Algebra Books
World Scientific Publishing Co Pte Ltd Applications Of Automata Theory And Algebra: Via
Book SynopsisThis book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as “The Wild Book”, became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now.This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics.The material and references have been brought up to date by the editor as much as possible, yet the book retains its distinct character and the bold yet rigorous style of the author. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of “punctuated equilibrium” (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life.The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds. removeTable of ContentsPrologue: Birth, Death, Time, Space, Existence, Understanding, Science and Religion; Introduction; What is Finite Group Theory?; A Generalization of Finite Group Theory to Finite Semigroups; A Reformulation of Physics; Automata Models and the Complexity of Finite State Machines; Applications: Introduction; Part I - Analysis and Classification of Biochemical Reactions; Part II - Complexity of Evolved Organisms, Appendix; Part III - The Lagrangian of Life: A. The Laws of Growing and Evolving Organisms; Part III - The Lagrangian of Life: B. Complexity, Emotion, Neurosis and Schizophrenia; Part IV - Complexity of Games.
£60.80
World Scientific Publishing Co Pte Ltd Matrix Partial Orders, Shorted Operators And
Book SynopsisThe present monograph on matrix partial orders, the first on this topic, makes a unique presentation of many partial orders on matrices that have fascinated mathematicians for their beauty and applied scientists for their wide-ranging application potential. Except for the Löwner order, the partial orders considered are relatively new and came into being in the late 1970s. After a detailed introduction to generalized inverses and decompositions, the three basic partial orders — namely, the minus, the sharp and the star — and the corresponding one-sided orders are presented using various generalized inverses. The authors then give a unified theory of all these partial orders as well as study the parallel sums and shorted matrices, the latter being studied at great length. Partial orders of modified matrices are a new addition. Finally, applications are given in statistics and electrical network theory.∗DeceasedTable of ContentsIntroduction; Decompositions and Generalized Inverses; Minus Order; Sharp Order; Star Order; One-Sided Orders; Lowner Order and Majorization; Unified Theory of Matrix Partial Orders through Generalized Inverses; Parallel Sums; Schur Complements and Shorted Operators; Shorted Operators II; Supremum and Infimum for a Pair of Matrices; Partial Orders for Modified Matrices; Statistics; Electrical Network Theory.
£94.05
World Scientific Publishing Co Pte Ltd Introduction To Non-abelian Class Field Theory,
Book SynopsisThis monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.Table of ContentsHigher Reciprocity Laws; Hilbert Class Fields over Imaginary Quadratic Fields; Indefinite Modular Forms; Dimension Formulas in the Case of Weight 1; 2-Dimensional Galois Representations of Odd Type and Non-Dihedral Cusp Forms of Weight 1; Maass Cusp Forms of Eigenvalue 1/4; Selberg's Eigenvalue Conjecture and the Ramanujan-Petersson Conjecture; Indefinite Theta Series; Hilbert Modular Forms of Weight 1; Appendix A: Some Dimension Formula and Traces of Hecke Operators for Cusp Forms of Weight 1;
£76.95
World Scientific Publishing Co Pte Ltd Graduate Course In Algebra, A - Volume 1
Book Synopsis'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very good book. It's pitched at the right level, it does a lot of serious stuff in preparation for what is coming the students' way in the future, and it does it well.'MAA ReviewsThis comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1-6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7-13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.
£49.40
World Scientific Publishing Co Pte Ltd Graduate Course In Algebra, A - Volume 2
Book Synopsis'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very good book. It's pitched at the right level, it does a lot of serious stuff in preparation for what is coming the students' way in the future, and it does it well.'MAA ReviewsThis comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1-6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7-13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.
£82.65
World Scientific Publishing Co Pte Ltd Graduate Course In Algebra, A - Volume 1
Book Synopsis'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very good book. It's pitched at the right level, it does a lot of serious stuff in preparation for what is coming the students' way in the future, and it does it well.'MAA ReviewsThis comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1-6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7-13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.
£82.65
World Scientific Publishing Co Pte Ltd Graduate Course In Algebra, A - Volume 2
Book Synopsis'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very good book. It's pitched at the right level, it does a lot of serious stuff in preparation for what is coming the students' way in the future, and it does it well.'MAA ReviewsThis comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1-6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7-13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.
£49.40
World Scientific Publishing Co Pte Ltd Exercises In Linear Algebra
Book SynopsisThis is a book of exercises in Linear Algebra. Through a systematic detailed discussion of 200 solved exercises, important concepts and topics are reviewed. The student is led to make a systematic review of topics from the basics to more advanced material, with emphasis on points that often cause the greatest difficulties. The solved exercises are followed by an additional 200 proposed exercises (with answers), thus guiding the student to a systematic consolidation of all topics.The contents follow closely the majority of the introductory courses of Linear Algebra. We consider in particular systems of linear equations, matrices, determinants, vector spaces, linear transformations, inner products, norms, eigenvalues and eigenvectors. The variety of exercises allows the adjustment to different levels in each topic.
