Algebra Books
Clarendon Press Fundamentals of Semigroup Theory 12 London Mathematical Society Monographs
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
£160.00
Oxford University Press Mathematical Theory of Quantum Fields
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
£212.50
Clarendon Press An Introduction to Algebraic Geometry and Algebraic Groups
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
£122.50
Clarendon Press Analytic Theory of Polynomials Critical Points Zeros and Extremal Properties 26 London Mathematical Society Monographs
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
£252.50
Clarendon Press The Structure of Groups of Prime Power Order 27 London Mathematical Society Monographs
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
£187.50
Clarendon Press Loop Groups
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.
£78.85
Clarendon Press Algebraic Riccati Equations Oxford Science Publications
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
£245.00
Clarendon Press Heuns Differential Equations
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
£162.50
Oxford University Press Lie Groups
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
£70.20
Oxford University Press (UK) Introduction to Banach Spaces and Algebras
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
£92.00
Oxford University Press An Introduction to the Theory of Numbers
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
£162.50
Oxford University Press, USA Advanced Topics in Linear Algebra Weaving Matrix Problems Through the Weyr Form
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
£99.75
Springer Lattices Semigroups and Universal Algebra
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£123.49
Springer Symmetries in Science Proceedings of an International Symposium Held in Bregenz Austria July 1318 1997 No 10 Language of Science
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£123.49
Springer Symplectic Methods for the Symplectic Eigenproblem
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£85.49
Springer New York The Arithmetic of Elliptic Curves
Book SynopsisFollowing a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields.Trade ReviewFrom the reviews of the second edition:"This well-written book covers the basic facts about the geometry and arithmetic of elliptic curves, and is sure to become the standard reference in the subject. It meets the needs of at least three groups of people: students interested in doing research in Diophantine geometry, mathematicians needing a reference for standard facts about elliptic curves, and computer scientists interested in algorithms and needing an introduction to elliptic curves..."-- MATHEMATICAL REVIEWS“The book under review is the second, revised, enlarged, and updated edition of J. Silverman’s meanwhile classical primer of the arithmetic of elliptic curves. … All together, this enlarged and updated version of J. Silverman’s classic ‘The Arithmetic of Elliptic Curves’ significantly increases the unchallenged value of this modern primer as a standard textbook in the field. … This makes the entire text a perfect source for teachers and students, for courses and self-study, and for further studies in the arithmetic of elliptic curves likewise.” (Werner Kleinert, Zentralblatt MATH, Vol. 1194, 2010)“For the second edition of his masterly book, the author considerably updated and improved several results and proofs. … book contains a great many exercises, many of which develop or complement the results from the main body of the book. … The reference list contains 317 items and reflects both classical and recent achievements on the topic. Notes on the exercises are an aid to the reader. … Summarizing, this is an excellent book … . useful both for experienced mathematicians and for graduate students.” (Vasil' I. Andriĭchuk, Mathematical Reviews, Issue 2010 i)“This is the second edition of an excellent textbook on the arithmetical theory of elliptic curves … . Although there are now a number of good books on this topic it has stood the test of time and become a popular introductory text and a standard reference. … The author has added remarks which point out their significance and connection to those parts of the theory he presents. These will give readers a good start if they want to study one of them.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 164 (3), November, 2011)“The book is written for graduate students … and for researchers interested in standard facts about elliptic curves. … A wonderful textbook on the arithmetic theory of elliptic curves and it is a very popular introduction to the subject. … I recommend this book for anyone interested in the mathematical study of elliptic curves. It is an excellent introduction, elegant and very well written. It is one of the best textbooks to graduate level studies I have ever had contact yet.” (Book Inspections Blog, 2012)Table of ContentsAlgebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell#x2013;Weil Group.- Algorithmic Aspects of Elliptic Curves.
