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All locations are subject to change)
Minicourses are open only to persons who register for the Joint Meetings and pay the Joint Meetings registration fee in addition to the appropriate minicourse fee. The MAA reserves the right to cancel any minicourse that is undersubscribed. Participants in minicourses #12 and #13 are required to bring their own laptop computer equipped with appropriate software. Instructions on how to download any data files needed for those courses will be provided by the organizers. All minicourses will be held in the Ile de France rooms (I, II, or III) located on the 3rd floor of the JW Marriott New Orleans Hotel. The enrollment in each minicourse is limited to 50; the cost of a minicourse is US$75.
Minicourse #1: Special relativity through a linear algebraic lens,organized by John de Pillis, University of California Riverside. Part 1: Friday, 1:00 p.m. - 3:00 p.m.; Part 2: Sunday, 1:00 p.m. - 3:00 p.m. Do all moving clocks run slow? Does a moving ruler actually shrink in the direction of motion? Anyone familiar with the basics of matrix theory has all the tools necessary to explore the ideas underlying the mysteries and paradoxes of special relativity. As an example consider how we pass from "reality" to a mathematical model. We see a real observer on a train platform at point x and time. This defines the mathematical ordered pair (x,t) which, it turns out, is invested with a full vector space structure. This is our link between observed reality and the mathematical model. In this minicourse we will investigate how this mathematical structure along with the standard tools of matrix theory resolve several well-known paradoxes of special relativity.
Minicourse #2: Getting mathematics majors to think outside the book: Course activities that promote exploration, discovery, conjecture, and proof, organized by Suzanne Dorée, Augsburg College; Jill Dietz, St. Olaf College; and Brian Hopkins, St. Peter's College. Part 1: Thursday, 2:15 p.m. - 4:15 p.m.; Part 2: Saturday, 2:15 p.m. - 4:15 p.m. Mathematics majors should explore, make and test conjectures, and prove mathematics of their own creation. Discovery-based activities designed to develop these skills can enliven any mathematics course, deepen student understanding, and help students make the sometimes difficult transition from book-based learners to independent investigators, especially in undergraduate research projects. In this minicourse we will work on sample activities from the undergraduate curriculum including discrete mathematics and other courses, discuss attributes of successful activities in any course, present curricular models incrementally building these skills throughout the major, and help participants plan how to incorporate these ideas in their own courses and program.
Minicourse #3: Geometry and algebra in mathematical music theory, organized by Thomas M. Fiore, University of Michigan-Dearborn; Dmitri Tymoczko, Department of Music, Princeton University; and Robert Peck, School of Music, Louisiana State University. Part 1: Friday, 8:00 a.m. - 10:00 a.m. Part 2: Sunday, 9:00 a.m. - 11:00 a.m. Mathematical music theory is a treasure trove of ideas and examples, especially for instructors looking to enhance their abstract algebra and topology courses. We will present two current areas, transformational theory and musical orbifolds, and provide mathematicians with musical examples that can be easily incorporated into math courses. We will discuss the structure of the neo-Riemannian group, how it transforms chords, its geometric depictions, and recent results on commuting groups. We will also describe how orbifolds provide a natural mathematical framework for modeling a range of musical problems. In these spaces points represent individual musical objects, such as chords, while line segments represent transitions between objects--called "voice leadings" by music theorists. Main topics are the construction and interpretation of relevant geometries, along with their analytical and theoretical applications. Successful REU projects will also be discussed briefly.
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Minicourse #4: Getting students involved in undergraduate research, organized by Aparna Higgins, University of Dayton, and Joseph Gallian, University of Minnesota-Duluth. Part 1: Thursday, 9:00 a.m. - 11:00 a.m.; Part 2: Saturday, 9:00 a.m. - 11:00 a.m. This course will cover many aspects of facilitating research by undergraduates, such as getting students involved in research, finding appropriate problems, deciding how much help to provide, and presenting and publishing the results. Similarities and differences between research conducted during summer programs and research that can be conducted during the academic year will be discussed. Although the examples used will be primarily in the area of discrete mathematics, the strategies discussed can be applied to any area of mathematics.
