Algebra Books

Book Synopsis"Revised and expanded edition of Matrix mathematics, retitled Scalar, vector, and matrix mathematics"--Preface.Trade ReviewPraise for the previous editions: "When a matrix question is thrown my way, I will now refer my correspondents ... to Bernstein's handbook."--Philip J. Davis, SIAM News Praise for the previous editions: "The amount of material that is covered is quite impressive and well structured... I highly recommend the book as a source for retrieving or verifying matrix results that one would otherwise have to search for in the extensive literature on matrix theory."--Paul Van Dooren, IEEE Control Systems Magazine Praise for the previous editions: "The author was very successful in collecting the enormous amount of results in matrix theory in a single source... A beautiful work and an admirable performance!"--Monatshefte fur Mathematik Praise for the previous editions: "A remarkable source of matrix results. I will put it on the shelf near to my desk so that I have quick access to it. The book is an impressive accomplishment."--Helmut Lutkepohl, Image Praise for the previous editions: "A well-organized treasure trove of information for anyone interested in matrices and their applications."--Henry Ricardo, MAA Reviews

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Book SynopsisA unique and effective way to learn Algebraâupdated with the latest instruction and reviewMust Know High School Algebra provides a fresh approach to learning. As part of our Must Know series, this new edition makes sure what you really need to know is clear up-front. Rather than starting with goals to be met, chapters begin by telling you the most important concepts about the topic at handâand then show you exactly how these concepts help you accomplish your goals.Written by excerpt algebra educators, Must Know High School Algebra, Second Edition provides updated lesson content and useful examples to help clarify each topic. Every chapter closes with reinforcing exercises to get you the practice you need to gain confidence. New features to this edition focus on extra support and helping you avoid common mistakes. In the end, you get everything you need to build your algebra skills quickly and painlessly.Features:Mo

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Book SynopsisRich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.Trade Review“The aim of this book is to survey the basic notions and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. … The author takes care in writing full proofs throughout the book and he shows also ways of possible applications. The text contains a wealth material and should serve as a textbook for readers interested in this field.” (Danica Jakubíková-Studenovská, zbMATH 1317.08001, 2015)Table of Contents1 About the course, and these notes.- Part I: Motivation and Examples.- 2 Making Some Things Precise.- 3 Free Groups.- 4 A Cook's Tour.- Part II: Basic Tools and Concepts.- 5 Ordered Sets, Induction, and the Axiom of Choice.- 6 Lattices, Closure Operators, and Galois Connections.- 7 Categories and Functors.- 8 Universal Constructions.- 9 Varieties of Algebras.- Part III: More on Adjunctions.- 10 Algebras, Coalgebras, and Adjunctions.- References.- List of Exercises.- Symbol Index.- Word and Phrase Index.

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Book SynopsisFinally a self-contained, one volume, graduate-level algebra text that is readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course contents. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.Trade ReviewFrom the book reviews:“This is a text for a first-year graduate course in abstract algebra. It covers all the standard topics and has more than enough material for a year course.” (Allen Stenger, MAA Reviews, September, 2014)Thomas W. HungerfordAlgebra"An excellent text from which to teach the beginning graduate survey course in algebra and I would recommend it to anyone considering a text for such a course."—LINEAR AND MULTILINEAR ALGEBRATable of ContentsIntroduction. Prerequisites and Preliminaries; 1. Groups; 2. The Structure of Groups; 3. Rings; 4. Modules; 5. Fields and Galois Theory; 6. The Structure of Fields; 7. Linear Algebra; 8. Commutative Rings and Modules; 9. The Structure of Rings; 10. Categories; List of Symbols; Bibliography; Index

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Combinatorics on words appears in many different areas of mathematics and theoretical computer science. With background material, full proofs whenever possible, and a discussion of further developments, this 2002 book is both a comprehensive introduction to the subject and a valuable reference source for researchers.

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Book SynopsisCONTEMPORARY ABSTRACT ALGEBRA, ELEVENTH EDITION is intended for a course whose main purpose is to enable students to do computations and write proofs. This text stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject which is currently being used by working physicists, chemists, and computer scientists.For more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.The author presents the concepts and methodologies of used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of gener

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisOver the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.Trade Review'The diagrams, over 60 in number and for the most part highly intricate computer-generated graphics, will leave the reader craving for more.' Tushar Das, MAA Reviews'With its plenitude of exercises, both closed- and open-ended, and its extensive index and bibliography, this book merits what a reviewer wrote of the first edition: its 'topic's central importance and the author's singular viewpoint earn this book a place in all academic libraries.' Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.' F. E. J. Linton, CHOICE'… the book provides an excellent overview of the developments of recent decades in the theory of hyperbolic 3-manifolds.' Thilo Kuessner, Mathematical ReviewsTable of ContentsList of illustrations; Preface; 1. Hyperbolic space and its isometries; 2. Discrete groups; 3. Properties of hyperbolic manifolds; 4. Algebraic and geometric convergence; 5. Deformation spaces and the ends of manifolds; 6. Hyperbolization; 7. Line geometry; 8. Right hexagons and hyperbolic trigonometry; Bibliography; Index.