£44.99
Springer Integers Polynomials and Rings
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£40.99
Springer A Field Guide to Algebra
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£49.99
Springer Undergraduate Algebra
Book SynopsisThe Integers.- Groups.- Rings.- Polynomials.- Vector Spaces and Modules.- Some Linear Groups.- Field Theory.- Finite Fields.- The Real and Complex Numbers.- Sets.Trade ReviewFrom the reviews of the third edition: "As is very typical for Professor Lang’s self demand and style of publishing, he has tried to both improve and up-date his already well-established text. … Numerous examples and exercises accompany this now already classic primer of modern algebra, which as usual, reflects the author’s great individuality just as much as his unrivalled didactic mastery and his care for profound mathematical education at any level. … The present textbook … will remain one of the great standard introductions to the subject for beginners." (Werner Kleinert, Zentralblatt MATH, Vol. 1063, 2005)Table of Contents* Foreword * The Integers * Groups * Rings * Polynomials * Vector Spaces and Modules * Some Linear Groups * Field Theory * Finite Fields * The Real and Complex Numbers * Sets * Appendix * Index
£49.99
Springer The Geometry of Syzygies
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£63.64
Springer New York The Geometry of Syzygies
Book SynopsisFirst textbook-level account of basic examples and techniques in this area.Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already.Trade ReviewFrom the reviews:"This book is devoted to offer … an approach to the study of this algebraic subject (syzygy = relation among generators of a module) … . a student would learn a lot of algebraic geometry from it. The double bet of the book is to be able to be a complete textbook … and at the same time to become a useful reference text for research work on the subject. I would say that both aspects of the bet have been gained … ." (Alessandro Gimigliano, Zentralblatt MATH, Vol. 1066, 2005)"This book may be regarded as a complement to the author’s Commutative Algebra … . It begins by explaining syzygies and their connection with the Hilbert function, and turns to describing various aspects of algebraic geometry … . Two appendices provide the background in commutative algebra and local cohomology. Together with exercises, it gives a good survey of topics often not covered." (Mathematika, Vol. 52, 2005)"This monograph is devoted to the geometric properties of a projective variety corresponding to the properties of its syzygies … . Altogether, this is a most welcome addition to the literature and will help many a reader bridge the gap between the abstractions of algebra and the more tangible field of geometry." (Ch. Baxa, Monatshefte für Mathematik, Vol. 150 (1), 2006)Aus den Rezensionen: “... Das vorliegende Buch beschäftigt sich mit der qualitativen geometrischen Theorie der Syzygien. ... Es gibt zwei sehr kompakt geschriebene Anhänge: Der erste führt in die lokale Kohomologie ein, der zweite stellt für das Buch nötige Vorkenntnisse der kommutativen Algebra ... zusammen. Dieses Buch ist sehr elegant geschrieben und vermittelt viele interessante Ideen. In der Lehre könnte es gut für weiterführende Vorlesungen über algebraische Geometrie verwendet werden.“ (Franz Pauer, in: Internationale Mathematische Nachrichten, December/2009, Issue 12, S. 45)“This very interesting book is the first textbook-level account of syzygies as they are used in algebraic geometry. … The reader will find two very good and useful appendices. … The book can be read, without any problem, by a student who has received already a little introduction in commutative algebra and algebraic geometry. I highly recommend this nice and deep textbook for all students and researchers studying algebraic geometry or commutative algebra.” (Dominique Lambert, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)Table of ContentsPreface: Algebra and Geometry * Free Resolutions and Hilbert Functions * First Examples of Free Resolutions * Points in P^2 * Castelnuovo—Mumford Regularity * The Regularity of Projective Curves * Linear Series and 1-Generic Matrices * Linear Complexes and the Linear Syzygy Theorem * Curves of High Degree * Clifford Index and Canonical Embedding * Appendix 1: Introduction to Local Cohomology * Appendix 2: A Jog Through Commutative Algebra * References * Index
