


    

Special Notice: Minicourse #6 has been CANCELLED. If you have registered for this course, please contact the MMSB at mmsb@ams.orgMinicourses 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 preregistration 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.
#1 TEACHING A GALOIS THEORY COURSE FOR UNDERGRADUATES John Swallow, Davidson College 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. TOP OF PAGE Cammey Cole Manning, Meredith College #3 INTRODUCTION TO THE MATHEMATICS OF MODERN
CRYPTOGRAPHY Jeffrey Ehme, Spelman College 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) online, 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. TOP OF PAGE Patrick J. Van Fleet, University of St. Thomas 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. TOP OF PAGE Michael J. Bardzell, Salisbury University 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 onedimensional 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. CANCELLED  #6
SONIFICATION FOR MATHEMATICS INSTRUCTION Steven M. Hetzler, Salisbury University 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 nonspeech 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 CDRW 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. #7 DIRECTING UNDERGRADUATE RESEARCH Aparna Higgins, University of Dayton 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. #8 MATHEMATICS AND GEOMETRY OF VOTING Donald G. Saari, University of California at Irvine 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. #9 CLASSROOM RESPONSE SYSTEMS: TEACHING WITH
CLICKERS Matthew Leingang, Harvard University Classroom response systems, or "clickers," are instructional technologies that enable teachers to rapidly collect and analyze students' responses to multiplechoice questions. In this minicourse, participants will learn how to use clickers to transform the way they use class timepromoting active participation, engagement, and discussion among students; assessing student learning in realtime during class; and adapting lessons to respond to the particular learning needs of one's students. This minicourse will also feature a questionwriting "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. #10 THE FIBONACCI AND CATALAN NUMBERS Ralph P. Grimaldi, RoseHulman Institute of Technology 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. #11 MORE MUSIC AND MATHEMATICS Leon Harkleroad, Wilton, Maine This session will focus on an allnew 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 spacefilling 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. #12 DEVELOPING DEPARTMENT SELFSTUDIES Donna Beers, Simmons College The selfstudy 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 forwardlooking, anticipating new areas for growth and contribution to the institutional mission. Since the selfstudy 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 selfstudy, which is usually conducted in response to an administrative mandate, can be a positive opportunity for departmental renewal. Enrollment limit is 50. #13 TEACHING AND THE PHILOSOPHY OF MATHEMATICS Martin Flashman, Humboldt State University 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. #14 BEYOND FORMULAS AND ALGORITHMS: TEACHING
A CONCEPTUAL/THEMATIC SINGLE VARIABLE CALCULUS COURSE Shahriar Shahriari, Pomona College 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 handson 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 openended 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. #15 EVALUATING STUDENT PRESENTATIONS IN
MATHEMATICS Suzanne Dorée, Augsburg College Do your students give inclass 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 minicourse 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. #16 A BEGINNER'S GUIDE TO THE SCHOLARSHIP
OF TEACHING AND LEARNING IN MATHEMATICS Curtis Bennett, Loyola Marymount University 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. 