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Book SynopsisThis balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework, allowing readers to understand second-order and higher-order matrix analysis in a completely new light. Alongside the core subjects in matrix analysis, such as singular value analysis, the solution of matrix equations and eigenanalysis, the author introduces new applications and perspectives that are unique to this book. The very topical subjects of gradient analysis and optimization play a central role here. Also included are subspace analysis, projection analysis and tensor analysis, subjects which are often neglected in other books. Having provided a solid foundation to the subject, the author goes on to place particular emphasis on the many applications matrix analysis has in science and engineering, making this book suitable for scientists, engineers and graduate students alike.Trade Review'Matrix analysis is the engine room of scientific computing since, inevitably, most computational problems are reduced to linear algebra. Xian-Da Zhang's monograph presents a thoroughly modern introduction to this important subject in a form suitable for its many users. Without taking liberties with mathematical content, the text privileges an algorithmic approach and ventures into new and important areas, e.g. tensor analysis. This is a valuable addition to any applied mathematician's bookshelf.' Arieh Iserles, University of Cambridge'This book provides various new topics on Matrix Analysis and Applications, which are not covered by some popular books on matrix analysis and computation. The text is well written, easy to be understood. There are several classical books on matrix analysis and computation on my bookshelf. But I will be happy to have this book on my bookshelf too.' Liqun Qi, Hong Kong Polytechnic UniversityTable of ContentsPreface; Notation; List of abbreviations; List of algorithms; Part I. Matrix Algebra: 1. Introduction to matrix algebra; 2. Special matrices; 3. Matrix differential; Part II. Matrix Analysis: 4. Gradient analysis and optimization; 5. Singular value analysis; 6. Solving matrix equations; 7. Eigenanalysis; 8. Subspace analysis and tracking; 9. Projection analysis; Part III. Higher-Order Matrix Analysis: 10. Tensor analysis; References; Index.

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Book SynopsisThis is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.Trade Review'This 2-volume book is a very welcome addition to the existing literature in modular representation theory. It contains a wealth of material much of which is here presented in textbook form for the first time. It gives an excellent overview of the state of the art in this fascinating subject and also of the many challenging and fundamental open problems. It is well written and will certainly become a standard reference.' Burkhard Kűlshammer, MathSciNetTable of ContentsIntroduction; 6. Blocks and source algebras; 7. Modules over finite p-groups; 8. Local structure; 9. Isometries and bimodules; 10. Structural results in block theory; 11. Blocks with cyclic defect groups; 12. Blocks with Klein four defect groups; Appendix; References; Index.

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Book SynopsisStarting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.Table of ContentsPreface; 0. Preliminaries in Operator Theory; 1. Numerical Range; 2. Numerical Ranges of Special Operators; 3. Numerical Contraction; 4. Algebraic and Essential Numerical Ranges 5. Numerical Range and Dilation; 6. Numerical Range of Finite Matrix; 7. Numerical Range of Sn-Matrix; 8. Generalized Numerical Ranges; Appendix: Convex Set.

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Book SynopsisOn its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the CurtisAlvis duality map and Mackey''s theorem and the results that can be deduced from it, before moving on to a discussion of DeligneLusztig induction and Lusztig''s Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.Trade Review'… a useful resource for beginning graduate students in algebra as well as seasoned researchers.' Mathematical Reviews Clippings'… clearly written; there are useful examples, motivational comments, and exercises scattered throughout the text.' Mark Hunacek, The Mathematical GazetteTable of Contents1. Basic results on algebraic groups; 2. Structure theorems for reductive groups; 3. (B, N)-pairs; parabolic, Levi, and reductive subgroups; centralisers of semi-simple elements; 4. Rationality, the Frobenius endomorphism, the Lang–Steinberg theorem; 5. Harish–Chandra theory; 6. Iwahori–Hecke algebras; 7. The duality functor and the Steinberg character; 8. l-adic cohomology; 9. Deligne–Lusztig induction; the Mackey formula; 10. The character formula and other results on Deligne–Lusztig induction; 11. Geometric conjugacy and Lusztig series; 12. Regular elements; Gelfand–Graev representations; regular and semi-simple characters; 13. Green functions; 14. The decomposition of Deligne–Lusztig characters; References; Index.