£33.99
Springer Difference Equations
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£82.83
Springer Difference Equations
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£44.99
Springer Multiplicative Ideal Theory in Commutative Algebra A Tribute to the Work of Robert Gilmer
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£123.49
Springer A First Course in Differential Equations
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£36.99
Springer Applied Linear Algebra and Matrix Analysis Undergraduate Texts in Mathematics
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£44.99
Springer Introduction to Boolean Algebras
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£38.99
Springer Integers Polynomials and Rings A Course in Algebra Undergraduate Texts in Mathematics
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£63.99
Springer Algebra Volume I 1
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£54.99
Springer Algebra Volume II 2
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£54.99
Springer New York Number Theory
Book SynopsisThis book deals with several aspects of what is now called "explicit number theory." The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions.Trade ReviewFrom the reviews:"Cohen (Université Bordeaux I, France), an instant classic, uniquely bridges the gap between old-fashioned, naive treatments and the many modern books available that develop the tools just mentioned … . Summing Up: Recommended. … Upper-division undergraduates through faculty." (D. V. Feldman, CHOICE, Vol. 45 (5), January, 2008)"The book deals with aspects of ‘explicit number theory’. … The central theme … is the solution of Diophantine equations. … It combines an interesting ‘philosophy’ of the subject with an encyclopedic grasp of detail. The extension of the author’s reach via the contributed chapters is a good idea. Perhaps it is the start of a trend, as the subject grows more and more. … It will undoubtedly be mined by instructors for their graduate courses, particularly for the purpose of including some recently-proved content." (R. C. Baker, Mathematical Reviews, Issue 2008 e)“This is the second volume of a highly impressive two-volume textbook on Diophantine analysis. … readers are presented with an almost overwhelming amount of material. This … text book is bound to become an important reference for students and researchers alike.” (C. Baxa, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)Table of ContentsAnalytic Tools.- Bernoulli Polynomials and the Gamma Function.- Dirichlet Series and L-Functions.- p-adic Gamma and L-Functions.- Modern Tools.- Applications of Linear Forms in Logarithms.- Rational Points on Higher-Genus Curves.- The Super-Fermat Equation.- The Modular Approach to Diophantine Equations.- Catalan’s Equation.
£44.99
Springer A Concrete Introduction to Higher Algebra
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£66.49
Springer Universal Algebra
Book SynopsisUniversal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.Each chapter is followed by an extensive list of exercises and problems.Table of ContentsBasic Concepts.- Subalgebras and Homomorphisms.- Partial Algebras.- Constructions of Algebras.- Free Algebras.- Independence.- Elements of Model Theory.- Elementary Properties of Algebraic Constructions.- Free Structures.- Appendix 1. General Survey.- Appendix 2. The Problems.- Appendix 3. Congruence Varieties.- Appendix 4. Equational Logic by Walter Taylor.- Appendix 5. Primality the influence of Boolean Algebras in Universal Algebra.- Appendix 6 Equational Compactness.- Appendix 7 The Independence Proof.
