Joint Mathematics Meetings - January 6 - 9, 2008 - Sunday - Wednesday - San Diego Convention Center

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MAA Minicourses

Special Notice: Minicourse #6 has been CANCELLED. If you have registered for this course, please contact the MMSB at mmsb@ams.org

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 fee for each course is US $60. This fee applies before and during the meeting.

The deadline for pre-registration has passed. Please register at the meeting. The Joint Meetings Registration Desk (JMRD) will be located in Hall B1, San Diego Convention Center (SDCC). It will be open between 3:00 p.m. and 7:00 p.m. on Saturday (1/5); 7:30 a.m. to 4:00 p.m. on Sunday (1/6), Monday (1/7), Tuesday (1/8); and 7:30 a.m. to 2:00 p.m. on Wednesday (1/9).

The MAA reserves the right to cancel any minicourse that is undersubscribed. Participants in Minicourses #1-#6 are required to come with a laptop computer equipped with appropriate software. Instructions to download any data files needed for those courses will be provided by the organizers.

Please click on each number to go to that minicourse number and description.
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#1 TEACHING A GALOIS THEORY COURSE FOR UNDERGRADUATES

John Swallow, Davidson College
Part 1: Sunday, January 6, 9:00 a.m. to 11:00 a.m.
Part 2: Tuesday, January 8, 9:00 a.m. to 11:00 a.m.

Participants explore Galois theory from an undergraduate perspective, gaining materials and technological tools for use teaching an undergraduate course. The course outlines the theory from a concrete, computational point of view, assuming only one semester of abstract algebra. The course also introduces AlgFields, a package for use with Maple or Mathematica, to facilitate computation in number fields. Participants study examples, solve exercises, and pose new problems, all built around the concept of an algebraic number with complex approximation. Handouts and web links to the freely available package will be distributed. Participants in this course are required to come with a laptop computer equipped with appropriate software. Their laptops should be equipped with either Maple (version 9 or later) or Mathematica (version 4.2 or later), but no prior experience with Mathematica or Maple is required. Participants who wish to use Maple but who do not have access to that software can be provided with a temporary license in advance of the workshop. Email John Swallow at joswallow@davidson.edu for more information about this option.
Enrollment limit is 30.

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#2 SOME DETERMINISTIC MODELS IN MATHEMATICAL BIOLOGY AND THEIR SIMULATIONS

Cammey Cole Manning, Meredith College
Huseyin Kocak, University of Miami
James Selgrade, North Carolina State University
Part 1: Sunday, January 6, 2:15 p.m. to 4:15 p.m.
Part 2: Tuesday, January 8, 1:00 p.m. to 3:00 p.m.

This minicourse will present and analyze discrete and continuous models from physiology (e.g., the Hodgkin-Huxley model), pharmacokinetics, and population biology (e.g., the chemostat model). The class will be conducted in a computer lab where participants will use the software Phaser to simulate model behavior. Each of the four topics will be discussed for 30 minutes followed by 30 minutes of computer experimentation. The participants will be provided electronic copies of the web-based notes, simulations, and the software. Familiarity with the material in undergraduate courses in ordinary differential equations and linear algebra will be helpful. Participants for this minicourse will be required to bring a laptop equipped with at least 100MB of available disk space, 512MB RAM, with a CDROM drive and with one of the three operating systems: Windows 2000/XP/Vista, Mac OS X (10.4.5 or later, with Java 5 or greater installed) or Linux. A free and fully functional evaluation copy of Phaser 3.0 may be downloaded at: http://www.phaser.com/ Each prospective registrant should download and install a copy of Phaser on his/her laptop to prepare for the minicourse. Technical support for any installation related issues should be addressed to Jason Glick (jason@phaser.com). Each registrant of the minicourse will be provided a license activation key for the copy of Phaser downloaded at no additional charge. Enrollment limit is 30.

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#3 INTRODUCTION TO THE MATHEMATICS OF MODERN CRYPTOGRAPHY

Jeffrey Ehme, Spelman College
Colm Mulcahy, Spelman College
Part 1: Sunday, January 6, 4:45 p.m. to 6:45 p.m.
Part 2: Tuesday, January 8, 3:30 p.m. to 5:30 p.m.