£61.75
World Scientific Publishing Co Pte Ltd Exercises In Linear Algebra
Book SynopsisThis is a book of exercises in Linear Algebra. Through a systematic detailed discussion of 200 solved exercises, important concepts and topics are reviewed. The student is led to make a systematic review of topics from the basics to more advanced material, with emphasis on points that often cause the greatest difficulties. The solved exercises are followed by an additional 200 proposed exercises (with answers), thus guiding the student to a systematic consolidation of all topics.The contents follow closely the majority of the introductory courses of Linear Algebra. We consider in particular systems of linear equations, matrices, determinants, vector spaces, linear transformations, inner products, norms, eigenvalues and eigenvectors. The variety of exercises allows the adjustment to different levels in each topic.
£30.40
World Scientific Publishing Co Pte Ltd First Course In Linear Algebra, A
Book SynopsisA First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines.This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.
£38.00
World Scientific Publishing Co Pte Ltd First Course In Linear Algebra, A
Book SynopsisA First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines.This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.
£69.35
World Scientific Publishing Co Pte Ltd Course On Abstract Algebra, A
Book SynopsisThis textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's theorem and Sylow's theorems follow as applications of group theory. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials.Three whole new chapters are added to this second edition. Group action is introduced to give a more in-depth discussion on Sylow's theorems. We also provide a formula in solving combinatorial problems as an application. We devote two chapters to module theory, which is a natural generalization of the theory of the vector spaces. Readers will see the similarity and subtle differences between the two. In particular, determinant is formally defined and its properties rigorously proved.The textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.
£73.15
World Scientific Publishing Co Pte Ltd Category Theory And Applications: A Textbook For
Book Synopsis'It is written in a pedagogical, at times discursive, style and is both mathematically rigorous and easy to read … The book has an extensive index and can serve as a reference for key definitions and concepts in the subject. It will serve as an easy text for an introductory course in category theory and prove particularly valuable for the student or researcher wishing to delve further into algebraic topology and homological algebra.'Mathematical Reviews Clippings
£85.50
World Scientific Publishing Co Pte Ltd Linear Algebra And Its Applications
Book SynopsisFrom Tzuong-Tsieng Moh, a seasoned expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh covers the many standard aspects comprising linear algebra, such as echelon forms, matrix algebra, linear transformations, and more. Moh further includes several advanced topics and applications, as well as self-correcting codes, Heisenberg's uncertainty principle, Maxwell's equations in relativity form, Google's search engine, and the theory of finitely generated modules over a PID. This book is ideal for both newcomers and experienced readers who want to attain a deeper understanding on both the basics and advanced topics of linear algebra and its vast applications. The wide range of topics combined with the depth of each discussion make it essential to be on the shelf of every mathematical beginner and enthusiast.
£85.50
World Scientific Publishing Co Pte Ltd Numerical And Symbolic Computations Of
Book SynopsisWe introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.
£139.50
World Scientific Publishing Co Pte Ltd Course On Abstract Algebra, A
Book SynopsisNew Edition: A Course on Abstract Algebra (2nd Edition)This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions.This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.Table of ContentsAlgebraic Structure of Numbers; Sets and Functions; Basic Group Theory; Elementary Group Theory; Group Homomorphisms; Direct Products of Finite Abelian Groups; Sylow's Theorems and Applications; Symmetric Groups; Basic Ring Theory; Special Properties of Rings; Field Theory; Basic Galois Theory.
£51.30
World Scientific Publishing Co Pte Ltd Algebraic Approach To Differential Equations
Book SynopsisMixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest. It presents material from a school organized by The Abdus Salam International Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the International Centre for Pure and Applied Mathematics (CIMPA).Table of ContentsAlgebraic Methods To Study D-Modules (F Castro); Asymptotic Expansion of Singular Integrals (E Delabaere); Hypergeometric Functions and Hyperplane Arrangements (M Jambu); Geometry and Monodromy (L D Trang); Differential Algebraic Group (B Malgrange); D-Modules in Dimension 1 (L Narvaez); D-Modules in Characteristic P (Z Mebkhout); Stratifications and Constructible Sheaves (B Teissier).
