Teaching

Earlier in my career, I viewed teaching as a performance. This approach has some strengths but can lead to a passive student experience. Today I instead emphasize active and group learning methods in class, using a mixture of slides, worksheets, discussions, and computer exercises. I think that homework should feature deep and interesting questions while exams are better suited for predictable checks of core definitions and techniques.

I've recently started to experiment with collaborative exams.

I like Terry Tao's essay: Does one have to be a genius to do maths?

Nonstandard content in standard courses

Here are some course topics listings with some nontraditional choices:

Calculus III includes the multidimensional Newton method, for zero-finding and for optimization (slides)
Differential Equations
Computational Linear Algebra includes discussion of the barycentric formulas, Chebyshev polynomials, interpolative matrix decomposition, nonnegative matrix factorization

Student-centered syllabi

Here are some readable syllabi from recent courses:

Calculus II
Differential Equations

Exam questions

Other resources

A solution of Laplace's equation on the unit square; e.g. a soap film stretched over a square with one side bent up into a ridge.

Report abuse