Minicourse #5: A Game Theory path to quantitative literacy, organized by David Housman, Goshen College, and Richard Gillman, Valparaiso University. Part 1. Friday, 10:30 a.m. - 12:30 p.m.; Part 2: Sunday, 1:00 p.m. - 3:00 p.m. Game Theory, defined in the broadest sense, can be used to model many real-world scenarios of decision-making in situations involving conflict and cooperation. Further, mastering the basic concepts and tools of Game Theory require only an understanding of basic algebra, probability, and formal reasoning. These two features of Game Theory make it an ideal path to developing habits of quantitative literacy among our students. This audience-participation minicourse develops some of the material used by the presenters in their general education courses on Game Theory and encourages participants to develop their own, similar, courses.
Minicourse #6: Green linear optimization, organized by Glenn Hurlbert, Arizona State University. Part 1: Friday, 9:00 a.m. - 11:00 a.m.; Part 2: Sunday, 9:00 a.m. - 11:00 a.m. No, not environmental, just inexperienced. How does it work? What is it good for? What are its big theorems? Can I teach it? Turns out, most experts place the Simplex algorithm among the top ten algorithms of the 20th century, due to its nearly unrivalled impact on the last 50 years of business, engineering, economics, and mathematics. While it is regularly taught to undergraduates in those other disciplines, it is a mystery why it is virtually missing from mathematics departments. Needing little more than the first few weeks of linear algebra, students can experience connections with geometry, probability, combinatorics, algorithms, computing, game theory, economics, graph theory, and modeling. Whether you'd like to offer a course in your department, make connections with your own research, or just satisfy your curiosity, come see what all the fuss is about. This will be a very hands-on experience, with games, puzzles, and experiments motivating main results and techniques. A laptop is not necessary, but if you want to bring yours, you can download WebSim from my homepage to use (http://mingus.la.asu.edu~hurlbert/), and even run Maple if you like.
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Minicourse #7: The mathematics of Islam and its use in the teaching of mathematics, organized by Victor J. Katz, University of the District of Columbia. Part 1: Thursday, 9:00 a.m. - 11:00 a.m.; Part 2: Saturday, 9:00 a.m. - 11:00 a.m. In the current world situation, it is critical that American students be exposed to some of the culture of Islam. Thus, this minicourse introduces college teachers to the mathematics of Islam and develops some ideas on using Islamic mathematical ideas in the teaching of mathematics. The course will consider mathematical ideas taken from arithmetic, algebra, geometry, and trigonometry. Participants will read from some of the original sources and discuss the ideas and their implications. In particular, we will consider how some of the examples of Islamic mathematics can be used in modern courses in high school and college.
Minicourse #8: The ubiquitous Catalan numbers and their applications, organized by Thomas Koshy, Framingham State University. Part 1: Thursday, 9:00 a.m. - 11:00 a.m.; Part 2: Saturday, 9:00 a.m. - 11:00 a.m. Catalan numbers are both fascinating and ubiquitous. They pop up in quite unexpected places, such as triangulations of convex polygons, correctly parenthesized algebraic expressions, rooted trees, binary trees, full binary trees, trivalent binary trees, latticewalking, Bertrand's ballot problem, abstract algebra, linear algebra, chess, and the World Series, to name a few. Beginning with a brief history of Catalan numbers, this minicourse presents numerous examples from different areas. We will develop a number of combinatorial formulas for computing them, investigate their parity and their primality-link to Mersenne numbers, and present the various ways they can be extracted from Pascal's triangle and several Pascal-like triangles. We will investigate both Lobb's generalization of Catalan's Parenthesization Problem and tribinomial coefficients, and show how Catalan numbers can be extracted from tribinomial coefficients.