£94.50
World Scientific Publishing Co Pte Ltd Algebraic Models For Accounting Systems
Book SynopsisThis book describes the construction of algebraic models which represent the operations of the double entry accounting system. It gives a novel, comprehensive, proof based treatment of the topic, using such concepts from abstract algebra as automata, digraphs, monoids and quotient structures.Table of ContentsModels in Accounting Theory - Introduction; Balance Vectors; Transactions; Abstract Accounting Systems; Quotient Systems and Homomorphisms; Accounting Systems as Automata; Accounting Systems with Restricted Transactions; Algorithms for Accounting Systems; Security Mechanisms and the Extended Model.
£75.05
World Scientific Publishing Co Pte Ltd Lambda-rings
Book SynopsisThis book gives a self-contained introduction to the theory of lambda-rings and closely related topics, including Witt vectors, integer-valued polynomials, and binomial rings. Many of the purely algebraic results about lambda-rings presented in this book have never appeared in book form before. This book concludes with a chapter on open problems related to lambda-rings.Table of Contentsλ-Rings; Universal λ-Rings; Adams Operations; Witt Vectors; Binomial Rings; Filtered λ-Rings, I; Filtered λ-Rings, II; Open Problems.
£57.95
World Scientific Publishing Co Pte Ltd Basic Commutative Algebra
Book SynopsisThis textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained.The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.Table of ContentsRings and Ideals; Modules and Algebras; Polynomials and Power Series Rings; Homological Tools I; Finiteness Conditions; Primary Decomposition; Filtrations and Completion; Numerical Functions; Dimension of Local Rings; Integral Extensions; Normal Domains; Integral Closure in a Finite Field Extension; Transcendental Extensions; Affine and Graded Rings; Valuation Rings and Valuations; Derivations and Differentials; Homological Tools II; Depth and Cohen-Macaulay Rings; Regular Rings; Divisor Class Groups.
£36.10
World Scientific Publishing Co Pte Ltd Basic Commutative Algebra
Book SynopsisThis textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained.The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.Table of ContentsRings and Ideals; Modules and Algebras; Polynomials and Power Series Rings; Homological Tools I; Finiteness Conditions; Primary Decomposition; Filtrations and Completion; Numerical Functions; Dimension of Local Rings; Integral Extensions; Normal Domains; Integral Closure in a Finite Field Extension; Transcendental Extensions; Affine and Graded Rings; Valuation Rings and Valuations; Derivations and Differentials; Homological Tools II; Depth and Cohen-Macaulay Rings; Regular Rings; Divisor Class Groups.
£77.90
World Scientific Publishing Co Pte Ltd Hands-on Matrix Algebra Using R: Active And
Book SynopsisThis is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.Table of ContentsR Preliminaries; Elementary Geometry and Algebra Using R; Vector Spaces; Matrix Basics and R Software; Determinant and Singularity; The Rank and Trace of a Matrix; Matrix Inverse and Solution of Linear Equations.
£87.40
World Scientific Publishing Co Pte Ltd Hands-on Matrix Algebra Using R: Active And
Book SynopsisThis is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.Table of ContentsR Preliminaries; Elementary Geometry and Algebra Using R; Vector Spaces; Matrix Basics and R Software; Determinant and Singularity; The Rank and Trace of a Matrix; Matrix Inverse and Solution of Linear Equations.
£43.70
World Scientific Publishing Co Pte Ltd Group Theory And Hopf Algebras: Lectures For
Book SynopsisThis book is addressed to graduate students and research workers in theoretical physics who want a thorough introduction to group theory and Hopf algebras. It is suitable for a one-semester course in group theory or a two-semester course which also treats advanced topics. Starting from basic definitions, it goes on to treat both finite and Lie groups as well as Hopf algebras. Because of the diversity in the choice of topics, which does not place undue emphasis on finite or Lie groups, it should be useful to physicists working in many branches.A unique aspect of the book is its treatment of Hopf algebras in a form accessible to physicists. Hopf algebras are generalizations of groups and their concepts are acquiring importance in the treatment of conformal field theories, noncommutative spacetimes, topological quantum computation and other important domains of investigation. But there is a scarcity of treatments of Hopf algebras at a level and in a manner that physicists are comfortable with. This book addresses this need superbly.There are illustrative examples from physics scattered throughout the book and in its set of problems. It also has a good bibliography. These features should enhance its value to readers.The authors are senior physicists with considerable research and teaching experience in diverse aspects of fundamental physics. The book, being the outcome of their combined efforts, stands testament to their knowledge and pedagogical skills.Table of ContentsGeneral Notions; Finite Groups; Lie Groups; The Poincare Group; Hopf Algebras in Physics.
