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Author: Paulo Ribenboim Publisher: Boston ; Toronto : Academic Press ISBN: Category : Mathematics Languages : en Pages : 392
Book Description
This text provides a historical study of the efforts of mathematicians to solve Catalan's problem. It covers divisibility conditions and analytical methods.
Author: Paulo Ribenboim Publisher: Boston ; Toronto : Academic Press ISBN: Category : Mathematics Languages : en Pages : 392
Book Description
This text provides a historical study of the efforts of mathematicians to solve Catalan's problem. It covers divisibility conditions and analytical methods.
Author: René Schoof Publisher: Springer Science & Business Media ISBN: 1848001851 Category : Mathematics Languages : en Pages : 125
Book Description
Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further. Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.
Author: Paul Freedman Publisher: Cornell University Press ISBN: 1501772244 Category : History Languages : en Pages : 355
Book Description
The Splendor and Opulence of the Past traces the career of Jaume Caresmar (1717–1791), a church historian and a key figure of the Catalan Enlightenment who transcribed tens of thousands of parchments to preserve and glorify Catalonia's medieval past in the face of its diminishing autonomy. As Paul Freedman shows, Caresmar's books, essays, and transcriptions—some only recently discovered—provide fresh insights into the Middle Ages as remembered in modern Catalonia and illustrate how a nation's past glories and humiliations can inform contemporary politics and culture. From the ninth to the sixteenth centuries, Catalonia was a thriving, independent set of principalities within what would become modern Spain. In the wake of the dismantling of its autonomy by the eighteenth-century Spanish state, Catalan scholars looked to the region's medieval independence and wealth as a means of maintaining a distinct Catalan identity and resisting Castilian hegemony. Through their writings and archival investigations, Caresmar and the canons at Santa Maria de Bellpuig de les Avellanes, where Caresmar was abbot, laid the foundations for not only the scholarly exploration of the Middle Ages but also the development of Catalan national sentiment. Although the eighteenth century is often regarded as a low point for the Catalan language and culture, The Splendor and Opulence of the Past emphasizes the importance of this period's antiquarians to Catalan projects of modernization and economic progress and links their historiography of the Middle Ages to struggles over Catalonia's relationship to the Spanish state over two centuries.
Author: Chris Bambery Publisher: Luath Press Ltd ISBN: 1912387417 Category : History Languages : en Pages : 353
Book Description
2017 saw Catalonia come under the world's spotlight as it again fought for independence and the preservation and protection of its unique Catalan culture. Answering the questions and complications behind the fight for Catalonian Independence, Catalonia Reborn is a detailed guide to the region's political, historical and cultural issues. For the layman as well as the expert, it takes the reader through the rich history of Catalonia – its language, culture and political background – to the present day, covering defining eras of the region from Franco's dictatorship to the 2017 independence referendum and elections.
Author: Carles Casacuberta Publisher: Springer ISBN: 3540473416 Category : Mathematics Languages : en Pages : 118
Book Description
The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.
Author: James Haglund Publisher: American Mathematical Soc. ISBN: 0821844113 Category : Mathematics Languages : en Pages : 178
Book Description
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
Author: Paulo Ribenboim
Author: Paulo Ribenboim
Author: René Schoof
Author: Paul Freedman
Author: Chris Bambery
Author: Carles Casacuberta
Author: Thomas Wyse
Author: Thomas WYSE (Right Hon. Sir.)
Author: Thomas Wyse (Rt. Hon. Sir, K.C.B.)
Author: sir Thomas Wyse
Author: James Haglund