MAA 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 4, 6, 7, and 15 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. The enrollment in each minicourse is limited to 50; the cost of a minicourse is US$80.
Minicourse #1: Heavenly mathematics: The forgotten art of spherical trigonometry, presented by Glen Van Brummelen, Quest University, and Joel Silverberg, Roger Williams University. Part A, Thursday, 9:00 a.m.–11:00 a.m.; Part B, Saturday, 9:00 a.m.–11:00 a.m. Trigonometry came into being at the birth of science itself: merging Greek geometric models of the motions of celestial bodies with the desire to predict where the planets will go. With the sky as the arena, spherical trigonometry was the “big brother” to the ordinary plane trigonometry our children learn in school. We shall explore the surprisingly elegant theory that emerges, as well as its appropriation into mathematical geography motivated by the needs of Muslim religious ritual. The beautiful modern theory of spherical trigonometry (including the pentagramma mirificum), developed by John Napier along with his logarithms, leads eventually to an astonishing alternate path to the subject using stereographic projection discovered only in the early 20th century. We conclude with a consideration of some of the ingenious techniques developed by navigators in the 19th century to find their locations, using as data only a couple of observations of stellar altitudes.
Minicourse #2: A Game Theory path to quantitative literacy, presented by David Housman, Goshen College; Part A, Thursday, 1:00 p.m.–3:00 p.m.; Part B, Saturday, 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 presenter in general education and math major courses on Game Theory and encourages participants to develop their own, similar, courses.
Minicourse #3: How to run a successful math circle, presented by Sam Vandervelde, St. Lawrence University; Japheth Wood, Bard College; and Amanda Katharine Serenevy, Riverbend Community Math Center; Part A, Wednesday, 4:45 p.m.–6:45 p.m.; Part B, Friday, 3:30 p.m.–5:30 p.m. A math circle brings together secondary school students and professional mathematicians on a regular basis to explore engaging topics. This course will focus on the logistics involved in organizing and sustaining a math circle as well as the fine art of conducting lively sessions. Facilitators will discuss how to adapt a promising topic for math circle use, provide tips for keeping a circle running smoothly, and address issues such as publicity and funding. Participants will craft a math circle lesson plan and take away a variety of materials including sample topics and a list of book and Web resources.
Minicourse #4. Experiments in circle packing, presented by Ken Stephenson, University of Tennessee, and G. Brock Williams, Texas Tech University. Part A, Wednesday, 2:15 p.m.–4:15 p.m.; Part B, 1:00 p.m.–3:00 p.m. Friday. Circle packing concerns configurations of circles with specified patterns of tangency. They were introduced in 1985 by Bill Thurston and provide as thorough and pleasing a blend of theory, computation, application, and visualization as you will find in all of mathematics. Moreover, their concrete visual nature make them uniquely accessible. This minicourse will give participants direct exposure to this topic through the creation, manipulation, display, and analysis of circle packings on their own laptops. We will use the open source software “CirclePack” with a variety of prepared “scripts” that will guide participants from the basics in Euclidean, hyperbolic, and spherical geometry, through selected advanced topics such as conformal mapping and Riemann surfaces, to opportunities for open-ended experiments and applications in areas from graph embedding to random triangulations.
The goal of the minicourse is to expose the participants to this fascinating new topic with tools that they can use to initiate their own explorations or to share with students and colleagues: “CirclePack” provides an experimental test bench for addressing problems from the undergraduate project to the research paper level.
The minicourse will assume no background in circle packing nor any but routine computer skills. A taste of the topic can be found in “Circle Packing: A Mathematical Tale”, (Notices of the AMS, 2003). (In particular, note that “sphere packing” is a mathematically distinct topic.) Deeper background material can be found in “Introduction to Circle Packing: the Theory of Discrete Analytic Functions” (Cambridge, 2005) and “Exploring Complex Analysis”, (MAA ebooks, due in 2012, Chapter 6).
