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The proof that both regions have the same eigenvalues uses the symmetries of the Laplacian. This idea has been generalized by Buser, Conway, Doyle, and Semmler [4] who constructed numerous similar examples. So, the answer to Kac's question is: for many shapes, one cannot hear the shape of the drum completely. However, some information can be ...
Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6–8.The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum ...
He is currently a professor of mathematics at Dartmouth College in Hanover, New Hampshire. [2] In 2001 Webb and co-author Carolyn S. Gordon were awarded the Mathematical Association of America Chauvenet Prize for their 1996 American Scientist paper, "You can't hear the shape of a drum". [3] [4]
Lecture Notes in Mathematics is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Springer Science+Business Media (formerly Springer-Verlag).
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
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In its most basic form, a student would recite verbatim poems or essays of others, [6] either to the teacher or tutor directly, or in front of a class or body of assembled students. In classes involving mathematics and engineering , a recitation is often used as the vehicle to perform derivations or solve problems similar to those assigned to ...
Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992.