£69.35
World Scientific Publishing Co Pte Ltd Property-preserving Petri Net Process Algebra In
Book SynopsisIn a component-based approach for system design, one of the challenging problems is the way to prove the correctness of the created components. Usually, the constituent components are supposed to be correct — possessing the desirable properties and free from undesirable ones. However, the operators may destroy these properties or create new ones, resulting in an undesirable new component. Hence, every created component has to go through a new process of verification, involving a tremendous amount of effort.This book presents a component -based methodology for the creation and verification of design specifications. The methodology is formally presented as an algebra called Property-Preserving Petri Net Process Algebra (PPPA). PPPA includes five classes of operators, and the authors show that every operator of PPPA can preserve a large number of basic system properties. Therefore, if the initial set of primitive components satisfies some of these properties, the created components will also “automatically” satisfy them without the need for further verification — thus greatly saving verification efforts.Table of ContentsFundamental Theory of Property-Preserving Petri Net Algebra: Introduction; Fundamentals on PPPA and Related Work; Petri Net Processes and Extension Operators; Composition Operators of PPPA; Property-Preserving Refinements; Property-Preserving Reductions; Place-Merging Operators for Resource Sharing; Applications to Software Engineering: Application of PPPA to Component-Based Design of Manufacturing Systems; Application of PPPA to Multi-Agent System Design; Application of PPPA to Job-Shop Scheduling Systems; Application of PPPA to Security Policy Design; Conclusion and Future Work.
£95.00
World Scientific Publishing Co Pte Ltd Rings Related To Stable Range Conditions
Book SynopsisThis monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.Table of ContentsNotational Conventions; Stable Range One; Unit 1-Stable Range; On m-Fold Stable Rings; Strongly Stable Rings; Weakly Stable Rings; Related Comparability; Generalized Stable Rings; QB-Rings; PB-Rings; Power-Cancellation; Stably Euclidean Rings; The n-Stable Range Condition; Stable Range for Ideals; Diagonal Reduction; Clean Properties, I; Clean Properties, II; Abelian Rings and Exchange.
£193.50
World Scientific Publishing Co Pte Ltd Matrix Calculus And Kronecker Product: A
Book SynopsisThis book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. Emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. All these fields are covered in detail. A key feature of the book is the many detailed worked-out examples. Computer algebra applications are also given. Each chapter includes useful exercises. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the second edition are: braid-like relations, Clebsch-Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product.Table of ContentsMatrix Calculus; Kronecker Product; Applications; Tensor Product; Braid-like Relations; Clebsch-Gordan Expansion; Nearest Kronecker Product; Clifford and Pauli Group; Universal Enveloping Algebra; Computer Algebra Implementation.
£70.30
World Scientific Publishing Co Pte Ltd Abstract Algebra: An Introduction To Groups,
Book SynopsisThis book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems.Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof.Table of ContentsLogic and Proofs; Set Theory; Cartesian Products and Relations, Maps and Binary Operations; The Integers with a Thorough Treatment of Congruences; Groups (including the Sylow Theorems); Permutation Groups; Rings, Integral, Domains and Fields; Latin Squares; Polya-Burnside Enumeration; Group Codes; Polynomial Codes; and other chapters.
£104.40
World Scientific Publishing Co Pte Ltd Hopf Algebras
Book SynopsisThe book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.Table of ContentsCoalgebras; Representations of Coalgebras; Filtrations and Gradings on Coalgebras; Bialgebras; The Convolution Algebra; Hopf Algebras; Hopf Modules and Co-Hopf Modules; Hopf Algebras as Modules Over Their Hopf Subalgebras; Integrals; Actions by Bialgebras and Hopf Algebras; Quasitriangular Bialgebras and Hopf Algebras; The Drinfel'd Double; Co-Quasitriangular Bialgebras and Hopf Algebras; Pointed Hopf Algebras; Finite-Dimensional Hopf Algebras Over a Field of Characteristic Zero.
£166.50
World Scientific Publishing Co Pte Ltd Abstract Algebra: An Introduction To Groups,
Book SynopsisThis book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems.Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof.Table of ContentsLogic and Proofs; Set Theory; Cartesian Products and Relations, Maps and Binary Operations; The Integers with a Thorough Treatment of Congruences; Groups (including the Sylow Theorems); Permutation Groups; Rings, Integral, Domains and Fields; Latin Squares; Polya-Burnside Enumeration; Group Codes; Polynomial Codes; and other chapters.