The mathematics of modern cryptography is for anyone with an interest in mathematics today, especially if that person also registers for classes (or submits grades) on-line, or pays bills or shops on the internet. Since that includes most of our students and most of us, it is a perfect subject for adding to the standard undergraduate curriculum, either in a regular or special topics course, or as a subject for directed research. There can be no better way of illustrating the application to everyday life of abstract mathematics and clever modern ideas. This minicourse will focus on the basics, assuming only a rudimentary knowledge of number theory and abstract algebra (e.g., Fermat's Little Theorem and the concept of an abelian group), and cover topics ranging from 1970s breakthroughs such as Diffie Hellman key exchange and the RSA cryptography, to the more recent methods of ElGamal, elliptic curves and Groebner bases. Participants are expected to bring laptops equipped with Maple, Adobe Acrobat Reader, and a CD drive. Enrollment limit is 30.

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#4 WAVELETS AND APPLICATIONS: A MULTI-DISCIPLINARY UNDERGRADUATE COURSE WITH AN EMPHASIS ON SCIENTIFIC COMPUTING

Patrick J. Van Fleet, University of St. Thomas
David K. Ruch, Metropolitan State College of Denver
Part 1: Monday January 7, 8:00 a.m. to 10:00 a.m.
Part 2: Wednesday, January 9, 9:00 a.m. to 11:00 a.m.

This minicourse provides a basic introduction to wavelets and applications. The wavelet transform is developed in an ad hoc manner. It is then used in applications such as data compression. Participants develop the necessary software and are encouraged to bring their own digital images or audio files to use. Our construction is easy to understand but is limited in applications. Thus we have the motivation for developing wavelets in a general context. The minicourse content provides an excellent template for an undergraduate class in wavelets and applications. We discuss how the course can be offered to undergraduates. Participants receive software and lecture materials that can be used to offer the course at their home institution. Participants in this course are required to come with a laptop computer equipped with appropriate software. They are expected to have one of Mathematica, Matlab, or Maple installed on their laptop as well as Adobe Acrobat Reader. For those interested in attending the workshop but who do not have a CAS on their laptop, please contact the organizers. For more information, please visit http://cam.mathlab.stthomas.edu/wavelets. Enrollment limit is 30.

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#5 VISUALIZING ABSTRACT MATHEMATICS WITH CELLULAR AUTOMATA

Michael J. Bardzell, Salisbury University
Donald E. Spickler, Salisbury University
Part 1: Monday, January 7, 10:30 a.m. to 12:30 p.m.
Part 2: Wednesday, January 9, 1:00 p.m. to 3:00 p.m.

Many undergraduate students are familiar with Pascal's triangle and, in some cases, Pascal's triangle mod n. This later construction is a type of infinite one-dimensional cellular automata generated over a finite group. Cellular automata, both finite and infinite, can be generated over other groups as well. Studying these dynamical systems necessitates simple techniques from abstract algebra, discrete mathematics, number theory, fractal geometry, and computer graphics. We present innovative classroom activities and undergraduate research projects that have evolved from this project. Participants in this course are required to come with a laptop computer equipped with appropriate software. The supporting computer software PascGaloisJE will be introduced. A basic knowledge of group theory is sufficient for the course. We will provide copies of the software at the workshop but it can take some time to install the package, although Windows users can run the software right from a provided CD. So we ask that the other participants download and install the software before the beginning of the workshop. You can get the software from http://pascgalois.org/ and follow the "A download site for PascGaloisJE, ..." link at the bottom of the page or go directly to the download site at http://faculty.salisbury.edu/~despickler/PascGaloisJE.htm. Enrollment limit is 30.

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CANCELLED - #6 SONIFICATION FOR MATHEMATICS INSTRUCTION

Steven M. Hetzler, Salisbury University
Robert M. Tardiff, Salisbury University
Part 1: Monday, January 7, 1:00 p.m. to 3:00 p.m.
Part 2: Wednesday, January 9, 3:30 p.m. to 5:30 p.m.

