Math Videos at Penrose
"In this captivating and richly illustrated videotape Boston University mathematics professor Robert L. Devaney communicates his deep understanding as will as his enthusiasm for the topics of chaos, fractals and dynamical systems. Starting at a level suitable for well-prepared high school students, he tells the mathematical story behind these fascinating topics. Using attractive graphs and diagrams, Devaney gives a clear and visually appealing introduction to the concepts. Computer generated graphics of the fractal Julia sets of the sine, cosine and exponential functions offer stunning proof of the beauty and complexity of these subjects. Devaney explains how the computer is used to make the still pictures and animations. Though the mathematical background required is elementary, those at the collegiate level and beyond will appreciate this tape for the clarity of exposition and the sheer beauty of the graphics.
In this video-lecture Prof. Robert L. Devaney explores and explains two of the more fascinating images that arise in the study of Dynamical Systems, namely the orbit (or bifurcation) diagram and the Mandelbrot Set. Both of these images arise when a quadratic function is iterated, so the level of mathematical sophistication necessary to understand the lecture is minimal. The main goal of the lecture is to describe the relationship between these two images, how they are generated as well as what they mean mathematically. Several important related concepts in dynamical systems theory are also described, including period doubling bifurcations, Feigenbaum's number, Sarkovskii's Theorem and the role of critical orbits. The mathematical concepts are illustrated with colorful slides, films and computer experiments done in real time."
"Lecturer George Polya leads an undergraduate class to discover the number of parts into which 3-space is divided by five arbitrary planes. He identifies the steps involved in plausible reasoning, and points out that they constitute a program for attacking any mathematical or scientific problem."
"A film biography of R. L. Moore, who received his doctorate in 1901 and since that time has produced, through his teaching, more outstanding mathematicians than any man in history. Describes the man, his philosophy, and his teaching methods as seen in his own words, through scenes in his class, and in his candid conversations with other mathematicians"
"Combining an informal interview and an introductory-level lecture on wavelets, this videotape makes an excellent classroom enrichment tool, as well as fascinating viewing for those interested in this cutting-edge topic. The interview portion of the tape contributes an engaging personal flavor as Daubechies covers some of the most important applications of wavelets and discusses how she became interested in mathematics and the challenges of balancing a family and a demanding career. In the lecture, Daubechies, one of the world's leading experts in wavelets, describes some of the important developments in the theory. Starting from basic definitions and presenting a clear and well-paced lecture, Daubechies makes the subject accessible to undergraduate mathematics majors."
Math Video Sites
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