Minicourse #9: Learning discrete mathematics via historical projects, organized by Jerry Lodder, Guram Bezhanishvili, and David Pengelley, New Mexico State University; and Janet Barnett, Colorado State University, Pueblo. Part 1: Thursday, 2:15 p.m. - 4:15 p.m.; Part 2: Saturday, 2:15 p.m. - 4:15 p.m. This minicourse is aimed at introducing curricular modules in discrete mathematics, combinatorics, logic, abstract algebra, and computer science based entirely on primary historical source material, developed by an interdisciplinary team of mathematics and computer science faculty at New Mexico State University and Colorado State University at Pueblo. In the first session we plan to discuss the pedagogy behind our approach, give a brief outline of the projects we have developed, and provide snapshots and initial hands-on participant work with four chosen projects. In the second session we will discuss the four projects in detail, including group discussions and more hands-on activity. The projects we have developed so far as well as our philosophy in teaching with historical sources can be found on our homepage: http://www.cs.nmsu.edu/ historical-projects/
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Minicourse #10: Teaching introductory statistics, organized by Michael Posner, Villanova University, and Carolyn Cuff, Westminster College. Part 1: Friday, 1:00 p.m. - 3:00 p.m.; Part 2: Sunday, 3:30 p.m. - 5:30 p.m. This minicourse, intended for instructors new to teaching statistics, exposes participants to the big ideas of statistics and the ASA-endorsed Guidelines for Assessment and Instruction in Statistics Education report. It considers ways to engage students in statistical literacy and thinking, and contrast conceptual and procedural understanding in the first statistics course. Participants will engage in many of the classic activities that all statistics instructors should know. Internet sources of real data, activities, and best practices articles will be examined. Participants will find out how they can continue to answer the three questions by becoming involved in statistics education related conferences, newsletters, and groups.
Minicourse #11: Using video case studies in teaching a proof-based gateway course to the mathematics major. organized by James Sandefur, Georgetown University; Connie Campbell, Millsaps College; and Kay Somers, Moravian College. Part 1: Thursday, 2:15 p.m. - 4:15 p.m.; Part 2: Saturday, 2:15 p.m. - 4:15 p.m. Many colleges and universities have a gateway course to help mathematics students make the transition to more theoretical courses, with a goal of helping students learn how to understand and construct proofs. The organizers have been videotaping students writing proofs for problems used in gateway courses, and have been using these videos to expand their understanding of students' difficulties and to learn what support helps the students. They have also been using these videos to help students learn to reflect on their own approaches to writing proofs. In this minicourse we will view some of these videos and discuss strategies implied by them, as well as help faculty learn how they might use these videos in their own transition course.
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Minicourse #12: Concepts, data and models: College algebra for the real world, organized by Sheldon P. Gordon, Farmingdale State College, and Florence S. Gordon, New York Institute of Technology. Part 1: Friday, 9:00 a.m. - 11:00 a.m.; Part 2: Sunday, 9:00 a.m. - 11:00 a.m. Almost all students taking college algebra do so to fulfill requirements for other disciplines. The current mathematical needs of our partner disciplines, especially for lab science and data-dependent social science courses are very different from courses that prepare students for calculus. Students need a focus on conceptual understanding, data and statistical analysis, and realistic problem-solving via mathematical modeling to prepare for the mathematical applications they will encounter in those courses. Families of functions and data are the two primary motivating themes around which this approach is centered. A significant amount of statistical reasoning and methods is integrated in natural ways as applications of college algebra topics. All participants are expected to bring a laptop computer to the minicourse.
Minicourse #13: Creating demonstrations and guided explorations for multivariable calculus using CalcPlot3D, organized by Paul Seeburger, Monroe Community College.Part 1: Friday, 1:00 p.m. - 3:00 p.m.; Part 2: Sunday, 1:00 p.m. 3:00 p.m. It is often difficult for students to develop an accurate and intuitive understanding of the geometric relationships of calculus from static diagrams alone. This course explores a collection of freely available Java applets designed to help students make these connections. Our primary focus will be visualizing multivariable calculus using CalcPlot3D, a versatile new applet developed by the presenter through NSF-DUE-0736968. Participants will also learn how to customize this applet to create demonstrations and guided exploration activities for student use. Images created in this applet can be pasted into participants' documents. See http://web.monroecc.edu/calcNSF/. Some basic HTML experience is helpful. All participants are expected to bring a laptop computer to the minicourse.
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