Download or read book Hilbert s Tenth Problem Relations with Arithmetic and Algebraic Geometry written by Jan Denef and published by American Mathematical Soc.. This book was released on 2000 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bücchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation. The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory
Download or read book Hilbert s Tenth Problem An Introduction to Logic Number Theory and Computability written by M. Ram Murty and published by American Mathematical Soc.. This book was released on 2019-05-09 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists. This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.
Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2012-08-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2012, held in Maribor, Slovenia, in September 2012. The 28 full papers presented were carefully reviewed and selected for inclusion in this book. One of the main themes of the CASC workshop series, namely polynomial algebra, is represented by contributions devoted to new algorithms for computing comprehensive Gröbner and involutive systems, parallelization of the Gröbner bases computation, the study of quasi-stable polynomial ideals, new algorithms to compute the Jacobson form of a matrix of Ore polynomials, a recursive Leverrier algorithm for inversion of dense matrices whose entries are monic polynomials, root isolation of zero-dimensional triangular polynomial systems, optimal computation of the third power of a long integer, investigation of the complexity of solving systems with few independent monomials, the study of ill-conditioned polynomial systems, a method for polynomial root-finding via eigen-solving and randomization, an algorithm for fast dense polynomial multiplication with Java using the new opaque typed method, and sparse polynomial powering using heaps.
Download or read book Hilbert s Tenth Problem written by Alexandra Shlapentokh and published by Cambridge University Press. This book was released on 2007 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description
Download or read book Arithmetic Geometry written by Jean-Louis Colliot-Thélène and published by Springer. This book was released on 2010-10-27 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.
Download or read book Theory and Applications of Models of Computation written by Rahul Jain and published by Springer. This book was released on 2015-04-15 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014, held in Singapore, in May 2015. The 35 revised full papers presented were carefully reviewed and selected from 78 submissions. The papers treat all topics relating to the theory and applications of models computation, for example recursion theory and mathematical logic; computational complexity and Boolean functions; graphy theory; quantum computing; parallelism and statistics; learning, automata and probabilistic models; parameterised complexity.
Download or read book Algorithmic Number Theory written by Claus Fieker and published by Springer Science & Business Media. This book was released on 2002-06-26 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-organized criticality (SOC) has become a magic word in various scientific disciplines; it provides a framework for understanding complexity and scale invariance in systems showing irregular fluctuations. In the first 10 years after Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic appeared. Seismology has been a field in earth sciences where the SOC concept has already deepened the understanding, but there seem to be much more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader into the basics of fractals, chaos and SOC, the book presents established and new applications of SOC in earth sciences, namely earthquakes, forest fires, landslides and drainage networks.
Download or read book Model Theory in Algebra Analysis and Arithmetic written by Lou van den Dries and published by Springer. This book was released on 2014-09-20 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Download or read book Martin Davis on Computability Computational Logic and Mathematical Foundations written by Eugenio G. Omodeo and published by Springer. This book was released on 2017-01-27 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Download or read book Computation Cryptography and Network Security written by Nicholas J. Daras and published by Springer. This book was released on 2015-09-16 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications. It discusses directions and pursuits of scientists that pertain to engineering sciences. It is also presents the theoretical background required for algorithms and techniques applied to a large variety of concrete problems. A number of open questions as well as new future areas are also highlighted. This book will appeal to operations research analysts, engineers, community decision makers, academics, the military community, practitioners sharing the current “state-of-the-art,” and analysts from coalition partners. Topics covered include Operations Research, Games and Control Theory, Computational Number Theory and Information Security, Scientific Computing and Applications, Statistical Modeling and Applications, Systems of Monitoring and Spatial Analysis.
Download or read book Algebraic Informatics written by Dimitrios Poulakis and published by Springer Nature. This book was released on 2022-10-17 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 9th International Conference on Algebraic Informatics, CAI 2022, held as virtual event, in October 27–29, 2022. The 2 abstracts, 3 full papers of invited speakers, and 12 contributed papers presented in this volume were carefully reviewed and selected from 17 submissions. The papers contain original and unpublished research; the topics of them lie in automata theory, cryptography, coding theory, DNA computation, computer algebra, and theory of software architectures.
Download or read book Verification Model Checking and Abstract Interpretation written by Viktor Kuncak and published by Springer Science & Business Media. This book was released on 2012-01-12 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2012, held in Philadelphia, PA, USA, in January 2012, co-located with the Symposium on Principles of Programming Languages, POPL 2012. The 26 revised full papers presented were carefully reviewed and selected from 70 submissions. The papers cover a wide range of topics including program verification, model checking, abstract interpretation, static analysis, deductive methods, program certification, debugging techniques, abstract domains, type systems, and optimization.
Download or read book Higher Dimensional Varieties and Rational Points written by Károly Jr. Böröczky and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.
Download or read book Geometric and Algorithmic Aspects of Computer Aided Design and Manufacturing written by Ravi Janardan and published by American Mathematical Soc.. This book was released on 2005 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer-Aided Design and Manufacturing (CAD/CAM) is concerned with all aspects of the process of designing, prototyping, manufacturing, inspecting, and maintaining complex geometric objects under computer control. As such, there is a natural synergy between this field and Computational Geometry (CG), which involves the design, analysis, implementation, and testing of efficient algorithms and data representation techniques for geometric entities such as points, polygons, polyhedra, curves, and surfaces. The DIMACS Center (Piscataway, NJ) sponsored a workshop to further promote the interaction between these two fields. Attendees from academia, research laboratories, and industry took part in the invited talks, contributed presentations, and informal discussions. This volume is an outgrowth of that meeting.
Download or read book Interpreting Godel written by Juliette Kennedy and published by Cambridge University Press. This book was released on 2014-08-21 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