£71.24
Springer Digital and Microprocessor Engineering Ellis Horwood series in electrical and electronic engineering
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£71.24
Springer Mirrors and Reflections
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£54.99
Springer New York Symmetry Representations and Invariants Graduate Texts in Mathematics 255
Book SynopsisThis book is a significant reworking of an earlier work by the authors. It offers a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that includes a broader range of applications.Trade ReviewFrom the reviews:"This is a terrific book, succeeding in its considerable ambitions, and doing so in the remarkable style … . Symmetry, Representations, and Invariants is indeed capable of instructing the reader in the three themes given in its title, taking him from elementary and foundational notions to very advanced material … . Symmetry, Representations, and Invariants promises to be a graduate text of major importance." (Michael Berg, The Mathematical Association of America, August, 2009)“The book under review is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups. … can be used as a source for various kinds of courses. … supported by the rich collections of exercises (mostly with detailed hints for solutions) accompanying each section. Local reading is well supported by the structure of the book. The book can be recommended for a … wide audience of readers: for graduate and postgraduate students as well as for researchers as a reference work.” (Sergei Platonov, Zentralblatt MATH, Vol. 1173, 2009)“The book under review is a substantial rewriting and extension of the authors’ previous work ‘Representations and Invariants of the Classical Groups’. It is a thorough and comprehensive treatment of the geometry of Lie and algebraic group actions. … More than 350 exercises are presented. This monograph is written with great care and provides an excellent basis for a variety of courses from this field.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)“The book will serve as a useful reference for a broad range of mathematicians, as well as physicists seeking a rigorous, systematic development of the representation theory underlying much of modern quantum mechanics. Detailed and careful statements of definitions, theorems, and proofs are provided, as well as over 350 exercises, many of them substantial. … can be used as the basis for graduate-level courses in Lie groups and algebraic groups, representation theory, invariant theory, and a variety of applications.” (Peter J. Olver, SIAM Review, Vol. 53 (3), 2011)“This volume is clearly a labour of love on the part of the authors, who have obviously thought very carefully about the best way to explain and motivate this often sophisticated material. … The authors have taken great pains to make this book a textbook as well as a useful reference. … It should be in the library of every university with a graduate mathematics program, as well as on the shelf of every lecturer teaching, or with research interests in, the material covered here.” (Mark Hunacek, The Mathematical Gazette, Vol. 96 (536), July, 2012)Table of ContentsLie Groups and Algebraic Groups.- Structure of Classical Groups.- Highest-Weight Theory.- Algebras and Representations.- Classical Invariant Theory.- Spinors.- Character Formulas.- Branching Laws.- Tensor Representations of GL(V).- Tensor Representations of O(V) and Sp(V).- Algebraic Groups and Homogeneous Spaces.- Representations on Spaces of Regular Functions.
£53.99
Springer New York Introduction to Lie Algebras and Representation
