Quadratic Irrationals

Quadratic Irrationals
Author: Franz Halter-Koch
Publisher: CRC Press
Total Pages: 431
Release: 2013-06-17
Genre: Mathematics
ISBN: 1466591846

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Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T

Mathematics and Its History

Mathematics and Its History
Author: John Stillwell
Publisher: Springer Science & Business Media
Total Pages: 672
Release: 2010-08-02
Genre: Mathematics
ISBN: 144196052X

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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Effective Polynomial Computation

Effective Polynomial Computation
Author: Richard Zippel
Publisher: Springer Science & Business Media
Total Pages: 364
Release: 2012-12-06
Genre: Computers
ISBN: 1461531888

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Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

From China to Paris

From China to Paris
Author: Yvonne Dold-Samplonius
Publisher: Franz Steiner Verlag
Total Pages: 486
Release: 2002
Genre: Mathematics
ISBN: 9783515082235

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The reports of a conference of 11 scholars who began the task of examing together primary sources that might shed som elight on exactly how and in what fomrs mathematical problems, concepts, and techniques may have been transmitted between various civilizations, from antiquity down to the European Renaissance following more or less the legendary silk routes between China and Western Europe.

A Tribute to Emil Grosswald: Number Theory and Related Analysis

A Tribute to Emil Grosswald: Number Theory and Related Analysis
Author: Marvin Isadore Knopp
Publisher: American Mathematical Soc.
Total Pages: 624
Release: 1993
Genre: Mathematics
ISBN: 0821851551

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Emil Grosswald was a mathematician of great accomplishment and remarkable breadth of vision. This volume pays tribute to the span of his mathematical interests, which is reflected in the wide range of papers collected here. With contributions by leading contemporary researchers in number theory, modular functions, combinatorics, and related analysis, this book will interest graduate students and specialists in these fields. The high quality of the articles and their close connection to current research trends make this volume a must for any mathematics library.

Handbook of Mathematics

Handbook of Mathematics
Author: I.N. Bronshtein
Publisher: Springer Science & Business Media
Total Pages: 1206
Release: 2007-08-15
Genre: Technology & Engineering
ISBN: 3540721223

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This incredibly useful guide book to mathematics contains the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Now in its fifth updated edition, it is easy to understand, and convenient to use. Inside you’ll find the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes. For the 5th edition, the chapters "Computer Algebra Systems" and "Dynamical Systems and Chaos" have been revised, updated and expanded.

An Introduction to Formal Languages and Machine Computation

An Introduction to Formal Languages and Machine Computation
Author: Song Y. Yan
Publisher: World Scientific
Total Pages: 424
Release: 1998
Genre: Computers
ISBN: 9789810234225

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This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.

Continued Fractions

Continued Fractions
Author: Doug Hensley
Publisher: World Scientific
Total Pages: 261
Release: 2006
Genre: Mathematics
ISBN: 9812774688

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This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context.

Quadratics

Quadratics
Author: Richard A. Mollin
Publisher: CRC Press
Total Pages: 422
Release: 2018-04-27
Genre: Computers
ISBN: 1351420763

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The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders. This is not a book that is primarily about tables, although there are 80 pages of appendices that contain extensive tabular material (class numbers of real and complex quadratic fields up to 104; class group structures; fundamental units of real quadratic fields; and more!). This book is primarily a reference book and graduate student text with more than 200 exercises and a great deal of hints! The motivation for the text is best given by a quote from the Preface of Quadratics: "There can be no stronger motivation in mathematical inquiry than the search for truth and beauty. It is this author's long-standing conviction that number theory has the best of both of these worlds. In particular, algebraic and computational number theory have reached a stage where the current state of affairs richly deserves a proper elucidation. It is this author's goal to attempt to shine the best possible light on the subject."

Aspects of Ergodic, Qualitative and Statistical Theory of Motion

Aspects of Ergodic, Qualitative and Statistical Theory of Motion
Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
Total Pages: 456
Release: 2004-03-23
Genre: Mathematics
ISBN: 9783540408796

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Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.