Algebra Books
Springer Verlag, Singapore Recent Progress on the Donaldson–Thomas Theory: Wall-Crossing and Refined Invariants
Book SynopsisThis book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi–Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar–Vafa invariant, which was first proposed by Gopakumar–Vafa in 1998, but its precise mathematical definition has not been available until recently.This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.Trade Review“The book is directed at readers with a solid foundation in algebraic geometry. … the main definitions and theorems are nicely illustrated by examples. … The book will serve as a guide to further reading for those wishing to learn more details about the theory.” (Matthew B. Young, Mathematical Reviews, March, 2023)Table of Contents1Donaldson–Thomas invariants on Calabi–Yau 3-folds.- 2Generalized Donaldson–Thomas invariants.- 3Donaldson–Thomas invariants for quivers with super-potentials.- 4Donaldson–Thomas invariants for Bridgeland semistable objects.- 5Wall-crossing formulas of Donaldson–Thomas invariants.- 6Cohomological Donaldson–Thomas invariants.- 7Gopakumar–Vafa invariants.- 8Some future directions.
£49.49
Springer Verlag, Singapore Rings, Monoids and Module Theory: AUS-ICMS 2020,
Book SynopsisThis book contains select papers on rings, monoids and module theory which are presented at the 3rd International Conference on Mathematics and Statistics (AUS-ICMS 2020) held at the American University of Sharjah, United Arab Emirates, from 6–9 February 2020. This conference was held in honour of the work of the distinguished algebraist Daniel D. Anderson. Many participants and colleagues from around the world felt it appropriate to acknowledge his broad and sweeping contributions to research in algebra by writing an edited volume in his honor. The topics covered are, inevitably, a cross-section of the vast expansion of modern algebra. The book is divided into two sections—surveys and recent research developments—with each section hopefully offering symbiotic utility to the reader. The book contains a balanced mix of survey papers, which will enable expert and non-expert alike to get a good overview of developments across a range of areas of algebra. The book is expected to be of interest to both beginning graduate students and experienced researchers. Table of ContentsDavid F. Anderson, Dan Anderson and his Mathematics.- David F. Anderson, F. GOTTI, Bounded and Finite Factorization Domains.- A.A. ALTIDOR, H.E. BRUCH, J.R. JUETT, Factorization and Irreducibility in Modules.- M. ZAFRULLAH, On *-Potent Domains and *-Homogeneous Ideals.- M. GOTTI, M. M. TIRADOR, On the Set of Molecules of Numerical and Puiseux Monoids.- D. E. DOBBS, Where Some Inert Minimal Ring Extensions of A Commutative Ring Come From, II.- E. Abuosba and M. Ghanem, A Survey on EM Conditions.- David F. Anderson, Some Remarks on the D + M Construction.- Roy O. Quintero Contreras, On a Problem about Lowest Terms Domains Posed.- S. Kabbaj and F. Suwayyid, Regularity and Related properties in Tensor Products of Algebras over a Field.- L. KLINGLER, R. WIEGAND and S. WIEGAND, Tame-Wild Dichotomy for Commutative Noetherian Rings : A Survey.- H. ANDEZ-ESPIET, R.M. ORTIZ-ALBINO, On the Characterization of — Atoms.- D. D. ANDERSON, P. V. DANCHEV, Bounded Periodic Rings.- C. P. MOONEY, On Gracefully and Harmoniously Labeling Zero-Divisor Graphs.- T. ASIR, K. MANO, and M. SUBATHRA, A Survey on Genus of Selected Graphs from Commutative Rings.- DONG-IL LEE, A Computational Approach to Shephard Groups.- M. FARAG and R. P. TUCCI, BZS Near-Rings and Rings.
£125.99
World Scientific Publishing Co Pte Ltd Groups, Combinatorics And Geometry
Book SynopsisOver the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups.This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications.Table of ContentsCurtis-Phan-Tits Theory, C.D. Bennett et al; Derangements in Simple and Primitive Groups, J. Fulman & R. Guralnick; Computing with Matrix Groups, W.M. Kantor & A. Seress; Bases of Primitive Permutation Groups, M.W. Liebeck & A. Shalev; Modular Subgroup Arithmetic, T.W. Muller; Counting Nets in the Monster, S.P. Norton; Overgroups of Finite Quasiprimitive Permutation Groups, C.E. Praeger; Old Groups Can Learn New Tricks, L. Pyber; Structure and Presentations of Lie-Type Groups, F.G. Timmesfeld; Computing in the Monster, R.A. Wilson; and other papers.