Book SynopsisThis book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations.Table of ContentsI. Basic Concepts.- 1. Definitions and first examples.- 1.1 The notion of Lie algebra.- 1.2 Linear Lie algebras.- 1.3 Lie algebras of derivations.- 1.4 Abstract Lie algebras.- 2. Ideals and homomorphisms.- 2.1 Ideals.- 2.2 Homomorphisms and representations.- 2.3 Automorphisms.- 3. Solvable and nilpotent Lie algebras.- 3.1 Solvability.- 3.2 Nilpotency.- 3.3 Proof of Engel’s Theorem.- II. Semisimple Lie Algebras.- 4. Theorems of Lie and Cartan.- 4.1 Lie’s Theorem.- 4.2 Jordan-Chevalley decomposition.- 4.3 Cartan’s Criterion.- 5. Killing form.- 5.1 Criterion for semisimplicity.- 5.2 Simple ideals of L.- 5.3 Inner derivations.- 5.4 Abstract Jordan decomposition.- 6. Complete reducibility of representations.- 6.1 Modules.- 6.2 Casimir element of a representation.- 6.3 Weyl’s Theorem.- 6.4 Preservation of Jordan decomposition.- 7. Representations of sl (2, F).- 7.1 Weights and maximal vectors.- 7.2 Classification of irreducible modules.- 8. Root space decomposition.- 8.1 Maximal toral subalgebras and roots.- 8.2 Centralizer of H.- 8.3 Orthogonality properties.- 8.4 Integrality properties.- 8.5 Rationality properties Summary.- III. Root Systems.- 9. Axiomatics.- 9.1 Reflections in a euclidean space.- 9.2 Root systems.- 9.3 Examples.- 9.4 Pairs of roots.- 10. Simple roots and Weyl group.- 10.1 Bases and Weyl chambers.- 10.2 Lemmas on simple roots.- 10.3 The Weyl group.- 10.4 Irreducible root systems.- 11. Classification.- 11.1 Cartan matrix of ?.- 11.2 Coxeter graphs and Dynkin diagrams.- 11.3 Irreducible components.- 11.4 Classification theorem.- 12. Construction of root systems and automorphisms.- 12.1 Construction of types A-G.- 12.2 Automorphisms of ?.- 13. Abstract theory of weights.- 13.1 Weights.- 13.2 Dominant weights.- 13.3 The weight ?.- 13.4 Saturated sets of weights.- IV. Isomorphism and Conjugacy Theorems.- 14. Isomorphism theorem.- 14.1 Reduction to the simple case.- 14.2 Isomorphism theorem.- 14.3 Automorphisms.- 15. Cartan subalgebras.- 15.1 Decomposition of L relative to ad x.- 15.2 Engel subalgebras.- 15.3 Cartan subalgebras.- 15.4 Functorial properties.- 16. Conjugacy theorems.- 16.1 The group g (L).- 16.2 Conjugacy of CSA’s (solvable case).- 16.3 Borel subalgebras.- 16.4 Conjugacy of Borel subalgebras.- 16.5 Automorphism groups.- V. Existence Theorem.- 17. Universal enveloping algebras.- 17.1 Tensor and symmetric algebras.- 17.2 Construction of U(L).- 17.3 PBW Theorem and consequences.- 17.4 Proof of PBW Theorem.- 17.5 Free Lie algebras.- 17. Generators and relations.- 17.1 Relations satisfied by L.- 17.2 Consequences of (S1)-(S3).- 17.3 Serre’s Theorem.- 17.4 Application: Existence and uniqueness theorems.- 18. The simple algebras.- 18.1 Criterion for semisimplicity.- 18.2 The classical algebras.- 18.3 The algebra G2.- VI. Representation Theory.- 20. Weights and maximal vectors.- 20.1 Weight spaces.- 20.2 Standard cyclic modules.- 20.3 Existence and uniqueness theorems.- 21. Finite dimensional modules.- 21.1 Necessary condition for finite dimension.- 21.2 Sufficient condition for finite dimension.- 21.3 Weight strings and weight diagrams.- 21.4 Generators and relations for V(?).- 22. Multiplicity formula.- 22.1 A universal Casimir element.- 22.2 Traces on weight spaces.- 22.3 Freudenthal’s formula.- 22.4 Examples.- 22.5 Formal characters.- 23. Characters.- 23.1 Invariant polynomial functions.- 23.2 Standard cyclic modules and characters.- 23.3 Harish-Chandra’s Theorem.- 24. Formulas of Weyl, Kostant, and Steinberg.- 24.1 Some functions on H*.- 24.2 Kostant’s multiplicity formula.- 24.3 Weyl’s formulas.- 24.4 Steinberg’s formula.- VII. Chevalley Algebras and Groups.- 25. Chevalley basis of L.- 25.1 Pairs of roots.- 25.2 Existence of a Chevalley basis.- 25.3 Uniqueness questions.- 25.4 Reduction modulo a prime.- 25.5 Construction of Chevalley groups (adjoint type).- 26. Kostant’s Theorem.- 26.1 A combinatorial lemma.- 26.2 Special case: sl (2, F).- 26.3 Lemmas on commutation.- 26.4 Proof of Kostant’s Theorem.- 27. Admissible lattices.- 27.1 Existence of admissible lattices.- 27.2 Stabilizer of an admissible lattice.- 27.3 Variation of admissible lattice.- 27.4 Passage to an arbitrary field.- 27.5 Survey of related results.- References.- Afterword (1994).- Index of Terminology.- Index of Symbols.
