检索结果-内蒙古大学图书馆

丛书名： Undergraduate Texts in Mathematics

1000年

作者： L. Lovász J. Pelikán K. Vesztergombi

ISBN: (数字)9780387217772

ISBN: (纸本)9780387955841;9780387955858

Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book. Laszlo Lovasz is a Senior Researcher in the theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize andthe Godel Prize for the top paper in computer Science. Jozsef Pelikan is Professor of Mathematics in the Department of algebra and number theory at Eotvos Lorand University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

关键词： Combinatorics number theory

来源：评论

学校读者我要写书评

暂无评论

Filters and mathematical systems 9

Filters and mathematical systems

引用

9th IEEE Symposium on Adaptive Processes, Decision and Control, SAP 1970

作者： Hammer, Preston C. Pennsylvania State University Department of Computer Science University ParkPA16802 United States

A filter in a set is any device which passes or does not pass each element in a set. The action of a filter is the dichotomy (A, B) of the base set where A is the set of elements passed or accepted and B is the complement of A. This innocent appearing definition which I first stated in 1967 is both general and suggestive of many applications. In particular, I chose the definition by direct abstraction from the filters of chemistry, electronics, cigarettes, and air conditioning. If I should not have differentiated between the filter as a device and its action, then the concept would be reduced to the algebra of sets. In the next section I will give a number of examples of filters and a short summary of a rudimentary theory. Thereafter I proceed to discussions of an assortment of generalizations I have made in which filters as such will appear mainly to indicate that they are ubiquitous. I will however, concentrate on the concepts which I know to be of importance in general systems theories. My approach has not followed the lines of making mathematical models of systems but to study mathematics as a system. While I have many years of work staked on the utility of such an approach, I do not pretend to have demonstrated to the satisfaction of many that applications are indeed possible. The semantics of mathematics, while more circumscribed than that of languages is not to be trivially described even if we choose to ignore its dynamic aspects. Even such a seemingly simple distinction as the one between abstraction and generalization have been confused partially because of the reluctance to admit that a generalization embraces the specific concept generalized, For example all groups are semigroups (by a poor choice of terminology) and thus semigroups are a generalization of groups, not an abstraction. On the other hand semigroups may be defined by abstracting certain conditions required of groups and in this sense they are the result of an abstraction process. © 1970 IEEE

关键词： Abstracting

来源：评论

学校读者我要写书评

暂无评论

algebraic 1

引用

丛书名： Mathematics and Its applications

1000年

作者： Hvedri Inassaridze

ISBN: (数字)9789401585699

ISBN: (纸本)9780792331858;9789048144792

algebraic;-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic;-theory are actively used in algebra and related fields, achieving interesting results.;This book presents the elements of algebraic;-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic;-theories, connections with topological;-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras.;This volume will be of interest to graduate students and research mathematicians who want to learn more about;-theory.

关键词： Field theory and polynomials algebraic Topology algebraic Geometry Functional Analysis Operator theory

来源：评论

学校读者我要写书评

暂无评论

MECHANIZATION OF TEDIOUS algebra - NEWCOMB OPERATORS OF PLANETARY theory

引用

COMMUNICATIONS OF THE ACM 1965年第1期8卷 27-&页

作者： GERARD, JM IZSAK, IG BARNETT, MP Massachusetts Institute of Technology Cambridge Massachusetts Institute of Technology Cambridge Smithsonian Institution Astrophysical Observatory Cambridge

The article focuses on a computer program that would generate tables of formulas for the Newcomb operators of planetary theory. Digital computers can be used to perform tedious algebraic and analytic processes. Programming systems are being developed and it seems that accounts of individual computer applications of this type may be of some general interest. Here the authors are concerned with an algebraic problem that arises in planetary theory. This is the construction of formulas for the classical Newcomb operators, that was developed to deal with the problem of near commensuration, such as occurs for certain minor planets. The Newcomb operators are used to form the coefficients in a multiply infinite series expansion of the potential function of the perturbing force which one planet exerts on another. The dominant considerations in the programming related to loop and branch control, saving storage and ensuring that the number representation gave an adequate range of magnitudes. The author remarks that one benefit of the simplicity of the coding methods is the ease with which the programs can be modified and extended to deal with further related problems.

关键词： computer software PLANETARY theory computer programming ELECTRONIC data processing PERTURBATION (Mathematics) CODING theory

来源：评论

学校读者我要写书评

暂无评论

computer algebra Recipes 1

引用

丛书名： Undergraduate Texts in Contemporary Physics

1000年

作者： Richard H. Enns George C. McGuire

ISBN: (数字)9781461301714

ISBN: (纸本)9780387951485;9781461265337

computer algebra systems have the potential to revolutionize the teaching of and learning of science. Not only can students work thorough mathematical models much more efficiently and with fewer errors than with pencil and paper, they can also work with much more complex and computationally intensive models. Thus, for example, in studying the flight of a golf ball, students can begin with the simple parabolic trajectory, but then add the effects of lift and drag, of winds, and of spin. Not only can the program provide analytic solutions in some cases, it can also produce numerical solutions and graphic displays.;Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, chemistry. The text is organized along a spiral, revisiting general topics such as graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral.;The heart of the text is a large number of computer algebra recipes. These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and a story that leads the reader through steps of the recipe. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further.

