How can we invent new certain knowledge in a methodical manner? This question stands at the heart of Salomon Maimon's theory of invention. Chikurel argues that Maimon's contribution to the ars inveniendi tradition lies in the methods of invention which he prescribes for mathematics. Influenced by Proclus' commentary on Elements, these methods are applied on examples taken from Euclid's Elements and Data. Centering around methodical invention and scientific genius, Maimon's philosophy is unique in an era glorifying the artistic genius, known as Geniezeit. Invention, primarily defined as constructing syllogisms, has implications on the notion of being given in intuition as well as in symbolic cognition. Chikurel introduces Maimon's notion of analysis in the broader sense, grounded not only on the principle of contradiction but on intuition as well. In philosophy, ampliative analysis is based on Maimon's logical term of analysis of the object, a term that has yet to be discussed in Maimonian scholarship. Following its introduction, a new version of the question quid juris? arises. In mathematics, Chikurel demonstrates how this conception of analysis originates from practices of Greek geometrical analysis.
This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.
The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Автор: G. Freudenthal Название: Salomon Maimon: Rational Dogmatist, Empirical Skeptic ISBN: 9048163633 ISBN-13(EAN): 9789048163632 Издательство: Springer Рейтинг: Цена: 27251.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The essays of leading scholars collected in this volume focus on Salomon Maimon`s (1753-1800) synthesis of `Rational Dogmatism` and `Empirical Skepticism`. This collection is of interest to scholars working in the fields of history of philosophy, metaphysics, epistemology, rationalism and empiricism as well as Jewish Studies.
Автор: Grosche Christian Название: Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae ISBN: 9814460079 ISBN-13(EAN): 9789814460071 Издательство: World Scientific Publishing Рейтинг: Цена: 19800.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition.In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.
Автор: Nielsen Mikkel Slot, Rohde Victor Ulrich Название: Undergraduate Convexity: Problems and Solutions ISBN: 9813143649 ISBN-13(EAN): 9789813143647 Издательство: World Scientific Publishing Цена: 5069.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here
Автор: Nielsen Mikkel Slot, Rohde Victor Ulrich Название: Undergraduate Convexity: Problems and Solutions ISBN: 9813146214 ISBN-13(EAN): 9789813146211 Издательство: World Scientific Publishing Цена: 8870.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here
Описание: Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples.Starting from linear inequalities and Fourier-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point algorithm. Study Guide here
Автор: Smilga, Voldemar (-) Название: In the search for beauty: unravelling non-euclidean geometry ISBN: 9813274352 ISBN-13(EAN): 9789813274358 Издательство: World Scientific Publishing Рейтинг: Цена: 11088.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This is a popular book that chronicles the historical attempts to prove the fifth postulate of Euclid on parallel lines that led eventually to the creation of non-Euclidean geometry. To absorb the mathematical content of the book, the reader should be familiar with the foundations of Euclidean geometry at the high school level. But besides the mathematics, the book is also devoted to stories about the people, brilliant mathematicians starting from Pythagoras and Euclid and terminating with Gauss, Lobachevsky and Klein. For two thousand years, mathematicians tried to prove the fifth postulate (whose formulation seemed to them too complicated to be a real postulate and not a theorem, hence the title In the Search for Beauty). But in the 19th century, they realized that such proof was impossible, and this led to a revolution in mathematics and then in physics. The two final chapters are devoted to Einstein and his general relativity which revealed to us that the geometry of the world we live in is not Euclidean.
Also included is an historical essay on Omar Khayyam, who was not only a poet, but also a brilliant astronomer and mathematician.
Автор: Specht Edward John Название: Euclidean Geometry and its Subgeometries ISBN: 3319237748 ISBN-13(EAN): 9783319237749 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs.
Автор: G.E. Martin Название: The Foundations of Geometry and the Non-Euclidean Plane ISBN: 0387906940 ISBN-13(EAN): 9780387906942 Издательство: Springer Рейтинг: Цена: 8378.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Suitable for junior, senior, and first-year graduate courses. This work interweaves historical material with a rigorous ruler - and protractor axiomatic development of the Euclidean and hyperbolic planes. It also includes topics such as axiom systems for three and four dimensional absolute geometry, and Pieri`s system based on rigid motions.
Описание: A work on barycentric calculus in Euclidean and hyperbolic geometry that provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry.
Автор: Sasane Amol Название: Plain Plane Geometry ISBN: 9814740446 ISBN-13(EAN): 9789814740449 Издательство: World Scientific Publishing Цена: 6336.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level.
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