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| Author | : Kalle Kaarli |
| Publisher | : CRC Press |
| Total Pages | : 376 |
| Release | : 2000-07-21 |
| Genre | : Mathematics |
| ISBN | : 1482285754 |
Download Polynomial Completeness in Algebraic Systems Book in PDF, ePub and Kindle
Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new direct
| Author | : Kalle Kaarli |
| Publisher | : CRC Press |
| Total Pages | : 378 |
| Release | : 2000-07-21 |
| Genre | : Mathematics |
| ISBN | : 9781584882039 |
Download Polynomial Completeness in Algebraic Systems Book in PDF, ePub and Kindle
Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra. In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and systematically extends another specific property of Boolean algebras: the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them. An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems.
| Author | : Norman R Reilly |
| Publisher | : Oxford University Press |
| Total Pages | : 524 |
| Release | : 2009-11-02 |
| Genre | : Mathematics |
| ISBN | : 0199709920 |
Download Introduction to Applied Algebraic Systems Book in PDF, ePub and Kindle
This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as well as a fairly complete discussion of major algebraic systems (such as rings, fields, and groups) with a view of their use in bar coding, public key cryptosystems, error-correcting codes, counting techniques, and elliptic key cryptography. This is the only entry level text for algebraic systems that includes an extensive introduction to elliptic curves, a topic that has leaped to prominence due to its importance in the solution of Fermats Last Theorem and its incorporation into the rapidly expanding applications of elliptic curve cryptography in smart cards. Computer science students will appreciate the strong emphasis on the theory of polynomials, algebraic geometry and Groebner bases. The combination of a rigorous introduction to abstract algebra with a thorough coverage of its applications makes this book truly unique.
| Author | : Hans J. Stetter |
| Publisher | : SIAM |
| Total Pages | : 487 |
| Release | : 2004-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898717976 |
Download Numerical Polynomial Algebra Book in PDF, ePub and Kindle
In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 335 |
| Release | : 2000-04-01 |
| Genre | : Mathematics |
| ISBN | : 0080954146 |
Download Algebra of Polynomials Book in PDF, ePub and Kindle
Algebra of Polynomials
| Author | : Yuen Fong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 940170337X |
Download Proceedings of the Third International Algebra Conference Book in PDF, ePub and Kindle
This volume contains one invited lecture which was presented by the 1994 Fields Medal ist Professor E. Zelmanov and twelve other papers which were presented at the Third International Conference on Algebra and Their Related Topics at Chang Jung Christian University, Tainan, Republic of China, during the period June 26-July 1, 200l. All papers in this volume have been refereed by an international referee board and we would like to express our deepest thanks to all the referees who were so helpful and punctual in submitting their reports. Thanks are also due to the Promotion and Research Center of National Science Council of Republic of China and the Chang Jung Christian University for their generous financial support of this conference. The spirit of this conference is a continuation of the last two International Tainan Moscow Algebra Workshop on Algebras and Their Related Topics which were held in the mid-90's of the last century. The purpose of this very conference was to give a clear picture of the recent development and research in the fields of different kinds of algebras both in Taiwan and in the rest ofthe world, especially say, Russia" Europe, North America and South America. Thus, we were hoping to enhance the possibility of future cooperation in research work among the algebraists ofthe five continents. Here we would like to point out that this algebra gathering will constantly be held in the future in the southern part of Taiwan.
| Author | : Bourama Toni |
| Publisher | : Springer |
| Total Pages | : 654 |
| Release | : 2016-08-19 |
| Genre | : Mathematics |
| ISBN | : 3319313231 |
Download Mathematical Sciences with Multidisciplinary Applications Book in PDF, ePub and Kindle
This book is the fourth in a multidisciplinary series which brings together leading researchers in the STEAM-H disciplines (Science, Technology, Engineering, Agriculture, Mathematics and Health) to present their perspective on advances in their own specific fields, and to generate a genuinely interdisciplinary collaboration that transcends parochial subject-matter boundaries. All contributions are carefully edited, peer-reviewed, reasonably self-contained, and pedagogically crafted for a multidisciplinary readership. Contributions are drawn from a variety of fields including mathematics, statistics, game theory and behavioral sciences, biomathematics and physical chemistry, computer science and human-centered computing. This volume is dedicated to Professor Christiane Rousseau, whose work inspires the STEAM-H series, in recognition of her passion for the mathematical sciences and her on-going initiative, the Mathematics of Planet Earth paradigm of interdisciplinarity. The volume's primary goal is to enhance interdisciplinary understanding between these areas of research by showing how new advances in a particular field can be relevant to open problems in another and how many disciplines contribute to a better understanding of relevant issues at the interface of mathematics and the sciences. The main emphasis is on important methods, research directions and applications of analysis within and beyond each field. As such, the volume aims to foster student interest and participation in the STEAM-H domain, as well as promote interdisciplinary research collaborations. The volume is valuable as a reference of choice and a source of inspiration for a broad spectrum of scientists, mathematicians, research students and postdoctoral fellows.
| Author | : Francis Sowerby Macaulay |
| Publisher | : |
| Total Pages | : 138 |
| Release | : 1916 |
| Genre | : Elimination |
| ISBN | : |
Download The Algebraic Theory of Modular Systems Book in PDF, ePub and Kindle
| Author | : Alicia Dickenstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2005-04-27 |
| Genre | : Computers |
| ISBN | : 3540243267 |
Download Solving Polynomial Equations Book in PDF, ePub and Kindle
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
| Author | : Etienne Bézout |
| Publisher | : Princeton University Press |
| Total Pages | : 363 |
| Release | : 2009-01-10 |
| Genre | : Mathematics |
| ISBN | : 1400826969 |
Download General Theory of Algebraic Equations Book in PDF, ePub and Kindle
This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