£143.10
World Scientific Publishing Co Pte Ltd Representations Of Real And P-adic Groups
Book SynopsisThe Institute for Mathematical Sciences at the National University of Singapore hosted a research program on “Representation Theory of Lie Groups” from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadić from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pandǽić from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.Table of ContentsThree Uncertainty Principles for an Abelian Locally Compact Group (T Przebinda); Lectures on Representations of p-Adic Groups (G Savin); Lectures on Harmonic Analysis for Reductive p-Adic Groups (S DeBacker); On Classification of Some Classes of Irreducible Representations of Classical Groups (M Tadic); Dirac Operators in Representation Theory (J S Huang & P Pand ic); On Multiplicity-Free Actions (C Benson & G Ratcliff); Multiplicity-Free Spaces and Schur-Weyl-Howe Duality (R Goodman)
£108.00
World Scientific Publishing Co Pte Ltd Function Field Arithmetic
Book SynopsisThis book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
£135.00
World Scientific Publishing Co Pte Ltd Geometric Linear Algebra (Volume 1)
Book SynopsisThis accessible book for beginners uses intuitive geometric concepts to create abstract algebraic theory with a special emphasis on geometric characterizations. The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.Table of ContentsThe Affine and Linear Structures of - 1, - 2 and - 3: The One-Dimensional Real Vector Space - (or - 1); The Two-Dimensional Real Vector Space - 2; The Three-Dimensional Real Vector Space - 3
£72.20
World Scientific Publishing Co Pte Ltd Numerical Solution Of Systems Of Polynomials
Book SynopsisWritten by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.Trade Review"The text is written in a very smooth and intelligent form, yielding a readable book whose contents are accessible to a wide class of readers, even to undergraduate students, provided that they accept that some delicate points of some of the proofs could be omitted. Its readability and fast access to the core of the book makes it recommendable as a pleasant read." Mathematical Reviews "This is an excellent book on numerical solutions of polynomials systems for engineers, scientists and numerical analysts. As pioneers of the field of numerical algebraic geometry, the authors have provided a comprehensive summary of ideas, methods, problems of numerical algebraic geometry and applications to solving polynomial systems. Through the book readers will experience the authors' original ideas, contributions and their techniques in handling practical problems ... Many interesting examples from engineering and science have been used throughout the book. Also the exercises are well designed in line with the content, along with the algorithms, sample programs in Matlab and author's own software 'HOMLAB' for polynomial continuation. This is a remarkable book that I recommend to engineers, scientists, researchers, professionals and students, and particularly numerical analysts who will benefit from the rapid development of numerical algebraic geometry." Zentralblatt MATHTable of ContentsBackground: Polynomial Systems; Homotopy Continuation; Projective Spaces; Probability One; Polynomials of One Variable; Other Methods; Isolated Solutions: Coefficient-Parameter Homotopy; Polynomial Structures; Case Studies; Endpoint Estimation; Checking; Positive Dimensional Solution Sets: Some Concepts from Algebraic Geometry; Basic Numerical Algebraic Geometry; Cascading Through Embedded Systems; The Numerical Irreducible Decomposition; Intersection of Algebraic Sets.