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Book SynopsisBased on the author''s university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck''s famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.Trade Review'This is a very rich and detailed monograph on an enormously important subject. It is written in the crystal clear and elegant style that is the hallmark of its author, and it offers a lot of information to specialists and novices alike. The book will certainly become an authoritative guide.' Dirk Werner, London Mathematical Society Student Texts'This book is jam packed with information, and should be an invaluable guide to anyone interested in these ideas … For the complete picture and the recent advances, Pisier's book is the place to go.' Bulletin of the American Mathematical SocietyTable of ContentsIntroduction; 1. Completely bounded and completely positive maps: basics; 2. Completely bounded and completely positive maps: a tool kit; 3. C*-algebras of discrete groups; 4. C*-tensor products; 5. Multiplicative domains of c.p. maps; 6. Decomposable maps; 7. Tensorizing maps and functorial properties; 8. Biduals, injective von Neumann algebras and C*-norms; 9. Nuclear pairs, WEP, LLP and QWEP; 10. Exactness and nuclearity; 11. Traces and ultraproducts; 12. The Connes embedding problem; 13. Kirchberg's conjecture; 14. Equivalence of the two main questions; 15. Equivalence with finite representability conjecture; 16. Equivalence with Tsirelson's problem; 17. Property (T) and residually finite groups. Thom's example; 18. The WEP does not imply the LLP; 19. Other proofs that C(n) < n. Quantum expanders; 20. Local embeddability into ${\mathscr{C}}$ and non-separability of $(OS_n, d_{cb})$; 21. WEP as an extension property; 22. Complex interpolation and maximal tensor product; 23. Haagerup's characterizations of the WEP; 24. Full crossed products and failure of WEP for $\mathscr{B}\otimes_{\min}\mathscr{B}$; 25. Open problems; Appendix. Miscellaneous background; References; Index.

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Book SynopsisThe 6th Edition of Intermediate Algebra continues the Miller/O''Neill/Hyde author team's approach in addressing the needs of developmental level students to help them get better results. Content updates include new end-of-section activities, prerequisite review exercises, and new study skills videos. This new edition is available in ALEKS 360. In a single platform, ALEKS provides a balance of adaptive practice for skill mastery and homework, tests, and quizzes for application and assessment so that you can create the assignments your students need to have the best outcome in your course. In addition to content updates to the text, we are continuously adding new features to ALEKS 360including new video assignments, an enhanced gradebook experience, end-of-chapter questions aligned to the text, and more.Table of ContentsReference: Review of Basic Algebraic ConceptsChapter 1: Linear Equations and Inequalities in One VariableChapter 2: Linear Equations in Two Variables and FunctionsChapter 3: Systems of Linear Equations and InequalitiesChapter 4: PolynomialsChapter 5: Rational Expressions and Rational EquationsChapter 6: Radicals and Complex NumbersChapter 7: Quadratic Equations and FunctionsChapter 8: Exponential and Logarithmic Functions and ApplicationsChapter 9: Conic SectionsChapter 10: Binomial Expansions, Sequences, and SeriesChapter 11 (Online): Transformations, Piecewise-Defined Functions, and Probability

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Book SynopsisThe 6th Edition of Beginning Algebra continues the Miller/O''Neill/Hyde author team's approach in addressing the needs of developmental level students to help them get better results. Content updates include new end-of-section activities, prerequisite review exercises, and new study skills videos. This new edition is available in ALEKS 360. In a single platform, ALEKS provides a balance of adaptive practice for skill mastery and homework, tests, and quizzes for application and assessment so that you can create the assignments your students need to have the best outcome in your course. In addition to content updates to the text, we are continuously adding new features to ALEKS 360including new video assignments, an enhanced gradebook experience, end-of-chapter questions aligned to the text, and more.Table of ContentsChapter 1: The Set of Real NumbersChapter 2: Linear Equations and InequalitiesChapter 3: Graphing Linear Equations in Two VariablesChapter 4: Systems of Linear Equations in Two VariablesChapter 5: Polynomials and Properties of ExponentsChapter 6: Factoring PolynomialsChapter 7: Rational Expressions and EquationsChapter 8: RadicalsChapter 9: Quadratic Equations, Complex Numbers, and Functions