Minicourse #5. Visualizing projective geometry through photographs and perspective drawings, presented by Annalisa Crannell, Franklin & Marshall College; Marc Frantz, Indiana University Bloomington; and Fumiko Futamura, Southwestern University. Part A, Wednesday, 9:00 a.m.–11:00 a.m.; Part B, Friday, 9:00 a.m.–11:00 a.m. Projective geometry is the study of properties invariant under projective transformations, often taught as an upper level course. Although projective geometry was born out of the ideas of Renaissance artists, it is often taught without any reference to perspective drawing or photography. This minicourse seeks to re-establish the link between mathematics and art, motivating several important concepts in projective geometry, including Desargues’ Theorem, Casey’s Theorem and its applications, and Eves’ Theorem. This minicourse will consist of hands-on activities, but no artistic experience is required.
Minicourse #6. Using randomization methods to build conceptual understanding of statistical inference, presented by Robin H. Lock, St. Lawrence University; Patti Frazer Lock, St. Lawrence University; Kari Lock Morgan, Duke University; Eric F. Lock, University of North Carolina, Department of Statistics and Operations Research; and Dennis F. Lock, Iowa State University, Department of Statistics. Part A, Wednesday, 9:00 a.m.–11:00 a.m.; Part B, Friday, 9:00 a.m.–11:00 a.m. The goal of this minicourse is to demonstrate how computer simulation techniques, such as bootstrap confidence intervals and randomization tests, can be used to introduce students to fundamental concepts of statistical inference in an introductory statistics course. Simulation methods are becoming increasingly important in statistics, and can be effective tools for building student understanding of inference. Through easy to use online tools and class activities, participants will see how to engage students and make these methods readily accessible.
Minicourse #7. Teaching and assessing writing and presentations: Collaborative development of pedagogy, presented by Susan Ruff, Massachusetts Institute of Technology; Mia Minnes, University of California, San Diego; and Joel Lewis, University of Minnesota. Part A, Wednesday, 4:45 p.m.–6:45 p.m.; Part B, Friday, 3:30 p.m.-5:30 p.m. In the first session we break into groups to characterize “good” math writing and “good” math presentations and to create sample materials for assessing student work. The second session is about how to teach students to communicate math effectively and will focus on participants’ specific interests. Existing resources will be presented from the mathematical communication pages of the MAA’s MathDL website, and open questions will be discussed in small groups. The session concludes with the optional formation of working groups to address open questions using available tools for collaborative development of pedagogy.
Participants will leave this highly interactive mini-course with a strategy for grading math writing and speaking, a clearer understanding of their own priorities for teaching math communication as well as the diverse priorities of other math educators, awareness of the wealth of resources for teaching mathematical communication available through MAA’s MathDL and, if desired, collaborators and a plan for addressing open questions in how to teach mathematical communication.
Minicourse #8. Getting students involved in undergraduate research, presented by Aparna Higgins, University of Dayton, and Joseph Gallian, University of Minnesota Duluth. Part A, Thursday, 9:00 a.m.–11:00 a.m.; Part B, Saturday, 9:00-11:00 a.m. This minicourse 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. It is designed for faculty who are beginners at directing undergraduate research. 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 #9. Shortest, quickest, or best: An introduction to the calculus of variations, presented by Jeffrey Ehme, Spelman College. Part A, Thursday, 1:00 p.m.–3:00 p.m.; Part B, Saturday, 1:00 p.m.–3:00 p.m. The calculus of variations is a nice blend of calculus, real analysis, and differential equations with many applications in physics, engineering, and mathematics. These techniques give an easy proof that the shortest distance between two points is a straight line and determine the path of quickest descent between two points among other results. This introductory minicourse will begin by introducing the topic and providing some historical background. Next, we will derive a necessary condition for extremals, the Euler-Lagrange equation, and apply it to several concrete problems. We also consider generalizations to higher order problems, problems with more dimensions, problems with constraints, least action formalizations, and the relationship between Hamilton’s principle and Newton’s laws. Lastly, we consider differential calculus in general Banach spaces and discuss possible student projects.
Minicourse #10. The mathematics of the Common Core, presented by William McCallum, Cody L. Patterson, and Ellen Whitesides, University of Arizona; and Kristin Umland, University of New Mexico. Part A, Wednesday, 9:00 a.m.–11:00 a.m.; Part B, Friday, 9:00 a.m.–11:00 a.m. The Common Core State Standards in Mathematics were designed to present mathematics to K–12 students in a progression that reveals the coherence of mathematics and encourages mathematical reasoning. This minicourse will dig into the details of both the content standards and the standards for mathematical practice and will provide resources for mathematicians interested in supporting the implementation of the Standards. Possible roles for mathematicians in professional development, in review of curriculum materials, and in writing assessments (for example) will be considered.
