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Author: Sheng Gong Publisher: American Mathematical Soc. ISBN: 0821827421 Category : Education Languages : en Pages : 218
Book Description
In 1919, Bieberbach posed a seemingly simple conjecture. That ``simple'' conjecture challenged mathematicians in complex analysis for the following 68 years! In that time, a huge number of papers discussing the conjecture and its related problems were inspired. Finally in 1984, de Branges completed the solution. In 1989, Professor Gong wrote and published a short book in Chinese, The Bieberbach Conjecture, outlining the history of the related problems and de Branges' proof. The present volume is the English translation of that Chinese edition with modifications by the author. In particular, he includes results related to several complex variables. Open problems and a large number of new mathematical results motivated by the Bieberbach conjecture are included. Completion of a standard one-year graduate complex analysis course will prepare the reader for understanding the book. It would make a nice supplementary text for a topics course at the advanced undergraduate or graduate level.
Author: Sheng Gong Publisher: American Mathematical Soc. ISBN: 0821827421 Category : Education Languages : en Pages : 218
Book Description
In 1919, Bieberbach posed a seemingly simple conjecture. That ``simple'' conjecture challenged mathematicians in complex analysis for the following 68 years! In that time, a huge number of papers discussing the conjecture and its related problems were inspired. Finally in 1984, de Branges completed the solution. In 1989, Professor Gong wrote and published a short book in Chinese, The Bieberbach Conjecture, outlining the history of the related problems and de Branges' proof. The present volume is the English translation of that Chinese edition with modifications by the author. In particular, he includes results related to several complex variables. Open problems and a large number of new mathematical results motivated by the Bieberbach conjecture are included. Completion of a standard one-year graduate complex analysis course will prepare the reader for understanding the book. It would make a nice supplementary text for a topics course at the advanced undergraduate or graduate level.
Author: Albert Baernstein (II) Publisher: American Mathematical Soc. ISBN: 0821815210 Category : Mathematics Languages : en Pages : 238
Book Description
Louis de Branges of Purdue University is recognized as the mathematician who proved Bieberbach's conjecture. This book offers insight into the nature of the conjecture, its history and its proof. It is suitable for research mathematicians and analysts.
Author: A.A. Gonchar Publisher: Springer Science & Business Media ISBN: 1461229669 Category : Mathematics Languages : en Pages : 463
Book Description
Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.
Author: Prem K. Kythe Publisher: CRC Press ISBN: 149871899X Category : Mathematics Languages : en Pages : 365
Book Description
Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. Assuming basic knowledge of complex analysis
Author: Mario Gonzalez Publisher: Routledge ISBN: 1351459384 Category : Mathematics Languages : en Pages : 544
Book Description
A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu
Author: Nicholas J. Higham Publisher: SIAM ISBN: 9780898719550 Category : Mathematics Languages : en Pages : 317
Book Description
This handy volume, enlivened by anecdotes, unusual paper titles, and humorous quotations, provides even more information on the issues you will face when writing a technical paper or talk, from choosing the right journal in which to publish to handling your references. Its overview of the entire publication process is invaluable for anyone hoping to publish in a technical journal.
Author: Boris Khesin Publisher: Springer Science & Business Media ISBN: 3540772634 Category : Mathematics Languages : en Pages : 304
Book Description
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Author: Ivars Peterson Publisher: Macmillan ISBN: 0805071598 Category : Mathematics Languages : en Pages : 273
Book Description
In the first edition of The Mathematical Tourist, renowned science journalist Ivars Peterson took readers on an unforgettable tour through the sometimes bizarre, but always fascinating, landscape of modern mathematics. Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on * the relationship between mathematical knots and DNA * how computers based on quantum logic can significantly speed up the factoring of large composite numbers * the relationship between four-dimensional geometry and physical theories of the nature of matter * the application of cellular automata models to social questions and the peregrinations of virtual ants * a novel mathematical model of quasicrystals based on decagon-shaped tiles Blazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.
Author: Richmond Campbell Publisher: Rowman & Littlefield Publishers ISBN: 1461601959 Category : Philosophy Languages : en Pages : 260
Book Description
Modern epistemology has run into several paradoxes in its efforts to explain how knowledge acquisition can be both socially based (and thus apparently context-relative) and still able to determine objective facts about the world. In this important book, Richmond Campbell attempts to dispel some of these paradoxes, to show how they are ultimately just 'illusions of paradox,' by developing ideas central to two of the most promising currents in epistemology: feminist epistemology and naturalized epistemology. Campbell's aim is to construct a coherent theory of knowing that is feminist and 'naturalized.' Illusions of Paradox will be valuable for students and scholars of epistemology and women's studies.
Author: William Aspray Publisher: U of Minnesota Press ISBN: 0816615675 Category : Mathematics Languages : en Pages : 396
Book Description
History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
Author: Sheng Gong
Author: Sheng Gong
Author: Albert Baernstein (II)
Author: A.A. Gonchar
Author: Prem K. Kythe
Author: Mario Gonzalez
Author: Nicholas J. Higham
Author: Boris Khesin
Author: Ivars Peterson
Author: Richmond Campbell
Author: William Aspray