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Book SynopsisThe 6th Edition of Beginning & Intermediate Algebra continues the Miller/O''Neill/Hyde author team's approach in addressing the needs of developmental level students to help them get better results. Content updates include new end-of-section activities, prerequisite review exercises, and new study skills videos.This new edition is available in ALEKS 360. In a single platform, ALEKS provides a balance of adaptive practice for skill mastery and homework, tests, and quizzes for application and assessment so that you can create the assignments your students need to have the best outcome in your course. In addition to content updates to the text, we are continuously adding new features to ALEKS 360including new video assignments, an enhanced gradebook experience, end-of-chapter questions aligned to the text, and more.Table of ContentsChapter 1: Set of Real NumbersChapter 2: Linear Equations and InequalitiesChapter 3: Graphing Linear Equations in Two VariablesChapter 4: Systems of Linear Equations in Two VariablesChapter 5: Polynomials and Properties of ExponentsChapter 6: Factoring PolynomialsChapter 7: Rational Expressions and EquationsChapter 8: Relations and FunctionsChapter 9: More Equations and InequalitiesChapter 10: Radicals and Complex NumbersChapter 11: Quadratic Equations and FunctionsChapter 12: Exponential and Logarithmic Functions and ApplicationsChapter 13: Conic SectionsChapter 14: Binomial Expansions, Sequences, and SeriesChapter 15 (Online): Transformations, Piecewise-Defined Functions, and Probability

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Book SynopsisMath for Business & Finance: An Algebraic Approach provides modern examples for students to understand business mathematics and make connections with real-world applications. The course covers mathematical concepts from an algebraic approach, combined with Business applications. Every chapter is devoted to a Personal Finance theme, with topics that include Payroll and the Cost of Purchasing a Home. There is also extensive integration of scientific calculator notation, and also has the Wall Street Journal and Kiplinger news clips that have been widely popular in Jeffrey Slater''s other two Business Math texts. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, and how they need it, so that your class time is more engaging and effective. Table of ContentsCHAPTER 1: Problem Solving with Math CHAPTER 2: Fractions CHAPTER 3: Percents and Their Applications Video Case: Project Management at Six Flags, New Jersey CHAPTER 4: Solving for the Unknown CHAPTER 5: Business Statistics CHAPTER 6: Banking and Budgeting CHAPTER 7: Payroll and Income Tax CHAPTER 8: Sales, Excise, and Property Taxes Video Case: EDP Renewables CHAPTER 9: Risk Management CHAPTER 10: Installment Buying and Revolving Charge Credit Cards CHAPTER 11: Discounts: Trade and Cash Video Case: Recycling at Subaru of Indiana Automotive CHAPTER 12: Markups and Markdowns: Perishables and Breakeven Analysis Video Case: Noodles & Company CHAPTER 13: How to Read, Analyze, and Interpret Financial Reports Video Case: Buycostumes.com CHAPTER 14: Depreciation CHAPTER 15: Inventory and Overhead CHAPTER 16: Simple Interest CHAPTER 17: Promissory Notes, Simple Discount Notes, and the Discount Process CHAPTER 18: The Cost of Home Ownership CHAPTER 19: Compound Interest and Present Value CHAPTER 20: Annuities and Sinking Funds Video Case: DHL Global Delivery Cumulative Review: A Word Problem Approach CHAPTER 21: Stocks, Bonds, and Mutual Funds APPENDIX A: Additional Homework by Learning Unit APPENDIX B: Worked-Out Solutions to Extra Practice Quizzes and You Try It Problems APPENDIX C: Check Figures APPENDIX D: Calculator Basics and the Metric System

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Book SynopsisTake the mystery out of basic math with the latest edition of BarCharts' best-selling Math Review QuickStudy guide. With updated content and an additional panel of information, Math Review includes hard-to-remember formulas and properties, along with numerous examples and illustrations to improve understanding. This comprehensive math guide will assist you way beyond your high school and college years.