£55.10
World Scientific Publishing Co Pte Ltd Quantized Algebra And Physics - Proceedings Of
Book SynopsisThe book aims to survey recent developments in quantum algebras and related topics. Quantum groups were introduced by Drinfeld and Jimbo in 1985 in their work on Yang-Baxter equations. The subject from the very beginning has been an interesting one for both mathematics and theoretical physics. For example, Yangian is a special example of quantum group, corresponding to rational solution of Yang-Baxter equation. Viewed as a generalization of the symmetric group, Yangians also have close connections to algebraic combinatorics. This is the proceeding for the International Workshop on Quantized Algebra and Physics. The workshop aims to gather experts and young investigators from China and abroad to discuss research problems in integrable systems, conformal field theory, string theory, Lie theory, quantum groups including Yangians and their representations.Table of ContentsA Note on Brauer-Schur Functions (K Aokage et al.); O-Operators on Associative Algebras, Associative Yang-Baxter Equations and Dendriform Algebras (C-M Bai et al.); Irreducible Wakimoto-like Modules for the Affine Lie Algebra (Y Gao & Z-T Zeng); Verma Modules Over Generic Exp-Polynomial Lie Algebras (X-Q Guo et al.); Partially Harmonic Tensors and Quantized Schur-Weyl Duality (J Hu & Z-K Xiao); On Local Equivalences (N-H Jing); 2-Partitions of Root Systems (B Li et al.); A Survey on Weak Hopf Algebras (F Li & Q-X Sun); The Equitable Presentation for the Quantum Algebra (Uq(f(k)) (Y Pan et al.).
£76.95
World Scientific Publishing Co Pte Ltd Operads And Universal Algebra - Proceedings Of
Book SynopsisThe book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.Table of ContentsGrobner-Shirshov Bases for Categories (L A Bokut et al.); Operads, Clones, and Distributive Laws (P-L Curien); Leibniz Supalgebras Graded by Finite Root Systems (N-H Hu et al.); Generalized Disjunctive Languages and Universal Algebra (Y Liu); Koszul Duality of the Category of Trees and Bar Construction for Operads (M Livernet); Some Problems in Operad Theory (J-L Loday); Hom-Dendriform Algebras and Rota - Baxter Hom-Algebras (A Makhlouf); Free Field Realizations of the Current Algebras Associated with (Super) Lie Algebras (W-L Yang); Free TD Algebras and Rooted Trees (C-Y Zhou); Encyclopedia of Types of Algebras 2010 (G W Zinbiel); and other papers.
£95.40
World Scientific Publishing Co Pte Ltd Finite Fields And Galois Rings
Book SynopsisA large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.Table of ContentsSets and Integers; Groups; Fields and Rings; Polynomials; Residue Class Rings; Structure of Finite Fields; Further Properties of Finite Fields; Bases; Factoring Polynomials over Finite Fields; Irreducible Polynomials over Finite Fields; Quadratic Forms over Finite Fields; More Group Theory and Ring Theory; Hensel's Lemma and Hensel Lift; Galois Rings.
£61.75
World Scientific Publishing Co Pte Ltd Proceedings Of The International Conference On
Book SynopsisThis volume is an outcome of the International Conference on Algebra in celebration of the 70th birthday of Professor Shum Kar-Ping which was held in Gadjah Mada University on 7-10 October 2010. As a consequence of the wide coverage of his research interest and work, it presents 54 research papers, all original and referred, describing the latest research and development, and addressing a variety of issues and methods in semigroups, groups, rings and modules, lattices and Hopf Algebra. The book also provides five well-written expository survey articles which feature the structure of finite groups by A Ballester-Bolinches, R Esteban-Romero, and Yangming Li; new results of Gröbner-Shirshov basis by L A Bokut, Yuqun Chen, and K P Shum; polygroups and their properties by B Davvaz; main results on abstract characterizations of algebras of n-place functions obtained in the last 40 years by Wieslaw A Dudek and Valentin S Trokhimenko; Inverse semigroups and their generalizations by X M Ren and K P Shum. Recent work on cones of metrics and combinatorics done by M M Deza et al. is included.Table of ContentsInterval-Valued Graphs; Injective Envelope; Structure of Finite Groups; Semilattices; Archimedean Semigroups; Grobner-Shirshov Basis; Stable Lie Algebras; Polygroups and Their Properties; Semigroups of N-Ary Operations on Finite Sets; Cones of Weighted and Partial Matrices; Menger Algebras of N-Place Functions; Bialgebras; Malcev Algebra; Ternary Semiring; Chen Lie Algebras and Resonance Varieties; Restriction and Ehresmann Semigroups; Partially Solvable Finite Groups; Ordered Semigroups; Derivatives of Algebras and Superalgebras; Representations of Dialgebras and Conformal Algebras; Frobenius-Schur Indicators; Zariski Topology on the Prime Spectrum of a Module; Almost Distributive Lattices; S-Relatively Normal Almost Distributive Lattices; Pseudo-Complemented Almost Distributive Lattices; Inverse Semigroups; Sheaves Over Boolean Spaces; Semirings; Cotorsion Pairs of Complexes; Non-Permutative and Non-Idempotent Semigroups.
