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MAA Section Visitors Program

Every MAA section is eligible to have one person, 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 purpose of this program is to maintain close links between the MAA leadership and the sections. Specifically, 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.

To achieve these goals, each Section Visitor will participate in as much of the section meeting as is 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.
• Participate in the social activities associated with the meeting.

After completing the visit, the Section Visitor will prepare a report for the MAA Executive Committee 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 healthy management practices within the section and areas in which the section leadership might improve. These reports will be sent to the Secretary of the MAA for circulation to the Executive Committee. The section visitor will prepare a similar report to send to the section chair person and the section governor.

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 who 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.

It is customary for the section leadership to waive any registration, banquet and social fees for the Section Visitor. The Section Visitor will pay his/her own travel expenses and will be reimbursed by the Association directly. The section leadership should designate someone to assist in making arrangements for the Section Visitor’s travel, lodging, meals, local transportation and registration.

Finally, it is important to note the distinction between the roles of the Polya Lecturers, the section Governors, and the Section Visitors. The Polya 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. The section Governor is the section’s official liaison with the Association; he or she reports the official actions of Board of Governors to the section and communicates issues from the section directly to the Board of Governors. Section Governors are provided materials by the Association to assist in this communication. In contrast, the 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.

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.

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The Fractal Geometry of the Mandelbrot Set

In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the "Devaney" sequence. There might even be a joke or two in the talk. This talk only supposes a knowledge of complex numbers and is accessible to undergraduates.

Chaos Games and Fractal Images

In this lecture we will describe some of the beautiful images that arise from the "Chaos Game." We will show how the simple steps of this game produce, when iterated millions of times, the intricate images known as fractals. We will describe some of the applications of this technique used in data compression as well as in Hollywood. We will also challenge students present to "Beat the Professor" at the chaos game and maybe win his computer. This talk is accessible even to high school students.

Spreadsheets: An amazing tool to enliven and animate mathematics

In this talk we will give a number of examples of how spreadsheets may be used to animate all sorts of different graphs that arise in the secondary school and college mathematics curriculum. Such a tool is extremely valuable since almost all students have access to and are familiar with spreadsheets. Furthermore, a spreadsheet allows the user to view both the data and the graph of the data, and when animated, this becomes ane even more valuable tool in mathematics. At the end of the talk, we will show participants how to incorporate scrollbars into spreadsheets to activate these animations.

Cantor and Sierpinski, Julia and Fatou: Crazy Topology in Complex Dynamics

In this talk, we shall describe some of the incredibly beautiful and interesting topological structures that arise as Julia sets of certain complex functions including the exponential and rational maps. These objects include Cantor bouquets, indecomposable continua, and Sierpinski curves, each which we will describe completely. This talk is appropriate for advanced undergrads who are familiar with the complex exponential function.

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Board, Committees, Councils, Sections and Staff

This talk describes the MAA organizational structure, how the MAA serves you and how you can serve the MAA.

Applying for Research and Education Grants in the Mathematical Sciences

This talk gives an overview of how those in the mathematical sciences can apply for research and education grants and will discuss sources of funding as well as tips on writing proposals.

Topics include: MAA's American Mathematics Competitions: Easy Problems, Hard Problems, History, and Outcomes, Financing the Penney-Ante Game, The Path of a Bicycle Back Tire.

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Mathematics and Architecture in the Baroque Era
The Scottish Cafe and Its Book

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A Geometric Introduction to Bargaining Games

Using a simple bargaining game, in which two players collaboratively agree on an outcome, this talk demonstrates the value of geometric thinking. Fundamental concepts of fairness are identified and alternative solution methods are explored as the audience appreciates more of the geometry hinted at in the library window scene of A Beautiful Mind.

Everyday Questions, Not-So-Everday Mathematics

The world is full of un-explored mathematical problems. This talk presents the stories of three problems that the presenter found in his everyday world and investigated with undergraduate research partners. One is solved completely, one quickly reaches deep and un-explored mathematical territory, and the third, while not solved, opens many paths for further exploration.

