14 March 2011 DRAFT program description
Student Last and First Name:
Program, Course or Contract Title: Methods of Mathematical Physics
Quarter and Academic Year: Fall & Winter, 2010-2011
DESCRIPTION written by E.J. Zita, Ph.D, Physics
In Fall and Winter quarters of Methods of Mathematical Physics, we studied Classical Mechanics; Modern
Physics, including intermediate Quantum Mechanics; Electromagnetism; and mathematics to support
these sciences, including Series, Complex numbers, Linear Algebra, Fourier Series and Transforms, and
Differential Equations. A unifying theme in Fall was Oscillations and various mathematical approaches to
identifying and solving oscillating systems, including damped and driven systems, qualitatively,
quantitatively, and graphically. We learned how to solve such systems with differential equations,
algebraically, and using matrices. We gained insight into mathematical systems by plotting their slope
fields, phase portraits, and more. We also learned how to apply our new methods to electrical circuits,
predator-prey systems, mixing problems, quantum spin matrices, particles in crossed electromagnetic
fields, and a variety of other systems. In Winter, we applied familiar mathematics and extensive new
studies in Vector Calculus to electrostatics and magnetostatics, and solved differential equations in
spherical and cylindrical coordinate systems in the context of both E&M and quantum mechanics, e.g. for
Laplace’s equation and Schrödinger’s equation.
Students usually had one homework assignment per week from Mathematical Methods in the Physical
Sciences by Mary L. Boas (Wiley 2006) and/or Differential Equations by Blanchard, Devaney, and Hall
(Brooks/Cole 2006), plus one assignment per week from two of our primary physics texts: Modern
Physics by Ken Krane (Wiley 1996) and Analytic Mechanics by Fowles & Cassiday (Thomson 2005) in
Fall, adding Introduction to Electromagnetism by Griffiths (Prentice Hall 1999). We also had 6 Friday
quizzes per quarter; students were permitted to retake these quizzes in fall and turn them in with
reflections on their learning. Students had two closed-book, open-portfolio, take-home exams each
quarter: a midterm and a final. They also were required to complete an online Seminar Quiz each
quarter.
Students did independent research individually and in small teams. Each individual presented two
informal “Brief Reports” on current issues of their choice, related to the program. More
substantially,.teams of 2-3 students planned research in fall and carried it out in winter. We had a series
of fall workshops designed to transform research topics of interest into open Questions which could be
actively explored; to articulate Hypotheses and design Tests for Research Questions; and to flesh out
Research Plans in several steps. Student teams presented their research ideas informally at midquarter,
and presented formal Research Proposals in the last week of fall. In winter, students built their research
projects, calculated their predictions, and carried out experimental tests. They presented midquarter and
final Research Presentations.
In Seminar we read about the evolution of the process of doing science, and some concepts of modern
and classical science and mathematics. Our primary fall texts were an article on critical thinking, Carl
Sagan’s Baloney Detection (from The Demon Haunted World, 1997); four high quality popular books on
science and math: Measuring the World, by Daniel Kehlmann (2007), The Ten Most Beautiful
Experiments, by George Johnson (2009), The Great Equations: Breakthroughs in Science from
Pythagoras to Heisenberg, by Robert Crease (2010), The God Particle, by Leon Lederman and Dick
Teresi; and three articles about current models attempting to unify General Relativity with Quantum
Mechanics: Lee Smolin on Loop Quantum Gravity (Scientific American, January 2004), Gordon Kane on
String Theory Predictions (Physics Today, Nov. 2010), and A. Garrett Lisi on A Geometric Theory of
Everything (Scientific American, Dec. 2010).
Our primary seminar texts in winter focused on the discovery and development of fission and quantum
mechanics as examples of paradigm shifts in physics, and on discovery processes in science. We read
Lise Meitner: A Life in Physics (Sime 1997), Women in Mathematics (Osen 1975), The Structure of
Scientific Revolutions (Kuhn 1962, 1996), Thirty Years that Shook Physics (Gamow 1966, 1985), Physics
& Philosophy (Heisenberg 1958, 2007), and Copenhagen (Frayn, 2000, 2010).
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14 March 2011 DRAFT program description
We used Don Finkel’s model of community-building for writing and responding to essays, with shared
goals of developing deeper wisdom and better communication skills. Each individual was to write 2 good
one-page essays, starting with an interesting question, using the essays to explore their question,
synthesizing and citing diverse sources. Each student was also to write 3 thoughtful and substantial
responses to peers’ essays, the week before each of their own essays. Due dates were important so that
peers could get prompt feedback to their essays, and work together toward better understanding of each
week’s material.
Students met in teams before each seminar to discuss reading assignments, and to generate “Points,
Insights, and Questions” (PIQs). Each team was to post online at least three good PIQs each, the day
before seminar (with sources appropriately referenced by author and page number), in order to stimulate
conversations and explore questions. Each team also had an opportunity to facilitate one seminar.
Students were evaluated on the quality, completeness, and timeliness of their seminar preparation,
participation, and essays and responses.
EVALUATION written by E.J. Zita, Ph.D, Physics
EQUIVALENCIES:
TOTAL CREDITS EARNED: _ / 16
CREDITS: 16 * upper division
_ / *4 cr Differential Equations and Mathematical Methods
_ / *6 cr Intermediate Electromagnetism and Modern Physics
_ / *4 cr Research project on __
_ / *2 cr Science Seminar on modern physics
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