Some students struggle to interpret standard graphic and symbolic representations of mathematics, and many of these students are primarily auditory learners. At http://faculty.salisbury.edu/~smhetzler/Minicourse2008/, there are illustrations of how auditory graphs can be used with spreadsheets to enhance calculus instruction. This minicourse is designed to teach participants how to use non-speech audio to improve student learning. Participants work together to create an activity that uses sound to teach interpretation of horizontal asymptotes. Then, working individually or in pairs, participants will develop another activity in their own area of interest. The minicourse will conclude with a discussion of the potential of sound for representing other mathematical concepts, and participants will receive a copy of all materials created in the sessions. Participants in this course are required to come with a laptop computer equipped with appropriate software. Their laptops will need to be running Windows XP and Microsoft Excel 2003 or higher, with a headphone jack for the soundcard and either a CD-RW drive or USB port. Partial support for this work was provided by the National Science Foundation - Course, Curriculum, and Laboratory Improvement program under grant 0442450. Enrollment limit is 30.

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#7 DIRECTING UNDERGRADUATE RESEARCH

Aparna Higgins, University of Dayton
Part 1; Sunday, January 6, 9:00 a.m. to 11:00 a.m.
Part 2: Tuesday, January 8, 9:00 a.m. to 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. Enrollment limit is 50.

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#8 MATHEMATICS AND GEOMETRY OF VOTING

Donald G. Saari, University of California at Irvine
Part 1: Sunday, January 6, 4:45 p.m. to 6:45 p.m.
Part 2: Tuesday, January 8, 3:30 p.m. to 5:30 p.m.

By now, most of us know that voting rules can cause unexpected outcomes and delicious paradoxes. It is possible for the standard plurality ranking, for instance, to be Alice > Barb > Connie while the "vote for two" outcome is precisely the opposite. The mathematical issues - which constitute the theme of this course - are to identify everything that can possibly happen - and why, how to construct any number of illustrating examples, to identify which voting rule is the "best," and to learn how to convert portions of this recent research into rich course offerings for our undergraduates. Enrollment limit is 50.

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#9 CLASSROOM RESPONSE SYSTEMS: TEACHING WITH CLICKERS

Matthew Leingang, Harvard University
Derek Bruff, Vanderbilt University
Kelly Cline, Carroll College
Mark Parker, Carroll College
Holly Zullo, Carroll College
Part 1: Sunday, January 6, 2:15 p.m. to 4:15 p.m.
Part 2: Tuesday, January 8, 1:00 p.m. to 3:00 p.m.

Classroom response systems, or "clickers," are instructional technologies that enable teachers to rapidly collect and analyze students' responses to multiple-choice questions. In this minicourse, participants will learn how to use clickers to transform the way they use class time-promoting active participation, engagement, and discussion among students; assessing student learning in real-time during class; and adapting lessons to respond to the particular learning needs of one's students. This minicourse will also feature a question-writing "workshop" and a mock clicker class as ways to explore the kinds of questions and activities that make the most of teaching with clickers. Enrollment limit is 50.

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#10 THE FIBONACCI AND CATALAN NUMBERS

Ralph P. Grimaldi, Rose-Hulman Institute of Technology
Part 1: Monday, January 7, 9:00 a.m. to 11:00 a.m.
Part 2: Wednesday, January 9, 9:00 a.m. to 11:00 a.m.

In many introductory courses in discrete mathematics or combinatorics, one often encounters the sequences of numbers called the Fibonacci numbers and the Catalan numbers. This minicourse is designed to demonstrate how certain properties of these sequences come about and to examine where ideas related to these sequences arise in applications dealing with geometry, trigonometry, set theory, number theory, tilings, permutations, chemistry, optics, electrostatics, probability, and graph theory. Enrollment limit is 50.

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#11 MORE MUSIC AND MATHEMATICS

Leon Harkleroad, Wilton, Maine
Part 1: Monday, January 7, 1:00 p.m. to 3:00 p.m.
Part 2: Wednesday, January 9, 1:00 p.m. to 3:00 p.m.

This session will focus on an all-new set of topics from the interface of math and music. We will explore subjects such as historical geometric methods to approximate equal tempering in instrument design, group theory in contradancing, and music from space-filling curves and fractals. This minicourse will not repeat material from the original minicourse (given in Atlanta, GA, in January 2005), and it will not assume that participants attended that earlier installment. Enrollment limit is 50.