£216.00
World Scientific Publishing Co Pte Ltd Computational And Algorithmic Linear Algebra And
Book SynopsisThis undergraduate textbook on Linear Algebra and n-Dimensional Geometry, in a self-teaching style, is invaluable for sophomore level undergraduates in mathematics, engineering, business, and the sciences. These are classical subjects on which there are many mathematics books in theorem-proof style, but this unique volume has its focus on developing the mathematical modeling as well as computational and algorithmic skills in students at this level. The explanations in this book are detailed, lucid, and supported with numerous well-constructed examples to capture the interest and encourage the student to master the material.Table of ContentsMethods for Formulating Real World Problems Using Systems of Simultaneous Linear Equations; Algorithms for Analyzing and Solving These Models; Fundamental Concepts in N-Dimensional Geometry, Matrices and Determinants; Eigen Values and Eigen Vectors and Their Importance; Software Systems for Linear Algebra Problems.
£53.20
World Scientific Publishing Co Pte Ltd Computational And Algorithmic Linear Algebra And
Book SynopsisThis undergraduate textbook on Linear Algebra and n-Dimensional Geometry, in a self-teaching style, is invaluable for sophomore level undergraduates in mathematics, engineering, business, and the sciences. These are classical subjects on which there are many mathematics books in theorem-proof style, but this unique volume has its focus on developing the mathematical modeling as well as computational and algorithmic skills in students at this level. The explanations in this book are detailed, lucid, and supported with numerous well-constructed examples to capture the interest and encourage the student to master the material.Table of ContentsMethods for Formulating Real World Problems Using Systems of Simultaneous Linear Equations; Algorithms for Analyzing and Solving These Models; Fundamental Concepts in N-Dimensional Geometry, Matrices and Determinants; Eigen Values and Eigen Vectors and Their Importance; Software Systems for Linear Algebra Problems.
£95.40
World Scientific Publishing Co Pte Ltd Introduction To Semi-tensor Product Of Matrices
Book SynopsisA generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.Table of ContentsMulti-Dimensional Data; Semi-Tensor Product of Matrices; Multilinear Mappings Among Vector Spaces; Right and General Semi-Tensor Products; Rank, Pseudo-Inverse, and Positivity of STP; Matrix Expression of Logic; Mix-Valued Logic; Logical Matrix, Fuzzy Set and Fuzzy Logic; Fuzzy Relational Equation; Fuzzy Control with Coupled Fuzzy Relations; Boolean Function with Galois Field Structure; Decomposition of Logical Functions; Boolean Calculus; Lattice, Graph, and Universal Algebra; Boolean Network; Boolean Control System; Game Theory; Multi-Variable Polynomials; Some Applications to Differential Geometry and Algebra; Morgan's Problem; Linearization of Nonlinear Control Systems; Stability Region of Dynamic System.
£185.25
World Scientific Publishing Co Pte Ltd Problems And Solutions For Groups, Lie Groups,
Book SynopsisThe book presents examples of important techniques and theorems for Groups, Lie groups and Lie algebras. This allows the reader to gain understandings and insights through practice. Applications of these topics in physics and engineering are also provided. The book is self-contained. Each chapter gives an introduction to the topic.Table of ContentsGroups; Lie Groups; Lie Algebras; Applications.
