Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves.
Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both...
The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology.
Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology.
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The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they ass...
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the ...
"I have studied with pleasure this] new book Beautiful examples Illuminating. I am convinced that Lieber's] original enterprise will get the recognition it so richly deserves." Albert Einstein
"The Liebers have written an ingenious, entertaining, and illuminating book." Saturday Review of Literature
"The book should be 'required reading' especially for non-mathematicians." E.T. Bell, author ofThe Development of Mathematics
First published in 1942, this whimsical exploration of how to think in a mathematical...
"A delightful book." New York Times
"I have studied with pleasure this] new book Beautiful examples Illuminating. I am convinced that...
Eric M. (Northwestern University, Evanston, Il, Friedlander Barry Mazur
This work provides a detailed exposition of a classical topic. It describes some foundational aspects of Lawson homology for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic...
This work provides a detailed exposition of a classical topic. It describes some foundational aspects of Lawson homology for complex projective algebr...