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Book SynopsisThis book focuses on the study of several properties of Banach spaces applied to diverse problems in functional and numerical analysis. Many problems in science, engineering and other disciplines can be expressed in the form of equations, inequalities or systems of equations using mathematical modelling. In particular, a large number of these problems can be solved using these spaces. A great multitude of examples showing the theoretical application developed appears throughout the work. Researchers and practitioners will find this book very useful as a source book, utilize its methods and also use it as a classroom text for a senior undergraduate or graduate course. It is certainly an excellent must read book.Table of ContentsPrefaceRight Complex Caputo Fractional InequalitiesMixed Complex Fractional InequalitiesAdvanced Complex Fractional Ostrowski InequalitiesImproved Qualitative Analysis for Newtonlike Methods with ROrder of Convergence at Least Three in Banach SpacesDevelopments on the Convergence Region of Newtonlike Methods with Generalized Inverses in Banach SpacesModified NewtonType Compositions for Solving Equations in Banach SpacesBall Convergence for Optimal Derivative Free MethodsBall Convergence for a Derivative Free Method with MemoryWeaker Convergence Conditions of an Iterative Method for Nonlinear IllPosed EquationsBall Convergence Theorem for a Fifth Order Method in Banach SpacesExtended Convergence of KingWernerlike Methods without DerivativesOn an Eighth Order SteffensenType Solver Free of DerivativesLocal Convergence of Osadas Method for Finding Zeros with MultiplicityExpanding the Applicability of an EighthOrder Method in Banach Space under Weak ConditionsLocal Convergence for Three Step Eighth Order Method under Weak ConditionsBall Convergence for a ThreeStep One Parameter Efficient Method in Banach Space under Generalized ConditionsOn the Convergence of NewtonMoser Method from Data at One PointApproximating Inverse Operators by a FourthOrder Iterative MethodInitial Value Problems in Clifford Analysis Using Associated SpacesComputational Approach of Initial Value Problems in Clifford Analysis Using Associated SpacesAsymmetric Convexity and Smoothness: Quantitative Lyapunov Theorems, Lozanovskii Factorisation, Walsh Chaos and Convex DualityCopies of Sequence Spaces and Basic Properties of Anisotropic Function SpacesInterpolation and Bounded Extension of HӧlderLipschitz Mappings between Function, NonCommutative and Other Banach SpacesDifferential Equations with a Small Parameter in a Banach SpaceRole of HansonAntczakType V Invex Functions in Sufficient Efficiency Conditions for Semiinfinite Multiobjective Fractional ProgrammingIndex.

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Book SynopsisLinear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. Systems of linear equations with several unknowns are naturally represented using the formalism of matrices and vectors. So we arrive at the matrix algebra, etc. Linear algebra is central to almost all areas of mathematics. Many ideas and methods of linear algebra were generalised to abstract algebra. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Linear algebra is also used in most sciences and engineering areas because it allows for the modelling of many natural phenomena, and efficiently computes with such models. ''Hot Topics in Linear Algebra'' presents original studies in some areas of the leading edge of linear algebra. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed herein include recent advances in analysis of various dynamical systems based on the Gradient Neural Network; Cramer's rules for quaternion generalized Sylvester-type matrix equations by using noncommutative row-column determinants; matrix algorithms for finding the generalized bisymmetric solution pair of general coupled Sylvester-type matrix equations; explicit solution formulas of some systems of mixed generalised Sylvester-type quaternion matrix equations; new approaches to studying the properties of Hessenberg matrices by using triangular tables and their functions; researching of polynomial matrices over a field with respect to semi-scalar equivalence; mathematical modelling problems in chemistry with applying mixing problems, which the associated MP-matrices; and some visual apps, designed in Scilab, for the learning of different topics of linear algebra.Table of ContentsPreface; Computing Generalized Inverses Using Gradient-Based Dynamical Systems; Cramers Rules for Sylvester-Type Matrix Equations; BICR Algorithm for Computing Generalized Bisymmetric Solutions of General Coupled Matrix Equations; System of Mixed Generalized Sylvester-Type Quaternion Matrix Equations; Hessenberg Matrices: Their Properties and Some Applications; Equivalence of Polynomial Matrices over a Field; Matrices in Chemical Problems Modeled Using Directed Graphs and Multigraphs; Engaging Students in the Learning of Linear Algebra; Index.

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Book SynopsisElementary Linear Algebra

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Book SynopsisLinear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalised in operator theory. It has extensive applications in the natural sciences and the social sciences, since non-linear models can often be approximated by linear ones.

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Book SynopsisThis book presents and discusses new developments in the study of evolution equations. Topics discussed include global attractors for semi-linear parabolic equations with delays; exact controllability for the vibrating plate equation in a non smooth domain; weighted pseudo almost automorphic solutions for some partial functional differential equations in fading memory spaces; periodic solutions to the non-linear parabolic equation; and infinite-time admissibility of observation operators for volterra systems.