£121.50
World Scientific Publishing Co Pte Ltd Linear Algebra: Examples And Applications
Book SynopsisThis short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. It is intended for students with various interests in mathematics, as well as established scientists seeking to refresh their basic mathematical culture.The book is also a good introduction to functional analysis and quantum theory since it discusses the general principles of linear algebra without finiteness assumptions.Table of Contents# Linear Systems: Elimination Method # Vector Spaces # Matrix Multiplication # Linear Maps # The Rank Theorem # Eigenvectors and Eigenvalues # Inner-Product Spaces # Symmetric Operators # Duality # Determinants # Applications # Normal Operators
£85.50
World Scientific Publishing Co Pte Ltd Linear Algebra: Examples And Applications
Book SynopsisThis short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. It is intended for students with various interests in mathematics, as well as established scientists seeking to refresh their basic mathematical culture.The book is also a good introduction to functional analysis and quantum theory since it discusses the general principles of linear algebra without finiteness assumptions.Table of Contents# Linear Systems: Elimination Method # Vector Spaces # Matrix Multiplication # Linear Maps # The Rank Theorem # Eigenvectors and Eigenvalues # Inner-Product Spaces # Symmetric Operators # Duality # Determinants # Applications # Normal Operators
£45.60
World Scientific Publishing Co Pte Ltd Automorphic Representations Of Low Rank Groups
Book SynopsisThe area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings”. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E : F] = 2.The book develops the technique of comparison of twisted and stabilized trace formulae and considers the “Fundamental Lemma” on orbital integrals of spherical functions. Comparison of trace formulae is simplified using “regular” functions and the “lifting” is stated and proved by means of character relations.This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent.There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne's (proven) conjecture on the fixed point formula.Table of ContentsOn the Symmetric Square Lifting: Functoriality and Norms; Orbital Integrals; Twisted Trace Formula; Total Global Comparison; Applications of a Trace Formula; Computation of a Twisted Character; Automorphic Representations of the Unitary Group U(3, E/F): Local Theory; Trace Formula; Liftings and Packets; Zeta Functions of Shimura Varieties of U(3): Automorphic Representations; Local Terms; Real Representations; Galois Representations.
£144.00
World Scientific Publishing Co Pte Ltd Lectures On Algebra - Volume 1
Book SynopsisThis book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling.The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.Trade Review"I cannot imagine that any mathematician would read even a few pages of this book without learning something new or seeing a new connection or gaining an insight into something that they thought they already knew. And between those insights and his writing, you will soon find yourself captivated by Abhyankar as well. I recommend that anyone with an interest in algebra find a copy of this book and flip through it."MAA Online Book Review"What is the book good for? The book covers a lot of material for several courses like basic commutative algebra, commutative algebra or algebraic geometry, as well as additional material for basic courses in algebra. It might be used as an encyclopedia for commutative ring theory with a view towards algebraic geometry ... it might be used as a source for inspiration for additional, interesting themes for courses as mentioned above ... It might be recommended to anybody who is willing to see the fascinating, concrete as well as abstract development of algebra during the last centuries, including its applications to algebraic geometry and its potential ... It is a consequence of the author's masterpiece to bring together so many aspects of commutative ring theory. All together, it is not a classical textbook in the style 'groups, rings, fields'. It is a unique, original exposition full of valuable insights."Mathematical ReviewsTable of ContentsQuadratic Equations (Rings); Curves and Surfaces (Fields); Tangents and Polars (Valuations); Varieties and Models (Ideals); Projective Varieties (Modules); Pause and Refresh (Groups).
£80.75
World Scientific Publishing Co Pte Ltd Course In Linear Algebra With Applications, A
Book SynopsisThis is the second edition of the best-selling introduction to linear algebra. Presupposing no knowledge beyond calculus, it provides a thorough treatment of all the basic concepts, such as vector space, linear transformation and inner product. The concept of a quotient space is introduced and related to solutions of linear system of equations, and a simplified treatment of Jordan normal form is given.Numerous applications of linear algebra are described, including systems of linear recurrence relations, systems of linear differential equations, Markov processes, and the Method of Least Squares. An entirely new chapter on linear programing introduces the reader to the simplex algorithm with emphasis on understanding the theory behind it.The book is addressed to students who wish to learn linear algebra, as well as to professionals who need to use the methods of the subject in their own fields.Table of ContentsMatrix Algebra; Systems of Linear Equations; Determinants; Introduction to Vector Spaces; Basis and Dimension; Linear Transformations; Orthogonality in Vector Spaces; Eigenvectors and Eigenvalues; More Advanced Topics; Linear Programing.
£108.00
World Scientific Publishing Co Pte Ltd Problems And Solutions In Introductory And
Book SynopsisAs an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students. The coverage includes systems of linear equations, linear differential equations, functions of matrices and the Kronecker product. Many of the problems are related to applications in areas such as group theory, Lie algebra theory and graph theory. Thus, physics and engineering students will also benefit from the book. Exercises for matrix-valued differential forms are also included.Table of ContentsBasic Operations; Linear Equations; Determinants and Traces; Eigenvalues and Eigenvectors; Commutators and Anticommutators; Decomposition of Matrices; Functions of Matrices; Linear Differential Equations; Kronecker Product; Norms and Scalar Products; Groups and Matrices; Lie Algebras and Matrices; Graphs and Matrices.