A Game Theory Approach to Quantitative Literacy

This workshop explores the ways in which game theory topics can be used to motivate a general audience of students to review basic mathematics skills, and to utilize them to solve real problems from a quantitative perspective. Over the course of the four hours, participants play deterministic games, strategic games, bargaining games, and coalition games while exploring key solution concepts.

Arithmetic Functions on the Mosaic of n

In 1963, Albert Mullin introduced the mosaic of an integer as the array of primes that results from the repeated application of the Fundamental Theorem of Arithmetic to the integer and its exponents. In a series of papers, he explored the properties of various number theoretic functions defined on the mosaic. In the early 1990's, the presented continued this investigation by generalizing the mosaic concepts and of the corresponding the functions. Recently, a team of undergraduate REU students introduced a generalized the notion of a divisor applicable to the mosaic and expanded the family of functions defined on the mosaic. This talk summarized these results and posits several open questions.

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Mathematics to DIE for: The Battle Between Counting and Matching

Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n × n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.

The Combinatorialization of Linear Recurrences

Binet’s formula for the nth Fibonacci number, F_n= 1/√5 [((1+√5)/2)^n-((1-√5)/2)^n ], is a classic example of a closed form solution for a homogenous linear recurrence with constant coefficients. Proofs range from matrix diagonalization to generating functions to strong induction. Could there possibility be a better way? A more visual approach? A combinatorial method? This talk introduces a combinatorial model using weighted tiles. Coupled with a sign reversing involution, Binet’s formula becomes a direct consequence of counting exceptions. But better still, the weightings generalize to find solutions for any homogeneous linear recurrences with constant coefficients.

Proofs That Really Count

Every proof in this talk reduces to a counting problem---typically enumerated in two different ways. Counting leads to beautiful, often elementary, and very concrete proofs. While not necessarily the simplest approach, it offers another method to gain understanding of mathematical truths. To a combinatorialist, this kind of proof is the only right one. I have selected some favorite identities using Fibonacci numbers, binomial coefficients, Stirling numbers, and more. Hopefully when you encounter identities in the future, the first question to pop into your mind will not be "Why is this true?" but "What does this count?" This talk is a “Choose your own adventure”™ where the content is guided by the input and desires of the audience.

Fibonacci’s Flower Garden

It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci’s garden.

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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

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.

Topics include: New MAA Programs and Initiatives; Mathematical Mentors; Intriguing Everyday Mathematics Problems; The View from Capitol Hill; Gems from Math Horizons, Magic Squares, and Workshop:  Writing Successful Grants.

Topics include: Dimension, Fractals, and Wild Cantor Sets; Issues in the undergraduate geometry course

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Extreme calculus

Abstract: There is more to elementary calculus than may first meet the eye, especially to those of us who teach it again and again. With appropriate help from graphical, numerical, and algebraic computing, well-worn calculus techniques and topics---polynomials, optimization, root-finding, methods of integration, and more---often point to deeper, more general, more interesting, and sometimes surprising mathematical ideas and techniques. I'll illustrate my thesis with figures, examples, and a lot of e-calculation, aiming to take elementary calculus to its interesting extremes.

Picturing Ideas and Theorems in Analysis

Abstract: It's standard operating procedure to "think in pictures" about geometry, graph theory, elementary calculus, and other visually rich areas of mathematics. Less obvious, but equally valuable, are visual insights --- available with, and often only with, high-level computing --- into key ideas and theorems from elementary real and complex analysis.

Revisiting Familiar Places: What I Learned at the Magazine

Abstract: Among the perks of editing Mathematics Magazine for me was to learn a lot of mathematics. Much of it was new to me, but could there possibly be anything new to learn about cubic polynomials? Countable sets? Equilateral triangles? Bijective functions? The short answer is yes. The Magazine and other MAA journals are rich sources of novel --- and often surprising --- views of supposedly familiar, thoroughly understood, topics from undergraduate mathematics. I'll give some examples hat worked for me. That such examples exist derives not only from the speaker's ignorance but also from the depth and richness of our subject.

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