£53.20
World Scientific Publishing Co Pte Ltd Contemporary Ring Theory 2011 - Proceedings Of
Book SynopsisThe study of noncommutative rings is a major area in modern algebra. The structure theory of noncommutative rings was originally concerned with three parts: The study of semi-simple rings; the study of radical rings; and the construction of rings with given radical and semi-simple factor rings. Recently, this has extended to many new parts: The zero-divisor theory, containing the study of coefficients of zero-dividing polynomials and the study of annihilators over noncommutative rings, that is related to the Köthe's conjecture; the study of nil rings and Jacobson rings; the study of applying ring-theoretic properties to modules; representation theory; the study of relations between algebraic and concepts of other branches (for example, analytic and topological), etc. Thus, noncommutative rings are ubiquitous in mathematics, and occur in numerous sciences.This volume consists of a collection of original articles refereed by world experts that was presented at the Sixth China-Japan-Korea International Conference on Ring Theory. These articles exhibit new ideas, tools and techniques needed for successful research and investigation in noncommutative ring theory, and show the trend of current research. It is a useful resource book for beginners and advanced experts in ring theory.Table of ContentsAn Extension of Rings and Hochschild 2-Cocycles (M Tamer Kosan, Tsiu-Kwen Lee and Yiqiang Zhou); A Short Proof that Continuous Modules are Clean (V P Camillo, D Khurana, T Y Lam and W K Nicholson); Notes on Weakly d-Koszul Modules (Jia-Feng Lu and Xiao-Lan Yu); The Galois Map and Its Induced Maps (George Szeto and Lianyong Xue); A Note on Quasi-Johns Rings (Liang Shen); A New Pseudorandom Number Generator AST (Huiling Song); Von Neumann Regular Rings Satisfying Generalized Almost Comparability (Mamoru Kutami); On Symmetric Biderivations of Semiprime Rings (Asma Ali and Faiza Shujat); When Do the Direct Sums of Modules Inherit Certain Properties? (Gangyong Lee, S Tariq Rizvi and Cosmin Roman); Imprimitive Regular Action in the Ring of Integers Modulo n (Juncheol Han, Yang Lee and Sangwon Park); Notes on Simple-Baer Modules and Rings (Lixin Mao); A Note on Prime Rings with Left Derivations (Nadeem Ur Rehman); On Rings in Which Every Ideal is Prime (Hisaya Tsutsui); Rings over which Polynomial Rings are NI (Juncheol Han, Yang Lee and Sung Pil Yang); On the Faith Conjecture (Kiyoichi Oshiro); Study on the Algebraic Structures in Terms of Geometry and Deformation Theory (Fumiya Suenobu and Fujio Kubo); Structures on S G Near-Rings and -Groups (Yong Uk Cho); Some Commutativity Theorems Concerning Additive Mappings and Derivations on Semiprime Rings (Shakir Ali, Basudeb Dhara and Ajda Fosner).
£86.45
World Scientific Publishing Co Pte Ltd Geometry Of The Octonions, The
Book SynopsisThere are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.Table of ContentsIntroduction; Division Algebras; Rotations; Lorentz Transformations; Spinors; The Right Eigenvalue Problem; The Exceptional Jordan Algebra; The Jordan Eigenvalue Problem; Lie Groups and Lie Algebras; Exceptional Lie Groups; The Dirac Equation; Octonionic Projective Spaces.
£90.25
World Scientific Publishing Co Pte Ltd Homological Algebra: The Interplay Of Homology
Book SynopsisIn this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations.These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system.The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a ‘Coherence Theorem for homological algebra’. (On the contrary, a ‘non-distributive’ homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.)The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences.We thus establish an effective method of working with spectral sequences, called ‘crossword chasing’, that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.Table of ContentsIntroduction; Coherence and Models in Homological Algebra; Puppe-Exact Categories; Involutive Categories; Categories of Relations as RE-Categories; Theories and Models; Homological Theories and Their Universal Models; Appendix A: Some Points of Category Theory; Appendix B: A Proof for the Universal Exact System.
£108.00
World Scientific Publishing Co Pte Ltd Polygroup Theory And Related Systems
Book SynopsisThis monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics.Table of ContentsA Brief Excursion into Group Theory; Hypergroups: Definitions and Examples of Hypergroups; Some Kinds of Subhypergroups; Homomorphism of Hypergroups; Regular and Strongly Regular Relations; Complete Hypergroups; Join Spaces; Polygroups: Definition and Examples of Polygroups; Extensions of Polygroups by Polygroups; Subpolygroups and Quotient Polygroups; Isomorphism Theorem of Polygroups; γ* Relation on Polygroups; Generalized Permutation; Permutation Polygroups; Representation of Polygroups; Polygroup Hyperrings; Solvable Polygroups; Nilpotent Polygroups; Weak Polygroups: Weak Hyperstructures; Weak Polygroups; Fundamental Relation on Weak Polygroups; Small Weak Polygroups; Combinatorial Aspects of Polygroups: Chromatic Polygroups; Polygroups Derived from Cogroups; Conjugation Lattice.
£61.75
World Scientific Publishing Co Pte Ltd Homological Algebra: In Strongly Non-abelian
Book SynopsisWe propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on ‘Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups’, published by the same Editor, but can be read independently of the latter.The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell — a moderate generalisation of abelian categories that is nevertheless crucial for a theory of ‘coherence’ and ‘universal models’ of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework.According to the present definitions, a semiexact category is a category equipped with an ideal of ‘null’ morphisms and provided with kernels and cokernels with respect to this ideal. A homological category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple.Extending abelian categories, and also the p-exact ones, these notions include the usual domains of homology and homotopy theories, e.g. the category of ‘pairs’ of topological spaces or groups; they also include their codomains, since the sequences of homotopy ‘objects’ for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets.Table of ContentsIntroduction; Semiexact categories; Homological Categories; Subquotients, Homology and Exact Couples; Satellites; Universal Constructions; Applications to Algebraic Topology; Homological Theories and Biuniversal Models; Appendix A. Some Points of Category Theory.
