Topological Invariants of Plane Curves and Caustics PDF Download
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Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
ISBN: 9780821882641
Category : Mathematics
Languages : en
Pages : 76
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Book Description
This text is the first exposition of a new theory which unifies the theories of knots, plane curves, caustics, and wavefronts in differential, symplectic, and contact geometry and topology.
Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
ISBN: 9780821882641
Category : Mathematics
Languages : en
Pages : 76
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Book Description
This text is the first exposition of a new theory which unifies the theories of knots, plane curves, caustics, and wavefronts in differential, symplectic, and contact geometry and topology.
Author: Harold Hilton
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 416
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Book Description
Author: Eduardo Casas-Alvero
Publisher: Cambridge University Press
ISBN: 0521789591
Category : Mathematics
Languages : en
Pages : 363
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Book Description
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author: Diane Maclagan
Publisher: American Mathematical Society
ISBN: 1470468565
Category : Mathematics
Languages : en
Pages : 363
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Book Description
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina
Author: Julian Lowell Coolidge
Publisher: Courier Corporation
ISBN: 9780486495767
Category : Mathematics
Languages : en
Pages : 554
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Book Description
A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 942
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Book Description
Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 896
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Book Description
Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 0486138186
Category : Mathematics
Languages : en
Pages : 254
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Book Description
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Author:
Publisher:
ISBN:
Category : Mathematicians
Languages : en
Pages : 514
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Book Description
Includes section "Recent publications."
Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 886
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Book Description