关键词： algebra Mathematical and Computational Engineering applications of Mathematics Symbolic and algebraic Manipulation Physics, general Computational Intelligence

来源：评论

学校读者我要写书评

暂无评论

ON THE applications OF LIFTING TECHNIQUES

ON THE APPLICATIONS OF LIFTING TECHNIQUES

引用

作者： Esmaeil Mehrabi Western University

学位级别：博士

Lifting techniques are some of the main tools in solving a variety of different compu- tational problems related to the field of computer algebra. In this thesis, we will consider two fundamental problems in the fields of computational algebraic geometry and number theory, trying to find more efficient algorithms to solve such problems. The first problem, solving systems of polynomial equations, is one of the most fun- damental problems in the field of computational algebraic geometry. In this thesis, we discuss how to solve bivariate polynomial systems over either k(T ) or Q using a combi- nation of lifting and modular composition techniques. We will show that one can find an equiprojectable decomposition of a bivariate polynomial system in a better time com- plexity than the best known algorithms in the field, both in theory and practice. The second problem, polynomial factorization over number fields, is one of the oldest problems in number theory. It has lots of applications in many other related problems and there have been lots of attempts to solve the problem efficiently, at least, in prac- tice. Finding p-adic factors of a univariate polynomial over a number field uses lifting techniques. Improving this step can reduce the total running time of the factorization in practice. We first introduce a multivariate version of the Belabas factorization algo- rithm over number fields. Then we will compare the running time complexity of the factorization problem using two different representations of a number field, univariate vs multivariate, and at the end as an application, we will show the improvement gained in computing the splitting fields of a univariate polynomial over a rational field.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Discrete Mathematics for Computing 1

引用

1000年

作者： Peter Grossman

Written in a clear and informal style aimed especially at students with a limited background in mathematics, this introduction to discrete mathematics presents the material that forms the essential mathematical background for studies in computing and information systems. The topics covered include number systems, logic, relations, functions, induction, recursion, Boolean algebra, combinatorics, graph theory and number theory. The text contains many examples of applications of the theory to problems in computing, including a chapter on the representation and manipulation of numbers in a computer, examples of the use of propositional logic in program design, a section discussing the relationship between the mathematical and programming concepts of a function, and a chapter on the estimation of the time complexity of algorithms. A feature of the book is the use of algorithms written in pseudo code in many examples throughout the text. The exercises at the end of each chapter provide both routine drill of basic techniques and more challenging problems designed to enhance and extend the students' understanding. Answers to most of the exercises are provided at the back of the book. With its emphasis on presenting mathematical concepts clearly and simply, without compromising on mathematical correctness, and with its frequent use of examples drawn from computing, Discrete Mathematics for Computing is suitable for use as a text for a one-semester introductory course in discrete mathematics, particularly for students who are undertaking studies in computing and information systems.

关键词： Discrete Mathematics in computer Science

来源：评论

学校读者我要写书评

暂无评论

Boolean Differential Equations 1

引用

丛书名： Synthesis Lectures on Digital Circuits & Systems

1000年

作者： Bernd Steinbach Christian Posthoff

ISBN: (数字)9783031798610

ISBN: (纸本)9783031798603

The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits. Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The solution of such a BDE is a set of Boolean functions. This is a significant extension of Boolean equations, which have sets of Boolean vectors as solutions. In the simplest BDE a derivative operation of the BDC on the left-hand side is equal to a logic function on the right-hand side. The solution of such a simple BDE means to execute an operation which is inverse to the given derivative. BDEs can be applied in the same fields as the BDC, however, their possibility to express sets of Boolean functions extends the application field significantly.

关键词： Engineering, general Circuits and Systems Robotics and Automation computer Hardware

来源：评论

学校读者我要写书评

暂无评论

THEOREM ON INVARIANT AMPLITUDES

引用

JOURNAL OF MATHEMATICAL PHYSICS 1971年第4期12卷 612-&页

作者： GUERTIN, RF Department of Physics and Lawrence Radiation Laboratory University of California Berkeley California 94720

It is shown that any basis of covariant polynomials for a two‐particle scattering process yields invariant amplitudes free of kinematical singularities, provided (a) the total number of basis polynomials equals the number of spin space components of the scattering amplitude and (b) the polynomials of each of the two parity signatures are separately linearly independent at all points where three of the particle 4‐momenta are linearly independent. This result allows one to directly identify good basis sets without going through the very tedious algebra involved in comparing them to the sets of Hepp and Williams. The latter are not useful for practical applications because the spinor indices belonging to different particles are coupled and these sets do not transform into themselves under the relevant discrete symmetry operations.

关键词： polynomials Invariant amplitudes Particle scattering Singularity theory Spin scattering

来源：评论

学校读者我要写书评

暂无评论

Complex Analysis 1

引用

丛书名： Graduate Texts in Mathematics

1000年

作者： Jane P. Gilman Irwin Kra Rubí E. Rodríguez

ISBN: (数字)9780387747156

This bookpresents fundamental material that should be part of the education of every practicing mathematician. This material will also be of interest to computer scientists, physicists, and engineers. Complex analysis is also known as function theory. In this text we address the theory of complex-valued functions of a single complex variable. This is a prerequisite for the study of many current and rapidlydevelopingareasofmathematics, includingthetheoryofseveral andin?nitely many complex variables, thetheoryofgroups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis has connections and applications to many other many other subjects in mathematics, and also to other sciences as an area where the classic and the modern techniques meet and bene?t from each other. We will try to illustrate this in the applications we give. Because function theory has been used by generations of practicing mathematicians working in a number of di?erent ?elds, the basic - sults have been developed and redeveloped from a number of di?erent perspectives. We are not wedded to any one viewpoint. Rather we will try to exploit the richness of the subject and explain and interpret standard de?nitions and results using the most convenient tools from analysis, geometry, and algebra.

关键词： Functions of a Complex Variable Several Complex Variables and Analytic Spaces

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：