Courses that I regularly teach include:
In the Calculus/Linear Algebra Sequence
- Math 20: Elementary Functions Review of intermediate algebra and geometry. Linear, quadratic, and higher degree polynomial functions and their graphs. The sequence Mathematics 20 and 23 is designed to prepare students for calculus. Prerequisite: three years of high school mathematics (two years of algebra and one year of geometry) and a satisfactory score on the mathematics placement examination.
offered every Fall semester
- Math 23: Transcendental Functions A continuation of Mathematics 20. Exponential and logarithmic functions with applications. Practical and analytic trigonometry. Introduction to limits and derivatives of polynomial functions. Enrollment is limited. Prerequisite: a grade of C or above in Mathematics 20 or satisfactory score on placement examination.
offered every semester
- Math 30: Calculus I Limits, derivatives, integrals, mean value theorems, the fundamental theorem of the calculus. Prerequisite: Mathematics 22, 23, or satisfactory score on placement examination.
offered every semester
- Math 31: Calculus II Transcendental functions, techniques of integration, infinite series, and related material. Prerequisite: Mathematics 30 (C- or better) or satisfactory score on placement examination.
offered every semester
- Math 32: Calculus III Vectors, curves and surfaces in space, partial derivatives, gradient, method of Lagrange multipliers, multiple integrals, Green's Theorem, Stokes' Theorem, flux and divergence theorem. Prerequisite: Mathematics 31 (C- or better) or satisfactory score on placement examination.
offered every semester
- Math 60: Linear Algebra
offered every Spring semester
Courses for Liberal Arts students
The following courses are intended to introduce the liberal arts student to the exciting world of mathematics. These courses have few (if any) prerequisites beyond basic high school mathematics, yet each still takes an in-depth journey into some serious and sophisticated mathematics.
- Math 7: The Mathematics of Games and Gambling An introduction to probability and game theory. Topics will include combinations, permutations, probability, expected value, Markov chains, graph theory, and game theory. Specific games such as keno, roulette, craps, poker, bridge, and backgammon will be analyzed. The course will provide excellent preparation for statistics courses as well as for uses of game theory in the Social Sciences.
offered in alternate years
- Math 8: Mathematics, Art and Aesthetics (This is a joint course with Pomona College) Addresses topics in mathematics that have figured prominently in the history of art and architecture. Explores the role of aesthetics within mathematics and the concept of mathematics itself as an art form. Readings are taken from material by philosophers, mathematicians, artists, and art historians ranging from the ancient Greeks to modern times. Students will solve mathematical problems and create art work in various media. Students exhibit their artwork at an end-of-semester show.
offered infrequently
- Math 10: The Mathematical Mystery Tour (This is a joint course with Pomona College) Introduces students to beautiful topics in mathematics that do not require a great deal of sophistication or previous knowledge. While ideally suited to liberal arts students, the course should be of interest to science majors as well. Stresses the intuition, creativity and aesthetics involved in one area of mathematics. The area of focus will vary from year to year. May be repeated for credit.
Courses that I have taught under this title include:
- Dynamical Systems, Chaos and Fractals. By means of computer experimentation, this course will explore the basic concepts of dynamical systems and the strange world of fractals. Topics will include fixed points, periodic points, attracting and repelling sets, families of functions, bifurcation, chaos and iterated function systems. We will investigate several famous examples including the Quadratic Family, the Henon map, Julia sets and the Mandlebrot set. No previous computer experience required. Some knowledge of calculus will be helpful but not required.
offered infrequently, perhaps every fifth year?
- Topology This course explores the shape of 1, 2, 3 and 4-dimensional space. Is the universe curved or flat? Could an astronaut return from a long journey as the mirror-image of herself? How can space be "constructed" from "ordinary space" by using knots? The course will be very visual---we will make models with paper, clay, string, and other materials that will allow us to "see" various properties of space. Topics will include surfaces, orientability, immersions and embeddings of surfaces in "ordinary" space, knot theory, graphs, the Four Color Theorem, turning spheres inside out (and other deformations!), and geometry of surfaces and 3-dimensional space. We will watch a number of films as well as read several science fiction classics.
offered every other year
- Writing About Life in Alternate Universes (Thanks are due to Professor Colin Adams at Willimas College for inspiring this course.) Through reading and writing of mathematical fiction, we will explore the nature of the space we live in. What would it be like to live in a 2-dimensional space, or a very small universe (which you could cross in a day)? We will read a number of stories where characters do just that, as well as write our own stories in alternative settings.
offered very infrequently
- Math 11 (Political Studies 111): Theories of Electoral Systems We analyze various voting systems such as majority rule, plurality rule, Borda counts, instant runoff voting, and proportional representation. A famous theorem by Arrow states that no matter how sophisticated a voting system may be, it is impossible to come up with one that is "perfect." How then, should be elect our political representatives?
Upper Division Mathematics Courses
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- Math 141: Hyperbolic Geometry An introduction to 2 and 3-dimensional hyperbolic space and to the theory of hyperbolic knots.
offered every other year in alternation with Math 148
- Math 148: Knot Theory An introduction to the theory of knots and links from combinatorial, geometric, and algebraic perspectives. Topics will include knot diagrams, p-colorings, Alexander, Jones, and Homfly polynomials, Seifert surfaces, genus, Seifert matrices, the fundamental group and representations of knot groups, covering spaces, surgery on knots, and important families of knots.
offered every other year in alternation with Math 141