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Book SynopsisThis book presents original studies on the leading edge of linear algebra. Each chapter has been carefully selected in an attempt to present substantial research results across a broad spectrum. The main goal of Chapter One is to define and investigate the restricted generalized inverses corresponding to minimization of constrained quadratic form. As stated in Chapter Two, in systems and control theory, Linear Time Invariant (LTI) descriptor (Differential-Algebraic) systems are intimately related to the matrix pencil theory. A review of the most interesting properties of the Projective Equivalence and the Extended Hermite Equivalence classes is presented in the chapter. New determinantal representations of generalized inverse matrices based on their limit representations are introduced in Chapter Three. Using the obtained analogues of the adjoint matrix, Cramer''s rules for the least squares solution with the minimum norm and for the Drazin inverse solution of singular linear systems have been obtained in the chapter. In Chapter Four, a very interesting application of linear algebra of commutative rings to systems theory, is explored. Chapter Five gives a comprehensive investigation to behaviors of a general Hermitian quadratic matrix-valued function by using ranks and inertias of matrices. In Chapter Six, the theory of triangular matrices (tables) is introduced. The main "characters" of the chapter are special triangular tables (which will be called triangular matrices) and their functions paradeterminants and parapermanents. The aim of Chapter Seven is to present the latest developments in iterative methods for solving linear matrix equations. The problems of existence of common eigenvectors and simultaneous triangularization of a pair of matrices over a principal ideal domain with quadratic minimal polynomials are investigated in Chapter Eight. Two approaches to define a noncommutative determinant (a determinant of a matrix with noncommutative elements) are considered in Chapter Nine. The last, Chapter 10, is an example of how the methods of linear algebra are used in natural sciences, particularly in chemistry. In this chapter, it is shown that in a First Order Chemical Kinetics Mechanisms matrix, all columns add to zero, all the diagonal elements are non-positive and all the other matrix entries are non-negative. As a result of this particular structure, the Gershgorin Circles Theorem can be applied to show that all the eigenvalues are negative or zero.

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Book SynopsisDisease in the prey population increases the risk of prey outcomes in predation or to be harvested. In this book, an eco-epidemiological model consisting of predator-prey model with SIS disease in the prey population is proposed and analysed. Furthermore, the authors discuss a mathematical S-E-I-L (Susceptible-Latently infected-Infected-Lost of sight) model for the spread of a directly transmitted infectious disease in an age-structured population; examine how starting from the classical Chebyshev ordinary differential equation (ODE), a generic realisation of its Lie algebra of point symmetries sl(3;R) is obtained in terms of the Chebyshev polynomials of first and second kind; and give a comparative summary of different recent contributions to the theme of the linear stability and nonlinear dynamics of solitary waves in the nonlinear Dirac equation in the form of the Gross-Neveu model.

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Book SynopsisFourth edition of Topics in Abstract Algebra aligns with CBCS syllabus, includes Automorphism of Groups. Ideal for UG Honours/Advanced level students, competitive exam takers. Features worked-out exercises, MCQs, online resources, historical insights. Market: UG and PG Mathematics.

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Book SynopsisThis concise introduction to the subject emphasizes the various classes of regular semigroups. More than 150 exercises, accompanied by references to the relevant research literature, direct readers to areas not explicitly covered in the text.Trade ReviewThe author succeeds admirably in his goal of providing an introduction to semigroup theory suitable for graduate students and non-specialists. At the same time, specialists will also find much to attract them. The book is highly readable, and the author takes pain to lead the reader gently through the longer proofs. I am sure that all specialists will want to own a copy of the book, that non-specialists will find it a most attractive and useful book for consulting, and that for many years to come research students will learn their subject from this book. * Bulletin of the London Mathematical Society *The book provides a useful survey of a rapidly developing topic and is suitable for specialists and as an introduction to the subject for non-specialists and graduate students. * Aslib Book Guide, vol.61, no.5, May 1996. *This book will still have its outstanding place as a general introduction to semigroup theory offering both an updated overview of the subject and a suitable entree for the graduate student * Monatshefte fur Mathematik Vol. 124 1997 *With this well-written and well-organised book I think the author has ensured that "Howie" will continue to be a byword for semigroup books * Edinburgh Mathematical Society 1997 *Table of Contents1. Introductory ideas ; 2. Green's equivalences; regular semigroups ; 3. 0-simple semigroups ; 4. Completely regular semigroups ; 5. Inverse semigroups ; 6. Other classes of regular semigroups ; 7. Free semigroups ; 8. Semigroup amalgams ; References ; List of symbols

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Book SynopsisThis is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.Trade Review'the self-contained monograph provides an introduction suitable for mathematics graduates to the basic properties of quantum fields' AslibTable of ContentsStates and observables ; Quantum theory ; The relativistic symmetry ; Local observables ; Scattering theory ; Sector theory ; Appendix A: Hilbert space and operators ; Appendix B: Operator algebras ; Appendix C: Free fields

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Book SynopsisAn accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results.The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remTrade Review'The author's intention was to write a quick introduction to the area of algebraic groups of the Lie type over fields of positive characteristic and I think he was very successful. The first part of the book can be recommended as a very suitable text for undergraduate students at the beginning of their studies.' * EMS Newsletter *The style of exposition in the book is very reader-friendly ... The proofs are clear and complete. * Mathematical Reviews *Table of Contents1. Algebraic sets and algebraic groups ; 2. Affine varieties and finite morphisms ; 3. Algebraic representations and Borel subgroups ; 4. Frobenius maps and finite groups of Lie type ; Bibliography ; Index

