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|Research, teaching, and media by this preceptor in Harvard's math department. Knill began in dynamical systems, tackling first ergodic and spectral theoretical questions, then probability theory and elementary number theory. This led to his "passion for mathematical problems in computer science especially inverse problems, whether in analysis, geometry or cryptology"; throughout, Knill has "always been fascinated by almost periodicity: almost periodic packings, almost periodic fluids, almost periodic Schroedinger operators, almost periodic random walks, almost periodic cellular automata, etc." Lecture notes, syllabi, exams, and other class materials, including from Harvard's summer school and extension school, cover linear algebra, differential equations, probability theory, geometry, multivariable calculus, dynamical systems, and complex analysis. Notes on pedagogy include the benefits and risks of media and technology in the class, Twitter in course websites, Harvard Calculus, enriching teaching with technology, and the pitfalls in teaching and learning calculus. Knill keeps a running annotated collection of Flash and Quicktime clips from hundreds of movies, TV shows, and other video productions that mention math. See also his selfreproducing programs, smallest 10 dimensional vector space, vintage Continuum game, personal encounters with Goldbach's conjecture, treasure hunting perfect Euler bricks (cuboids with integer side dimensions with both integer face diagonals and space diagonal), and convex optimization problems based on the optimal walking path to a straight street given its distance but not its location.|
|Levels:||Middle School (6-8), High School (9-12), College, Research|
|Resource Types:||Audiovisuals, Courses, Problems/Puzzles, Articles, Recreations|
|Math Topics:||Linear Algebra, Complex Analysis, Calculus (Multivariable), Communicating Math, Dynamical Systems, Geometry, Number Theory, Optimization, Probability, Art|
|Math Ed Topics:||Technology in Math Ed, Calculus Reform|
The Math Forum is a research and educational enterprise of the Drexel University School of Education.