MINICOURSES
Mini-courses offer four hours of focused instruction. The San Jose mini-courses were coordinated by John Maceli. Enrollment is limited and a separate registration fee, $75 before June 15 or $90 after June 15, is required.
MINICOURSE #1
A NOVEL APPROACH TO PROBLEM SOLVING IN DISCRETE MATHEMATICS
Andy Liu, University of Alberta
Part 1: Friday, August 3, 1:00 pm - 3:00 pm
Part 2: Saturday, August 4, 1:00 pm - 3:00 pm
At the University of Alberta, we have designed a very successful sophomore course on problem solving in discrete mathematics, using as an innovative text a mathematical novel in which the main character, a mathematical version of Sherlock Holmes, solves important, instructive and interesting problems for his clients. In this minicourse, we will run a simulated class and examine suitable problems from various sources. We will also provide a brief history and discuss the basic philosophy of our course. There are no prerequisites, and sample notes and problems will be distributed to the participants.
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MINICOURSE #2
INFUSING CONNECTIONS INTO CORE COURSES FOR SECONDARY TEACHERS
Steve Benson, Education Development Center
Al Cuoco, Education Development Center
Karen Graham, University of New Hampshire
Neil Portnoy, University of New Hampshire
Part 1: Saturday, August 4, 1:00 pm - 3:00 pm
Part 2: Sunday, August 5, 1:00 pm - 3:00 pm
National recommendations call for content courses for prospective teachers that make explicit connections between the mathematics that teachers learn and the mathematics they will use as teachers. Most content courses for preservice secondary teachers are core courses for the mathematics major and texts for these courses do not typically address these connections. Minicourse participants will work with materials that contain the mathematical rigor of an upper division course and help prospective teachers build connections to secondary mathematics, discuss implementation issues with colleagues who have used such materials, and begin to adapt these materials for the courses they teach.
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MINICOURSE #3
TEACHING A PROOF-BASED COURSE AS THE GATEWAY TO THE MATHEMATICS MAJOR
James Sandefur, Georgetown University
Part 1: Friday, August 3, 3:30 pm - 5:30 pm
Part 2: Sunday, August 5, 1:00 pm - 3:00 pm
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 organizer of this course, guided by 5 years of videotaping his students doing their homework for a proof-based course, will lead participates in an exploration of effective approaches to teaching "proof." We will discuss appropriate types of problems, the wording of problems, effective hints and prompts, and a variety of pedagogical approaches. Suggestions and questions from participants will be encouraged.
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MINICOURSE #4
MORE MUSIC AND MATHEMATICS
Leon Harkleroad, Wilton, Maine
Part 1: Friday, August 3, 1:00 pm - 3:00 pm
Part 2: Saturday, August 4, 3:30 pm -5:30 pm
We will offer a selection of various points of intersection between 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.
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MINICOURSE #5
SOME DETERMINISTIC MODELS IN MATHEMATICAL BIOLOGY AND THEIR SIMULATION
James Selgrade, North Carolina State University
Hüseyin Koçak, University of Miami
Part 1: Saturday, August 4, 3:30 pm - 5:30 pm
Part 2: Sunday, August 5, 3:30 pm - 5:30 pm
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 100MB of disk space, 512K memory, a CD drive and with one of the three operating systems, Windows XP, MAC OS 10.4 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. Support for installation related problems should be addressed to info@phaser.com. Each registrant of the minicourse will be provided a license activation key for the copy of Phaser downloaded at no additional charge.
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MINICOURSE #6
USING THE HISTORY OF CALCULUS TO ENRICH OUR TEACHING
David Bressoud, Macalester College
Paul Zorn, St Olaf College
Part 1: Friday, August 3, 3:30 pm - 5:30 pm
Part 2: Sunday, August 5, 3:30 pm - 5:30 pm
This course will explore how the history of mathematics can inform our teaching of calculus, focusing on examples, problems, and projects for deepening and expanding student understanding. In the first session, we will look at the historical development of the concepts of limit and convergence and the difficulties that mathematicians encountered in coming to grips with these ideas. In the second session, we will turn to Newton's Principia and suggest ways to help students investigate some of his insights and results.
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