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Book SynopsisPresents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.Trade ReviewPresents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications ... Brings to the subject an immense range of reference to the study of polynomials. Professional and academic mathematicians of complex analysis, approximation theory and theoretical numerical analysis; graduate students in mathematics; engineers, statisticians and theoretical physicists, who have an interest in the important results about polynomials, will not do better than start with reading and referring to this book. * Current Engineering Practice *A nicely written book that will be useful for scientists, engineers and mathematicians from other fields. It can be strongly recommended as an undergraduate or graduate text and as a comprehensive source for self study. * EMS *Table of Contents2. FUNDAMENTAL RESULTS ON CRITICAL POINTS ; 8. INCLUSION OF ALL ZEROS ; 12. GROWTH ESTIMATES

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Book SynopsisThis work summarises the development of a classification system of finite p-groups. The authors provide a careful summary and explanation of the many and difficult original research papers on the co-class conjecture and the structure theorem, thus elucidating the background research for those new to the area as well as for experienced researchers.Trade Review... there is considerable new material in this book ... The book is beautifully produced - a pleasure to the eyes, as well as to the mind, to read. * Zentralblatt MATH *Table of Contents1. Preliminaries ; 2. New groups from old ; 3. p-groups of maximal class ; 4. Finite p-groups acting uniserially ; 5. Lie Methods ; 6. The proof of Conjecture A ; 7. Pro-p-groups ; 8. Constructing finite p-groups ; 9. Homological algebra ; 10. Uniserial p-adic space groups ; 11. The structure of finite p-groups ; 12. Beyond coclass ; Bibliography ; Symbol index ; index

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Book SynopsisLoop groups are the simplest class of infinite dimensional Lie groups, and have important applications in elementary particle physics. They have recently been studied intensively, and the theory is now well developed, involving ideas from several areas of mathematics - algebra, geometry, analysis, and combinatorics. The mathematics of quantum field theory is an important ingredient. This book gives a complete and self-contained account of what is known about the subject and it is written from a geometrical and analytical point of view, with quantum field theory very much in mind. The mathematics used in connection with loop groups is interesting and important beyond its immediate applications and the authors have tried to make the book accessible to mathematicians in many fields.The hardback edition was published in December 1986.Trade Review'This is an outstanding book, of enormous interest to anyone interested in Lie groups, Lie algebras and/or Quantum Field Theory' MathematikaTable of ContentsIntroduction; PART 1 - Finite dimensional lie groups; Groups of smooth maps; Central extensions; The root system: KAC-Moody algebras; Loop groups as groups of operators in Hilbert space; The Grassmannian of Hilbert space and the determinant line bundle; The fundamental homogeneous space. PART 2 - Representation theory; The fundamental representation; The Borel-Weil theory; The spin representation; 'Blips' or 'vertex operators'; The KAC character formula and the Bernstein-Gelfand-Gelfand resolution; References; Index of notation; Index.

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Book SynopsisThis monograph provides a treatment of the theory of algebraic Riccati equations, an area of increasing interest in the mathematics and engineering communities. A range of applications are covered, demonstrating the use of these equations for providing solutions to complex problems.Table of Contents1. Preliminaries from the theory of matrices ; 2. Indefinite scalar products ; 3. Skew-symmetric scalar products ; 4. Matrix theory and control ; 5. Linear matrix equations ; 6. Rational matrix functions ; 7. Geometric theory: the complex case ; 8. Geometric theory: the real case ; 9. Constructive existence and comparison theorems ; 10. Hermitian solutions and factorizations of rational matrix functions ; 11. Perturbation theory ; 12. Geometric theory for the discrete algebraic Riccati equation ; 13. Constructive existence and comparison theorems ; 14. Perturbation theory for discrete algebraic Riccati equations ; 15. Discrete algebraic Riccati equations and matrix pencils ; 16. Linear-quadratic regulator problems ; 17. The discrete Kalman filter ; 18. The total least squares technique ; 19. Canonical factorization ; 20. Hoo control problems ; 21. Contractive rational matrix functions ; 22. The matrix sign function ; 23. Structured stability radius ; Bibliography ; List of notations ; Index

