Education
New York University; Rensselaer Polytechnic Institute.
(Calculus and linear algebra are two dominant themes in co...)
Calculus and linear algebra are two dominant themes in contemporary mathematics and its applications. The aim of this book is to introduce linear algebra in an intuitive geometric setting as the study of linear maps and to use these simpler linear functions to study more complicated nonlinear functions. In this way, many of the ideas, techniques, and formulas in the calculus of several variables are clarified and understood in a more conceptual way. After using this text a student should be well prepared for subsequent advanced courses in both algebra and linear differential equations as well as the many applications where linearity and its interplay with nonlinearity are significant. This second edition has been revised to clarify the concepts. Many exercises and illustrations have been included to make the text more usable for students.
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(These notes were the basis for a series of ten lectures g...)
These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, although others could understand the lectures. Author's Summary:Given a Riemannian Manifold $(M,g)$ one can compute the sectional, Ricci, and scalar curvatures. In other special circumstances one also has mean curvatures, holomorphic curvatures, etc. The inverse problem is, given a candidate for some curvature, to determine if there is some metric $g$ with that as its curvature. One may also restrict ones attention to a special class of metrics, such as Kahler or conformal metrics, or those coming from an embedding. These problems lead one to (try to) solve nonlinear partial differential equations. However, there may be topological or analytic obstructions to solving these equations. A discussion of these problems thus requires a balanced understanding between various existence and non-existence results. The intent of this volume is to give an up-to-date survey of these questions, including enough background, so that the current research literature is accessible to mathematicians who are not necessarily experts in PDE or differential geometry. The intended audience is mathematicians and graduate students who know either PDE or differential geometry at roughly the level of an intermediate graduate course.
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New York University; Rensselaer Polytechnic Institute.
His contributions include the Berger–Kazdan comparison theorem, which was a key step in the proof of the Blaschke conjecture and the classification of Wiedersehen manifolds. Kazdan received his bachelor"s degree in 1959 from Rensselaer Polytechnic Institute and his master"s degree in 1961 from New York University. He obtained his Doctor of Philosophy in 1963 from the Courant Institute of Mathematical Sciences at New York University. His thesis was entitled A Boundary Value Problem Arising in the Theory of Univalent Functions and was supervised by Paul Garabedian.
He then took a position as a Benjamin Peirce Instructor at Harvard University.
Since 1966, he has been a Professor of Mathematics at the University of Pennsylvania. In 2012 he became a fellow of the American Mathematical Society.
(These notes were the basis for a series of ten lectures g...)
(Calculus and linear algebra are two dominant themes in co...)
American Mathematical Society.