£34.20
World Scientific Publishing Co Pte Ltd Basic Lie Theory
Book SynopsisThis volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or on lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped.The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.Table of ContentsLie Groups and Lie Algebras: Introduction; Lie Groups; Haar Measure and its Applications; Elements of the Theory of Lie Algebras; The Structure of Compact Connected Lie Groups; Representations of Compact Lie Groups; Symmetric Spaces of Non-Compact Type; Semisimple Lie Algebras and Lie Groups; Lattices in Lie Groups; Density Results for Co-Finite Volume Subgroups.
£76.95
World Scientific Publishing Co Pte Ltd Geometric Linear Algebra (Volume 2)
Book SynopsisThis accessible book for beginners uses intuitive geometric concepts to create abstract algebraic theory with a special emphasis on geometric characterizations. The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.Table of ContentsThe Euclidean Structures of R1, R2 and R3: The Euclidean Plane R2; The Euclidean Space R3.
£111.60
World Scientific Publishing Co Pte Ltd Introduction To Non-linear Algebra
Book SynopsisThis unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.Table of ContentsSolving Equations. Resultants; Evaluation of Resultants and Their Properties; Discriminants of Polylinear Forms; Examples of Resultants and Discriminants; Eigenspaces, Eigenvalues and Resultants; Iterated Maps; Potential Applications.
£65.55
World Scientific Publishing Co Pte Ltd Continuous Symmetries, Lie Algebras, Differential
Book SynopsisThis textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang-Mills theory and string theory.Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation.Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang-Mills equation, and discrete Painlevé equations.Table of ContentsGroups; Lie Groups and Lie Transformation Groups; Infinitesimal Transformations; Lie Algebras; Introductory Examples; Differential Forms and Tensor Fields; Lie Derivative and Invariance; Invariance of Differential Equations; Lie-Backlund Vector Fields; Differential Equation for a Given Lie Algebra; A List of Lie Symmetry Vector Fields; Recursion Operators; Backlund Transformations; Lax Representations; Conservation Laws; Symmetries and Painleve Test; Lie Algebra Valued Differential Forms; Bose Operators and Lie Algebras; Maps and Invariants; Computer Algebra; Differential Manifolds.
£95.40
World Scientific Publishing Co Pte Ltd Ring Theory 2007 - Proceedings Of The Fifth
Book SynopsisRing theory has been developing through the interaction between the investigation of its own algebraic structure and its application to many areas of mathematics, computer science, and physics among others.This volume consists of a collection of survey articles by invited speakers and original articles refereed by world experts that was presented at the fifth China-Japan-Korea International Symposium. The survey articles provide some ideas of the application as well as an excellent overview of the various areas in ring theory. The original articles exhibit new ideas, tools and techniques needed for successful research investigation in ring theory and show the trend of current research.The articles cover all of the most important areas in ring theory, making this volume a useful resource book for researchers in mathematics — both beginners and advanced experts.Table of ContentsQuasi-Baer Rings; Endomorphism Rings; Torsion-Free Modules; Graded Algebras; Finitistic Dimensions; Projective Modules; ArtinA-Schelter Regular Algebras; Noncommutative Valuation Rings; Noncommutative Algebraic Geometry; AuslanderA-Gorenstein Rings; QF Rings; Hochschild Cohomology; Jordan Derivations in Rings; Harada Rings; Quaternoin Algebras; Representation Theory; Rings of Quotients; Lie Algebras; Skew Polynomial Rings; Hopf Algebras.
£110.70
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 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.
£37.05
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.
£89.10
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.
£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.
£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 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.
£69.35
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 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
Springer Verlag, Singapore Algebra 3: Homological Algebra and Its
Book SynopsisThis book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory. The book will be of value to graduate and higher undergraduate students specializing in any branch of mathematics. The author has tried to make the book self-contained by introducing relevant concepts and results required. Prerequisite knowledge of the basics of algebra, linear algebra, topology, and calculus of several variables will be useful.Trade Review“This is an excellent book on Homological Algebra. All topics dealt here are presented in a very systematic way. It is an ideal handbook for any person desirous of pursuing research in Homological Algebra. … At the end of each section of each chapter an exhaustive list of exercises is given.” (Veereshwar A. Hiremath, zbMATH 1474.01001, 2021)Table of ContentsChapter 1. Homological Algebra 1.- Chapter 2. Homological Algebra 2, Derived Functions.- Chapter 3. Homological Algebra 3, Examples and Applications.- Chapter 4. Sheaf Co-homology and Applications.