Minicourse #11. Teaching differential equations with modeling, presented by Darryl Yong, Harvey Mudd College; Ami Radunskaya, Pomona College; Tom LoFaro, Gustavus Adolphus College; Dan Flath, Macalester College; and Michael Huber, Muhlenberg College. Part A, Wednesday, 4:45 p.m.–6:45 p.m.; Part B, Friday, 3:30 p.m.–5:30 p.m. Participants will learn about incorporating modeling into their differential equations courses and will do some modeling themselves using technology. The workshop will have three segments: (1) a short overview of curricular goals, what is modeling and why it is important, how modeling benefits student learning in differential equations; (2) activities and discussions in small groups on specific projects, to include modeling the dynamics of flight, population growth/interaction models, modeling infectious disease outbreaks, deflection in steel beams, applications to physics, and others; and (3) a wrap-up with references, sharing of best practices, and online resources that are available to instructors and students. The bulk of the minicourse will involve participants modifying existing modeling projects or creating new modeling projects for use in their own classes. To take full advantage of the course, participants: (a) should bring their own laptops and (b) are encouraged to bring applications to model.
Minicourse #12. Teaching an applied topology course, presented by Colin Adams, Williams College, and Robert Franzosa, University of Maine. Part A, Wednesday, 2:15 p.m.–4:15 p.m. Part B, Friday, 1:00 p.m.–3:00 p.m. Applications of topology have proliferated in recent years. It is now possible to teach a course in topology, still covering much of the same material that would appear in a traditional topology course, but motivated entirely by applications. Typically, offering an “applied” topology course immediately doubles the enrollments. Applications include areas such as geographic information systems, robotics, chaos, fixed point theory in economics, knots in DNA and synthetic chemistry, and the topology of the spatial universe. Through the applications, students become engaged with the material. In this minicourse we will introduce the various applications, and provide participants with the background necessary to design and teach their own applied topology course.
Minicourse #13. Problem-based courses for teachers, future teachers, and math majors, presented by Gail Burrill, Michigan State University; Darryl Yong, Harvey Mudd College; Bowen Kerins, Education Development Center; and James King, University of Washington. Part A, Thursday, 9:00 a.m.–11:00 a.m.; Part B, Saturday, 9:00 a.m.–11:00 a.m. A math course can simultaneously engage a broad range of students and enlarge their understanding of what it means to do math. This minicourse—based on a decade of experience at the Park City Mathematics Institute—will illustrate a problem-based approach for doing just that. Participants will spend most of the time in an interactive, collaborative environment, working on problems connecting algebra, number theory and geometry and involving content such as Pythagorean triples, Gaussian integers, lattice geometry, polynomials with special properties, and complex numbers. We will discuss the issues of teaching such a course, originally developed for teachers at the Park City Mathematics Institute, for undergraduate majors, prospective teachers, or as part of continuing education programs for experienced teachers.
Minicourse #14. Teaching introductory statistics (for instructors new to teaching intro stats), presented by Michael Posner, Villanova University, and Carolyn Cuff, Westminster College. Part A, Wednesday, 2:15 p.m.–4:15 p.m.; Part B, Friday, 1:00 p.m.–3:00 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 (GAISE) 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 learn about the best practices for the first course in statistics by becoming involved in statistics education related conferences, newsletters, and groups.
Minicourse #15. WeBWorK: An open source alternative for generating and delivering online homework problems, presented by John Travis, Mississippi College, and Jason Aubrey, University of Missouri. Part A, Thursday, 1:00 p.m.–3:00 p.m.; Part B, Saturday, 1:00 p.m.–3:00 p.m. This minicourse introduces participants to the WeBWorK online homework system. Supported by grants from NSF, WeBWorK has been adopted by well over 500 colleges, universities, and secondary schools and is a popular open-source alternative to commercial products. WeBWorK can handle problems in college algebra, calculus, linear algebra, ODEs and more and comes with an extensive library of nearly 30,000 problems across the mathematics curriculum. WeBWorK recognizes a multitude of mathematical objects and allows for elegant solution checking. This minicourse will introduce participants to WeBWorK and equip participants with the knowledge and skills to use WeBWorK in the classroom.