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Book SynopsisHeun''s equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger''s equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).Trade ReviewThere is a wealth of important results and open problems and the book is a welcome addition to the literature on these important special functions and their applications. * B D Sleeman, Zbl. Math. 847/96. *Table of ContentsA. HEUN'S EQUATION ; I: GENERAL AND POWER SERIES ; II: HYPERGEOMETRIC FUNCTION SERIES ; B. CONFLUENT HEUN EQUATION ; C. DOUBLE CONFLUENT HEUN EQUATION ; D. BICONFLUENT HEUN EQUATION ; E. TRICONFLUENT HEUN EQUATION

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Book SynopsisLie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur''s lemma and its consequenTrade Review'A nice feature of this book is a variety of problems proposed at the end of each section; this makes it especially suitable as a textbook for a first course in Lie groups, addressed to an audience of mathematicians or physicists. MMA Reviews, March 2007, Fabio MainardiTable of ContentsPreface ; 1. The exponential map ; 2. Lie theory ; 3. The classical groups ; 4. Manifolds, homogeneous spaces, Lie groups ; 5. Integration ; 6. Representations ; Appendix: Analytic Functions and Inverse Function Theorem ; References ; Index

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Book SynopsisBanach spaces and algebras are a key topic of pure mathematics. Graham Allan''s careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author''s lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces.The main body of the text is an intTrade ReviewThis well-crafted and scholarly book ...leaves nothing to be desired: this is a fine way to get into this beautiful in a subject and will serve to reel in a huge number of futureews devotees. * Michael Berg, MAA Reviews *Table of ContentsPART I INTRODUCTION TO BANACH SPACES ; 1. Preliminaries ; 2. Elements of normed spaces ; 3. Banach spaces ; PART II BANACH ALGEBRAS ; 4. Banach algebras ; 5. Representation theory ; 6. Algebras with an involution ; 7. The Borel functional calculus ; PART III SCV AND BANACH ALGEBRAS ; 8. Introduction to several complex variables ; 9. The holomorphic functional calculus in several variables ; Bibliography ; Index

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Book SynopsisAn Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D.R. Heath-Brown this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today''s students through the key milestones and developments in number theory. Updates include a chapter by J.H. Silverman on one of the most important developments in number theory -- modular elliptic curves and their role in the proof of Fermat''s Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid readerThe text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year Trade ReviewReview from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable. * Nature *This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory. * Mathematical Gazette *...an important reference work... which is certain to continue its long and successful life... * Mathematical Reviews *...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own. * Matyc Journal *Table of ContentsPREFACE TO THE SIXTH EDITION; PREFACE TO THE FIFTH EDITION; APPENDIX; LIST OF BOOKS; INDEX OF SPECIAL SYMBOLS AND WORDS; INDEX OF NAMES; GENERAL INDEX

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Book SynopsisAdvanced Topics in Linear Algebra presents, in an engaging style, novel topics linked through the Weyr matrix canonical form, a largely unknown cousin of the Jordan canonical form discovered by Eduard Weyr in 1885. The book also develops much linear algebra unconnected to canonical forms, that has not previously appeared in book form. It presents common applications of Weyr form, including matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. The Weyr form clearly outperforms the Jordan form in many situations, particularly where two or more commuting matrices are involved, due to the block upper triangular form a Weyr matrix forces on any commuting matrix. In this book, the authors develop the Weyr form from scratch, and include an algorithm for computing it. The Weyr form is also derived ring-theoretically in an entirely different way to the classical derivation of the Jordan form. A fascinating duality exists between the two forms that allows one to flip back and forth and exploit the combined powers of each. The book weaves together ideas from various mathematical disciplines, demonstrating dramatically the variety and unity of mathematics. Though the book''s main focus is linear algebra, it also draws upon ideas from commutative and noncommutative ring theory, module theory, field theory, topology, and algebraic geometry.Advanced Topics in Linear Algebra offers self-contained accounts of the non-trivial results used from outside linear algebra, and lots of worked examples, thereby making it accessible to graduate students. Indeed, the scope of the book makes it an appealing graduate text, either as a reference or for an appropriately designed one or two semester course. A number of the authors'' previously unpublished results appear as well.Trade Review"The book covers both early and quite recent results, has informative remarks and thorough theoretical deductions, provides interesting footnotes and brief biographies of related mathematicians, and contains concrete and elegant proofs. Overall, the book is written in a self-contained, introductory, and inspiring fashion." Mathematical ReviewsTable of ContentsPreface ; Chapter 1. Background Linear Algebra ; Chapter 2. The Weyr Form ; Chapter 3. Centralizers ; Chapter 4. The Module Setting ; Chapter 5. Gerstenhaber's Theorem ; Chapter 6. Approximate Simultaneous Diagonalization ; Chapter 7. Algebraic Varieties ; Bibliography

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