£35.99
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 Descent Map From Automorphic Representations Of
Book SynopsisThis book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.Table of ContentsCertain Residual Eisenstein Series; Fourier Coefficients of Gelfand-Graev Type and Fourier-Jacobi Type; Jacquet Modules Corresponding to Gelfand-Graev Models; Jacquet Modules Corresponding to Fourier-Jacobi Models; The Tower Property; Non-Vanishing of the Descent; On the Global Genericity of the Descent and Rankin-Selberg Integrals; The Descent and Langlands Functoriality from Classical Groups to GL(n); Applications of the Descent (Generalized Endoscopy, Base Change).
£99.00
World Scientific Publishing Co Pte Ltd Shape Of Algebra In The Mirrors Of Mathematics,
Book SynopsisThe Shape of Algebra in the Mirrors of Mathematics is a unique text aiming to explain some elements of modern mathematics and to show its flavor and unity. It is neither a standard textbook nor a tour of algebra for a casual reader. Rather, it is an attempt to share authors' mathematical experiences and philosophy with readers who have more than a passing interest in mathematics, but only a traditional exposure to High School Algebra and some elements of Calculus. The book gives the readers a sense of visual nature of significant part of mathematics.The reader becomes an owner of and a researcher in VisuMatica, a virtual math laboratory. It is an original and comprehensive PC software package (a brainchild of the second author) that will enable the reader to experience mathematics both as a human intellectual endeavor and as an experimental science. Although it is possible to read and appreciate the book without ever visiting the VisuMatica lab, those who engage with the interactive demos found in the lab will greatly advance their understanding of the text. The book seeks to encourage an interactive, investigative style of learning that can promote the habits of mind characteristic of modern mathematical thinking.An outline of the topics that are discussed may read like a list of graduate courses: Abstract Algebra, Topology, Singularity Theory, Complex Analysis, and Number Theory. However, they are presented from an intuitive perspective that uses primarily visual models and concepts. Although the main subject is polynomials and polynomial equations, the true story line is the interplay between basic ideas from algebra, geometry, analysis and topology.The Shape of Algebra might serve as a text for an “appreciation” course in modern mathematics designed for non-mathematics majors or for students who are considering majoring in mathematics or related disciplines. The authors' goal is to present the reader with a fresh viewpoint on the sense and flavor of mathematics. The subject is often presented in a fashion that students find stale and uncompelling. The book's emphasis, in contrast, is on how a modern practitioner thinks about and works within the discipline.The book aims to attract students of all ages, particularly including professional mathematicians interested in pedagogy. In part, The Shape of Algebra is directed at secondary and college teachers and students who want to expand their horizons in the field and to find both a fresh presentation of familiar concepts and, perhaps, some unexpected results. Many of the topics and demos are self-contained and can be used individually to enhance traditional courses. Several of the ideas and materials developed in the book have been tested in high school and college classrooms. The book will enable readers to approach its content on three levels: the first level requires only some fluency with routine algebraic manipulations; the second also presumes familiarity with the notions of derivatives, and the third uses some basic concepts of multivariable calculus and linear algebra. All three levels are clearly marked in the text, and allow for a smooth reading enhanced by virtual experiments.Table of ContentsIntroduction - Maps upon Maps; Maps, Models, and the Coordinate Plane; The Universe of Quadratic Polynomials; The Complex Numbers; The Geometry of Complex Linear Polynomial Maps; Complex Polynomial Maps, Closed Plane Curves and their Invariants; Experimenting with the Geometry of Complex Polynomial Maps of Degrees Two and Three; The Old Art of Solving Cubic Equations and the New Science; Complex Polynomial Maps of Higher Degrees and the Fundamental Theorem of Algebra; Local and Global Geometry of Complex Polynomial Maps; The Fundamental Theorem and the Complex Viete Map; Appendices: Estimating Polynomial Expressions; More about the Taylor Formula for Polynomials; The Geometry of Discriminants; Line Integrals and an Analytical Proof of the Loop Theorem; Deformations of Complex Polynomials and the Braids.
£50.35
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 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 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.
£90.00
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
