Compact surfaces with no Bonnet mate

This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.Comment: 7 pages, LaTeX2

Quantity and number

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity

An Advanced Mathematics Program for Middle School Teachers

The Conference Board of the Mathematical Sciences (CBMS), National Council of Teachers of Mathematics, and other organizations recommend twenty-one credits of mathematics coursework for prospective middle school teachers, beginning with a foundation based on mathematics for the elementary school curriculum, and followed by advanced courses directly addressing middle school mathematics. Three simultaneous factors—the emergence of the Interdisciplinary Liberal Studies Program at James Madison University, the release of CBMS guidelines, and a statewide focus on a critical shortage of qualified middle school teachers—provided an immediate audience for new upper-division courses built around the guidelines in probability/statistics, algebra, geometry, and calculus/analysis. We will discuss our experience with course planning and adaptation of other programs