£95.40
World Scientific Publishing Co Pte Ltd Transformation Groups And Lie Algebras
Book SynopsisThis book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.Table of ContentsLocal transformation Groups: Preliminaries; One-Parameter Groups and Their Invariants; Groups Admitted by Differential Equations; Lie Algebras of Operators; Galois Groups via Symmetries; Approximate Transformation Groups: Preliminaries; Approximate Transformations; Approximate Symmetries; Applications.
£36.10
World Scientific Publishing Co Pte Ltd Linear Algebra: Pure & Applied
Book SynopsisThis is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it also includes more advanced topics such as the pseudoinverse and the singular value decomposition that make it appropriate for a more advanced course as well. As is becoming increasingly the norm, the book begins with the geometry of Euclidean 3-space so that important concepts like linear combination, linear independence and span can be introduced early and in a “real” context. The book reflects the author's background as a pure mathematician — all the major definitions and theorems of basic linear algebra are covered rigorously — but the restriction of vector spaces to Euclidean n-space and linear transformations to matrices, for the most part, and the continual emphasis on the system Ax=b, make the book less abstract and more attractive to the students of today than some others. As the subtitle suggests, however, applications play an important role too. Coding theory and least squares are recurring themes. Other applications include electric circuits, Markov chains, quadratic forms and conic sections, facial recognition and computer graphics.
£93.60
World Scientific Publishing Co Pte Ltd Linear Algebra: Pure & Applied
Book SynopsisThis is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it also includes more advanced topics such as the pseudoinverse and the singular value decomposition that make it appropriate for a more advanced course as well. As is becoming increasingly the norm, the book begins with the geometry of Euclidean 3-space so that important concepts like linear combination, linear independence and span can be introduced early and in a “real” context. The book reflects the author's background as a pure mathematician — all the major definitions and theorems of basic linear algebra are covered rigorously — but the restriction of vector spaces to Euclidean n-space and linear transformations to matrices, for the most part, and the continual emphasis on the system Ax=b, make the book less abstract and more attractive to the students of today than some others. As the subtitle suggests, however, applications play an important role too. Coding theory and least squares are recurring themes. Other applications include electric circuits, Markov chains, quadratic forms and conic sections, facial recognition and computer graphics.Table of ContentsEuclidean n-space; Matrices and Linear Equations; Determinants and Eigenvalues; Vector Spaces; Linear Transformations; Orthogonality; The Spectral Theorem.
£57.00
World Scientific Publishing Co Pte Ltd Bombay Lectures On Highest Weight Representations
Book SynopsisThe first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras — such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations — simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.Table of ContentsDefinition of Positive-Energy Representations of Vir; Complete Reducibility of the Oscillator Representations of Vir; Lie Algebras of Infinite Matrices; Boson - Fermion Correspondence; Schur Polynomials; N-Soliton Solutions; The Kac Determinant Formula; Nonabelian Generalization of Virasoro Operators: The Sugawara Construction; The Weyl - Kac Character Formula and Jacobi - Riemann Theta Functions; Completion of the Proof of the Kac Determinant Formula; Lambda - Bracket of Local Formal Distributions; Completion of U, Restricted Representations and Quantum Fields; Non-Commutative Wick Formula; Conformal Weights; Definition of a Vertex Algebra; Definition of a Representation of a Vertex Algebra; and other lectures.
£76.95
World Scientific Publishing Co Pte Ltd Bombay Lectures On Highest Weight Representations
Book SynopsisThe first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras — such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations — simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.Table of ContentsDefinition of Positive-Energy Representations of Vir; Complete Reducibility of the Oscillator Representations of Vir; Lie Algebras of Infinite Matrices; Boson - Fermion Correspondence; Schur Polynomials; N-Soliton Solutions; The Kac Determinant Formula; Nonabelian Generalization of Virasoro Operators: The Sugawara Construction; The Weyl - Kac Character Formula and Jacobi - Riemann Theta Functions; Completion of the Proof of the Kac Determinant Formula; Lambda - Bracket of Local Formal Distributions; Completion of U, Restricted Representations and Quantum Fields; Non-Commutative Wick Formula; Conformal Weights; Definition of a Vertex Algebra; Definition of a Representation of a Vertex Algebra; and other lectures.
£30.40
