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Diophantine Approximation 1

引用

丛书名： Developments in Mathematics

1000年

作者： Hans Peter Schlickewei Klaus Schmidt Robert F. Tichy

ISBN: (数字)9783211742808

ISBN: (纸本)9783211742792;9783211999097

This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavor. In particular, estimates for the number of solutions of diophantine equations as well as results concerning congruences and polynomials are established. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and to discrepancy theory. The articles are based on lectures given at a conference at the Erwin Schr6dinger Institute in Vienna in 2003, in which many leading experts in the field of diophantine approximation participated. The editors are very grateful to the Erwin Schr6dinger Institute and to the FWF (Austrian Science Fund) for the financial support and they express their particular thanks to Springer-Verlag for the excellent cooperation. Robert E Tichy Diophantine Approximation H. E Schlickewei et al. , Editors 9 Springer-Verlag 2008 THE MATHEMATICAL WORK OF WOLFGANG SCHMIDT Hans Peter Schlickewei Mathematik Informatik, und Philipps-Universitiit Hans-Meerwein-Strasse, Marburg, 35032 Marburg, Germany k. Introduction Wolfgang Schmidt's mathematical activities started more than fifty years ago in 1955. In the meantime he has written more than 180 papers - many of them containing spectacular results and breakthroughs in different areas of number theory.

关键词： algebra Computational Mathematics and Numerical Analysis number theory

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Parallel Computing 1

引用

1000年

作者： Roman Trobec Marián Vajteršic Peter Zinterhof

ISBN: (数字)9781848824096

ISBN: (纸本)9781848824089;9781849968416

The use of parallel programming and architectures is essential for simulating and solving problems in modern computational practice. There has been rapid progress in microprocessor architecture, interconnection technology and software devel- ment, which are in?uencing directly the rapid growth of parallel and distributed computing. However, in order to make these bene?ts usable in practice, this dev- opment must be accompanied by progress in the design, analysis and application aspects of parallel algorithms. In particular, new approaches from parallel num- ics are important for solving complex computational problems on parallel and/or distributed systems. The contributions to this book are focused on topics most concerned in the trends of today’s parallel computing. These range from parallel algorithmics, progr- ming, tools, network computing to future parallel computing. Particular attention is paid to parallel numerics: linear algebra, differential equations, numerical integ- tion, number theory and their applications in computer simulations, which together form the kernel of the monograph. We expect that the book will be of interest to scientists working on parallel computing, doctoral students, teachers, engineers and mathematicians dealing with numerical applications and computer simulations of natural phenomena.

关键词： computer System Implementation computer Communication Networks Numerical Analysis Numeric Computing Simulation and Modeling

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Some techniques for proving certain simple programs optimal

Some techniques for proving certain simple programs optimal

引用

IEEE Annual Symposium on Switching and Automata theory

作者： J. E. Hopcroft L. R. Kerr Department of Computer Science Cornell University Ithaca NY USA

This paper develops techniques for establishing a lower bound on the number of arithmetic operations necessary for sets of simple expressions. The techniques are applied to matrix multiplication. A modification of Strassen's algorithm is developed for multiplying n × p matrices by p × q matrices. The techniques are used to prove that this algorithm minimizes the number of multiplications for a few special cases. In so doing we establish that matrix multiplication with elements from a commutative ring requires fewer multiplications than with elements from a non-commutative ring.

关键词： Turing machines Registers polynomials computer science Digital arithmetic Commutation Modules (abstract algebra) Computational complexity computer aided instruction Input variables

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An Invitation to Representation theory 1

引用

丛书名： Springer Undergraduate Mathematics Series

1000年

作者： R. Michael Howe

ISBN: (数字)9783030980252

ISBN: (纸本)9783030980245

offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.;The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.;With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.

