Courses that I regularly teach include:
In the Calculus/Linear Algebra Sequence
- Math 25: Precalculus Review of intermediate algebra and geometry. Linear, quadratic, and higher degree polynomial functions and their graphs. Exponential and logarithmic functions with applications. Practical and analytic trigonometry. Introduction to limits. Mathematics 25 is designed to prepare students for calculus. Students who do not plan to take Math 30 in the Spring, should not take this class. Prerequisite: two years of high school mathematics.
offered every Fall semester
- Math 30: Calculus I Limits, derivatives, integrals, mean value theorems, the fundamental theorem of the calculus. Prerequisite: Mathematics 25, 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
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 10: The Mathematical Mystery Tour 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:
- Rubik's Cube and other Mathematical Puzzles An introduction to graph and group theory via Rubik's Cube and other puzzles such as the Soma cube, the 15 puzzle, ferrying puzzles, and peg solitaire. At the end of the course, we will all be able to solve the Cube in under 5 minutes.
- The Mathematics of Gambling An introduction to probability. Topics will include combinations, permutations, probability, expected value, and Markov chains. 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.
- 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.
- 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.
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