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#12 DEVELOPING DEPARTMENT SELF-STUDIES

Donna Beers, Simmons College
Richard Alan Gillman, Valparaiso university
Part 1: Sunday, January 6, 9:00 a.m. to 11:00 a.m.
Part 2: Tuesday, January 8, 9:00 a.m. to 11:00 a.m.

The self-study process and report are critical components of a departmental program review. They are retrospective, engaging department members and other interested parties (e.g., other departments and the administration) in examining the current status of all aspects of departmental programs. They are also forward-looking, anticipating new areas for growth and contribution to the institutional mission. Since the self-study entails honest discussion of issues confronting a department, it is both a process of reflection and a report. This minicourse enables participants to determine how a self-study, which is usually conducted in response to an administrative mandate, can be a positive opportunity for departmental renewal. Enrollment limit is 50.

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#13 TEACHING AND THE PHILOSOPHY OF MATHEMATICS

Martin Flashman, Humboldt State University
Part 1: Sunday, January 6, 2:15 p.m. to 4:15 p.m.
Part 2: Tuesday, January 8, 1:00 p.m. to 3:00 p.m.

The goal of this minicourse is to introduce participants to issues in the philosophy of mathematics that can be used to illuminate classroom topics in undergraduate courses at a variety of levels and provide a foundation for organizing an undergraduate course in the philosophy of mathematics for mathematics and philosophy students. The content of the minicourse: The course will focus primarily on issues related to i) the nature of the objects studied in mathematics (ontology) and ii) the knowledge of the truth of assertions about these objects (epistemology). Responses ascribed to many views such as platonism, formalism, intuitionism, constructivism, logicism, structuralism, and empiricism will be outlined. Enrollment limit is 50.

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#14 BEYOND FORMULAS AND ALGORITHMS: TEACHING A CONCEPTUAL/THEMATIC SINGLE VARIABLE CALCULUS COURSE

Shahriar Shahriari, Pomona College
Part 1: Sunday, January 6, 4:45 p.m. to 6:45 p.m.
Part 2: Tuesday, January 8, 3:30 p.m. to 5:30 p.m.

Many students enter college having seen the main ideas of calculus and knowing how to do routine calculus problems but without a firm grasp of the concepts underlying calculus. In this hands-on course, the participants will be introduced and will have a chance to explore an honors calculus class where the theme is approximations and one of the test cases is approximating the number of primes up to x. In this alternative calculus class, the students take an active role in formulating questions, and in developing the material. A thematic/conceptual approach using open-ended problems that incorporates some unusual mathematics (in this case, analytic number theory) allows us to take advantage of the students' prior experience with calculus to get a deeper understanding of the subject. Enrollment limit is 50.

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#15 EVALUATING STUDENT PRESENTATIONS IN MATHEMATICS

Suzanne Dorée, Augsburg College
Richard Jardine, Keene State College
Thomas Linton, Central College
Part 1: Monday, January 7, 9:00 a.m. to 11:00 a.m.
Part 2: Wednesday, January 9, 9:00 a.m. to 11:00 a.m.

Do your students give in-class presentations? Present their undergraduate research project at a conference or senior seminar? While most mathematics professors can tell a great mathematics talk from a truly horrible one, when it comes to grading student presentations we are often at a loss. In this mini-course we'll examine what makes a good student mathematics talk, offer concrete advice on helping students prepare to speak, discuss the use of rubrics for evaluating presentations, and explore the role of presentations in departmental curriculum and assessment. Participants will practice using rubrics to evaluate presentations on video and at the meetings themselves. Enrollment limit is 50.

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#16 A BEGINNER'S GUIDE TO THE SCHOLARSHIP OF TEACHING AND LEARNING IN MATHEMATICS

Curtis Bennett, Loyola Marymount University
Jackie Dewar, Loyola Marymount University
Part 1: Monday, January 7, 1:00 p.m. to 3:00 p.m.
Part 2: Wednesday, January 9, 1:00 p.m. to 3:00 p.m.

This course will introduce participants to the scholarship of teaching and learning in mathematics (SoTL). We will present a framework that illustrates the similarities between disciplinary research and SoTL work, offer examples of SoTL projects in mathematics at varying stages of development, discuss methods for investigation, and help participants begin projects of their own. Participants will be guided in transforming a teaching problem of their own into a problem for scholarly investigation. Suggestions for how to make this work public will also be given. Enrollment limit is 50.

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