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Assistant Professor Sternberg's Match 267 ("Infinite Lie Groups and the Differential Geometry of G-Structures") wont' come till spring, but his more elementary Math 266 (called simply "Lie Groups") meets this term at 10, and the only prerequisite: merely a general knowledge of differential manifolds...
What sad-eyed Professor Begle (pronounced beagle) did was to become the foremost disseminator of math reforms in U.S. schools. As director of Yale's School Mathematics Study Group. Begle, in 1958, began a rewriting of textbooks that has since enlightened Sallys across the nation. As one consequence, Stanford stole Sally's father from Yale. Stanford now aims to Beglize itself as "a national center in mathematics education...
...Math Cookery. The son of a clothespin manufacturer, Begle graduated from the University of Michigan ('36), took his doctorate at Princeton in topology (thesis title: "Locally Connected Spaces and Generalized Manifolds"), began teaching at Yale in 1942. As secretary of the American Mathematical Society, Begle was in a key spot when Sputnik-stirred mathematicians began to worry about U.S. high schools. They were shocked at "cook book" courses stuffed with unrelated rules, appalled at teachers who themselves hated math. With grants ($4,000,000 so far) from the National Science Foundation, Begle organized top mathematicians and teaching experts into...
Begle's group admired the exciting experiments of Mathematician Max Beberman at the University of Illinois (TIME, July 25, 1960)-superb classroom artistry that lures children into discovering math concepts for themselves. But to make every teacher into a Beberman was clearly impossible. Begle aimed to write courses that most teachers could handle with only an hour a week of extra study...
Seeing Fractions. Reversing the old order of math learning, Begle's books start with particular examples that awaken students to axioms or generalizations. The chief aim is a firm grasp of "real numbers," which form the central number system of mathematics. One early discovery is the semantic difference between a number and a numeral. The first is a permanent concept, the other, one of its many aliases. The idea of 9, for example, can be expressed equally well...