perspectives at a small school (Cedarville University) and a large school (Penn State University). My hope is that I will inspire you to complete such projects with your students and that you and I will get to talk about some mathematics along the way.

###### Hortensia Soto, Associate Secretary
University of Northern Colorado
Email: hortensia.soto@unco.edu
Available as a speaker: through Spring 2022

Topics include:

Diverse Assessments
Diverse assessments can inform us about students’ understanding of undergraduate mathematics and can shape our teaching. Oral assessments such as classroom presentations and individual student interviews can paint a better picture of students’ conceptions as well as their misconceptions. Reading assignments with structured questions allow students to get a glimpse of new content and their responses can be used to structure the classroom discussion. Perceptuo-motor activities offer opportunities for students to feel, experience, and be the mathematics. In this talk, I will share numerous diverse assessments that I have implemented, the benefits of such assessments, and the challenges in implementing these assessments.
Promoting Mathematics to Young and Diverse Women
Abstract: Las Chicas de Matemáticas: UNC Math Camp for Young Women is a free one-week residential camp for 30 young women from grades 9-12, who have completed algebra I. The goals of the camp are to introduce young women to college-level mathematics, college life, STEM related careers, and other women who are passionate about mathematics. In this presentation, I will discuss the structure and outcomes of the camp and offer suggestions for anyone wishing to take on such an endeavor.