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Mathematical Association of America Lecture Films

7 lecture films made by the Mathematical Association of America that feature prominent mathematicians of the 20th century. Lecturers include, George Pólya, A. S. Besicovitch, David Blackwell, Solomon Lefschetz, Marston Morse, and Mark Kac, and Richard Courant. The films were digitized with generous funding from the Simons Foundation.

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Can You Hear the Shape of a Drum?, Parts 1 and 2
A filmed lecture by Mark Kac on the degree to which the shape of a vibrating membrane is determined by its eigenvalues, or normal modes of vibration.
Fixed Points, Parts 1 and 2
Professor Solomon Lefschetz describes how his “magic number” applies to determine whether a surface has the fixed-point property (that is, that a continuous transformation must leave at least one point of the surface fixed). The film closes with an informal chat in which Professors Leon Cohen and Shizuo Kakutani join in to discuss the history of topology, Lefschetz’ education and early work, and more.
Göttingen and New York: Reflections of a Life in Mathematics
Source:Mathematical Association of America Records
A survey of the career of Richard Courant. His colleagues describe his influence and work, and Courant lectures on soap bubbles and minimal surfaces. A large part of the film consists of reminiscences of the formation of the Institutes at Göttingen and New York University.
Let Us Teach Guessing
Source:Mathematical Association of America Records
Professor George Pólya leads an undergraduate class to discover the number of parts into which 3-space is divided by five arbitrary planes.
Pits, Peaks, and Passes: A Lecture on Critical Point Theory, Parts 1 and 2
Professor Marston Morse, with models and animations, derives the simple formula (which is the beginning of Morse theory) relating the number of pits, peaks, and passes on an island with a single coastline.
Predicting at Random [Composite]
Source:Mathematical Association of America Records
A source sequentially generates 0’s or 1’s, and one must predict against it, with knowledge of success or failure after each prediction. What is the optimal strategy here? The distinguished probabilist and statistician David Blackwell solves this problem and then sketches its application.
The Kakeya Problem
Given a unit horizontal length in the plane, what is the minimum area in which this line segment may be (cleverly) turned, so that its direction is reversed? Professor A. S. Besicovitch, who solved this problem, shows that no such minimum area exists.