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Foundations of Analysis over Surreal Number Fields

Author : N.L. Alling

Publisher : Elsevier

Page : 391 pages

File Size : 45,23 MB

Release : 1987-04-01

Category : Mathematics

ISBN : 0080872522

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Book Description

In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given.Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.



Proceedings of the international conference "“NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS”

Author : Yaroslav D. Sergeyev

Publisher : Luigi Pellegrini Editore

Page : 153 pages

File Size : 24,92 MB

Release : 2013-06-27

Category : Mathematics

ISBN : 8868220334

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Book Description

This book contains Proceedings of the International Conference and Summer School NUMTA-2013 “Numerical Computations: Theory and Algorithms”. The Conference is organized jointly by the University of Calabria, Italy, and by the N.I. Lobachevsky State University of Nizhni Novgorod, Russia in cooperation with the Society for Industrial and Applied Mathematics (SIAM), USA. The goal of the Conference is to create a multidisciplinary round table for an open discussion on numerical modeling nature by using traditional and emerging computational paradigms. The Conference discusses all aspects of numerical computations and modeling from foundations and philosophy to advanced numerical techniques. New technological challenges and fundamental ideas from theoretical computer science, linguistic, logic, set theory, and philosophy meet requirements and new fresh applications from physics, chemistry, biology, and economy.



Pursuit of the Universal

Author : Arnold Beckmann

Publisher : Springer

Page : 388 pages

File Size : 12,56 MB

Release : 2016-06-13

Category : Computers

ISBN : 3319401890

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Book Description

This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.



Advances in $p$-adic and Non-Archimedean Analysis

Author : M. Berz

Publisher : American Mathematical Soc.

Page : 281 pages

File Size : 13,20 MB

Release : 2010-02-17

Category : Mathematics

ISBN : 0821847406

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Book Description

This volume contains the proceedings of the Tenth International Conference on $p$-adic and Non-Archimedean Analysis, held at Michigan State University in East Lansing, Michigan, on June 30-July 3, 2008. This volume contains a kaleidoscope of papers based on several of the more important talks presented at the meeting. It provides a cutting-edge connection to some of the most important recent developments in the field. Through a combination of survey papers, research articles, and extensive references to earlier work, this volume allows the reader to quickly gain an overview of current activity in the field and become acquainted with many of the recent sub-branches of its development.



Real Numbers, Generalizations of the Reals, and Theories of Continua

Author : P. Ehrlich

Publisher : Springer Science & Business Media

Page : 313 pages

File Size : 23,21 MB

Release : 2013-06-29

Category : Mathematics

ISBN : 9401582483

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Book Description

Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.



Games of No Chance 3

Author : Michael H. Albert

Publisher : Cambridge University Press

Page : 577 pages

File Size : 34,67 MB

Release : 2009-05-29

Category : Mathematics

ISBN : 0521861349

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Book Description

This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.



Ordered Algebraic Structures and Related Topics

Author : Fabrizio Broglia

Publisher : American Mathematical Soc.

Page : 390 pages

File Size : 17,21 MB

Release : 2017

Category : Mathematics

ISBN : 1470429667

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Book Description

Contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held in October 2015, at CIRM, Luminy, Marseilles. Papers cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.



On Numbers and Games

Author : John H. Conway

Publisher : CRC Press

Page : 253 pages

File Size : 16,28 MB

Release : 2000-12-11

Category : Mathematics

ISBN : 1439864152

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Book Description

Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class that includes both real numbers and ordinal numbers: surreal numbers. The second edition presents developments in mathematical game theory, focusing on surreal numbers and the additive theory of partizan games.



Advances in Ultrametric Analysis

Author : Alain Escassut

Publisher : American Mathematical Soc.

Page : 298 pages

File Size : 27,57 MB

Release : 2018-03-26

Category : Mathematics

ISBN : 1470434911

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Book Description

Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.



Advances in Non-Archimedean Analysis

Author : Helge Glöckner

Publisher : American Mathematical Soc.

Page : 346 pages

File Size : 15,89 MB

Release : 2016-05-20

Category : Mathematics

ISBN : 1470419882

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Book Description

This volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.