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The Problem of Catalan, Yuri F. Bilu; Yann Bugeaud; Maurice Mignotte


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Автор: Yuri F. Bilu; Yann Bugeaud; Maurice Mignotte
Название:  The Problem of Catalan
ISBN: 9783319362557
Издательство: Springer
Классификация:

ISBN-10: 3319362550
Обложка/Формат: Paperback
Страницы: 245
Вес: 0.37 кг.
Дата издания: 10.09.2016
Язык: English
Размер: 234 x 156 x 14
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

In 1842 the Belgian mathematician Eug ne Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 - 23 = 1 is the only solution of the equation xp - yq = 1 in integers x, y, p, q with xy 0 and p, q >= 2.

In this book we give a complete and (almost) self-contained exposition of Mihăilescus work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.




The Burnside Problem and Identities in Groups

Автор: Sergej I. Adian; John Lennox; James Wiegold
Название: The Burnside Problem and Identities in Groups
ISBN: 3642669344 ISBN-13(EAN): 9783642669347
Издательство: Springer
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Цена: 12577.00 р.
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The ADI Model Problem

Автор: Eugene Wachspress
Название: The ADI Model Problem
ISBN: 1493900196 ISBN-13(EAN): 9781493900190
Издательство: Springer
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Цена: 15672.00 р.
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Описание: This book presents the foundations of Alternating Direction Implicit iteration for systems with both real and complex spectra and extends work for real spectra into the complex plane with methods for computing optimum iteration parameters.

Using Design Research and History to Tackle a Fundamental Problem with School Algebra

Автор: Sinan Kanbir; M. A. (Ken) Clements; Nerida F. Elle
Название: Using Design Research and History to Tackle a Fundamental Problem with School Algebra
ISBN: 3319592033 ISBN-13(EAN): 9783319592039
Издательство: Springer
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Цена: 15372.00 р.
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Описание: In this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida Ellerton, tackle a persistent, and universal, problem in school mathematics--why do so many middle-school and secondary-school students find it difficult to learn algebra well? What makes the book important are the unique features which comprise the design-research approach that the authors adopted in seeking a solution to the problem.
The first unique feature is that the authors offer an overview of the history of school algebra. Despite the fact that algebra has been an important component of secondary-school mathematics for more than three centuries, there has never been a comprehensive historical analysis of factors influencing the teaching and learning of that component.
The authors identify, through historical analysis, six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. They also raise the question whether school algebra represents a unidimensional trait.
Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their intervention study (by which seventh-grade students significantly improved their elementary algebra knowledge and skills). Their theoretical frame combined Charles Sanders Peirce's triadic signifier-interpretant-signified theory, which is in the realm of semiotics, with Johann Friedrich Herbart's theory of apperception, and Ken Clements' and Gina Del Campo's theory relating to the need to expand modes of communications in mathematics classrooms so that students engage in receptive and expressive modes. Practicing classroom teachers formed part of the research team.
This book appears in Springer's series on the "History of Mathematics Education." Not only does it include an important analysis of the history of school algebra, but it also adopts a theoretical frame which relies more on "theories from the past," than on contemporary theories in the field of mathematics education. The results of the well-designed classroom intervention are sufficiently impressive that the study might havecreated and illuminated a pathway for future researchers to take.

Numerical Solutions of the N-Body Problem

Автор: A. Marciniak
Название: Numerical Solutions of the N-Body Problem
ISBN: 9027720584 ISBN-13(EAN): 9789027720580
Издательство: Springer
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Цена: 13275.00 р.
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Описание: Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics;

Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem

Автор: David E. Handelman
Название: Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem
ISBN: 3540184007 ISBN-13(EAN): 9783540184003
Издательство: Springer
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Цена: 3487.00 р.
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Описание: Emanating from the theory of C*-algebras and actions of tori theorem, this book discusses the problems that are outgrowths of random walk problems on lattices.

Problem-solving and selected topics in number theory

Автор: Rassias, Michael Th.
Название: Problem-solving and selected topics in number theory
ISBN: 1489981942 ISBN-13(EAN): 9781489981943
Издательство: Springer
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Цена: 7685.00 р.
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Описание: This self-contained introduction to classical number theory is written for undergraduate and graduate students, alike. Proofs of the theorems and solutions of the exercises are presented step-by-step.


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