关键词： Group theory and Generalizations

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Combinatorial Structures in algebra and Geometry 1

引用

丛书名： Springer Proceedings in Mathematics & Statistics

1000年

作者： Dumitru I. Stamate Tomasz Szemberg

ISBN: (数字)9783030521110

ISBN: (纸本)9783030521103

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic propertiesof line bundles in geometry and multiplier ideals in algebra.;This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded algebra and applications" (ISBN 978-3-319-90493-1).

关键词： Commutative Rings and algebras algebraic Geometry Combinatorics Graph theory Field theory and polynomials

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algebra for applications 3

Algebra for Applications

引用

丛书名： Springer Undergraduate Mathematics Series

1000年

作者： Arkadii Slinko

ISBN: (数字)9783031826269

ISBN: (纸本)9783031826252

This textbook provides mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Modern societies are awash with data that needs to be manipulated in many ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorized access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory. This textbook covers background topics in arithmetic, polynomials, groups, fields, and elliptic curves required for real-life applications like cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. The book illustrates the work of these applications using the free GAP computational package. It uses this package to help readers understand computationally hard problems and provide insights into protecting data integrity. This textbook covers a wide range of applications including recent developments, primarily intended for use as a textbook, with numerous worked examples and solved exercises suitable for self-study. This edition has been thoroughly revised with new topics and exercises, introducing hash functions for properly describing digital signatures, blockchains, and digital currencies in the latest version.

关键词： algebra Mathematical applications in computer Science Discrete Mathematics

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applications of computer algebra 1

引用

丛书名： Springer Proceedings in Mathematics & Statistics

1000年

作者： Ilias S. Kotsireas Edgar Martínez-Moro

ISBN: (数字)9783319569321

ISBN: (纸本)9783319569307;9783319860381

The applications of computer algebra (ACA) conference covers a wide range of topics from Coding theory to Differential algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of computer algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

关键词： Commutative Rings and algebras Field theory and polynomials Coding and Information theory Mathematical applications in computer Science algebraic Geometry

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A Readable Introduction to Real Mathematics 1

引用

丛书名： Undergraduate Texts in Mathematics

1000年

作者： Daniel Rosenthal Peter Rosenthal David Rosenthal

ISBN: (数字)9783319056548

Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.

关键词： Mathematics, general number theory Geometry

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Realization of Boolean polynomials based on incidence matrices

Realization of Boolean polynomials based on incidence matric...

引用

1959 Eastern Joint IRE-AIEE-ACM computer Conference, IRE-AIEE-ACM 1959

作者： Okada, S. Moriwaki, Y. Young, K.P. Microwave Research Institute of Polytechnic Institute of Brooklyn NY United States University of Tokyo Japan Microwave Research Institute of Polytechnic Institute of Brooklyn NY United States

This paper describes a general algebraic method of finding minimum contact networks for any given Boolean polynomial. Solutions obtained by this method may in general be any kind of connection with any number of contacts for each variable. Furthermore, any practical requirements such as series-parallel cases usually found in most electronic devices, and single contact for specified variables, can all be considered in the calculation, if necessary. A routine algorithm on incidence matrices will automatically yield any ingenious connections. The node-branch and branch loop incidence matrices which were revealed by G. R. Kirchhoff 1847, are adopted as unknown, especially those of modulo 2 which were elaborated by O. Veblen in 1916 are mostly used. However, simultaneous use of modulo zero (or infinity), 2 and other integers was found useful for combinatorial consideration in the multi-contact case. General Galois fields are already used in switching theory by Moisil and his Rumanian group. © 1959 Association for Computing Machinery, Inc. All rights reserved.

关键词： Matrix algebra

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Guide to Discrete Mathematics 1

引用

丛书名： Texts in computer Science

1000年

作者： Gerard O'Regan

ISBN: (数字)9783319445618

ISBN: (纸本)9783319830803

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill.;Features: provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics; examines the field of software engineering, describing formal methods; investigates probability and statistics.

关键词： Discrete Mathematics in computer Science Arithmetic and Logic Structures Logics and Meanings of Programs History of Computing Mathematical applications in computer Science Math applications in computer Science

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