£46.99
Springer FiniteDimensional Vector Spaces
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£37.99
Springer New York Lectures in Abstract Algebra Iii Theory Of Fields And Galois Theory 32 Graduate Texts in Mathematics
Book SynopsisThe parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory.Table of Contents1. Extension of homomorphisms.- 2. Algebras.- 3. Tensor products of vector spaces.- 4. Tensor product of algebras.- I: Finite Dimensional Extension Fields.- 1. Some vector spaces associated with mappings of fields.- 2. The Jacobson-Bourbaki correspondence.- 3. Dedekind independence theorem for isomorphisms of a field.- 4. Finite groups of automorphisms.- 5. Splitting field of a polynomial.- 6. Multiple roots. Separable polynomials.- 7. The “fundamental theorem” of Galois theory.- 8. Normal extensions. Normal closures.- 9. Structure of algebraic extensions. Separability.- 10. Degrees of separability and inseparability. Structure of normal extensions.- 11. Primitive elements.- 12. Normal bases.- 13 Finite fields.- 14. Regular representation, trace and norm.- 15. Galois cohomology.- 16 Composites of fields.- II: Galois Theory of Equations.- 1. The Galois group of an equation.- 2. Pure equations.- 3. Galois’ criterion for solvability by radicals.- 4. The general equation of n-th degree.- 5. Equations with rational coefficients and symmetric group as Galois group.- III: Abelian Extensions.- 1. Cyclotomic fields over the rationals.- 2. Characters of finite commutative groups.- 3. Kummer extensions.- 4. Witt vectors.- 5. Abelian p-extensions.- IV: Structure Theory of Fields.- 1. Algebraically closed fields.- 2. Infinite Galois theory.- 3. Transcendency basis.- 4. Lüroth’s theorem.- 5. Linear disjointness and separating transcendency bases.- 6. Derivations.- 7. Derivations, separability and p-independence.- 8. Galois theory for purely inseparable extensions of exponent one.- 9. Higher derivations.- 10. Tensor products of fields.- 11. Free composites of fields.- V: Valuation Theory.- 1. Real valuations.- 2. Real valuations of the field of rational numbers.- 3. Real valuations of ?(x) which are trivial in ?.- 4. Completion of a field.- 5. Some properties of the field of p-adic numbers.- 6. Hensel’s lemma.- 7. Construction of complete fields with given residue fields.- 8. Ordered groups and valuations.- 9. Valuations, valuation rings, and places.- 10. Characterization of real non-archimedean valuations.- 11. Extension of homomorphisms and valuations.- 12. Application of the extension theorem: Hilbert Nullstellensatz.- 13. Application of the extension theorem: integral closure.- 14. Finite dimensional extensions of complete fields.- 15. Extension of real valuations to finite dimensional extension fields.- 16. Ramification index and residue degree.- VI: Artin-Schreier Theory.- 1. Ordered fields and formally real fields.- 2. Real closed fields.- 3. Sturm’s theorem.- 4. Real closure of an ordered field.- 5. Real algebraic numbers.- 6. Positive definite rational functions.- 7. Formalization of Sturm’s theorem. Resultants.- 8. Decision method for an algebraic curve.- 9. Equations with parameters.- 10. Generalized Sturm’s theorem. Applications.- 11. Artin-Schreier characterization of real closed fields.- Suggestions for further reading.
£80.99
Springer Linear Algebra
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£54.99
Springer Linear Algebra
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£59.99
Springer Linear Algebra
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£46.99
Springer The Fundamental Theorem of Algebra
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£66.49
Springer New York A First Course in Noncommutative Rings
Book Synopsis1 WedderburnArtin Theory.- 2 Jacobson Radical Theory.- 3 Introduction to Representation Theory.- 4 Prime and Primitive Rings.- 5 Introduction to Division Rings.- 6 Ordered Structures in Rings.- 7 Local Rings, Semilocal Rings, and Idempotents.- 8 Perfect and Semiperfect Rings.- References.- Name Index.Trade ReviewFrom the reviews of the second edition: "Ten years ago, the first edition ... of this book appeared. It is quite rare that a book can become a classic in such a short time, but this did happen for this excellent book. Of course minor changes were made for the second edition; new exercises and an appendix on uniserial modules were added. Every part of the text was written with love and care. The explanations are very well done, useful examples help to understand the material ... ." (G. Pilz, Internationale Mathematische Nachrichten, Issue 196, 2004) "This is the second edition of the book with the same title published in 1991. The entire text has been retyped, some proofs were rewritten, and numerous improvements in the exposition have been included. ... The original exercises in the first edition have been replaced by 400 exercises of the Problem Book published by the author in 1995 ... . As the publication ... impressively shows, the book is indeed very suitable as a text for a full-year graduate course in non-commutative ring theory." (H. Mitsch, Monatshefte für Mathematik, Vol. 136 (4), 2002) "The book under review is the new edition of the 1st edition of this book which was published ten years ago. In the intervening period, the book has become a standard textbook for a graduate course in non commutative rings. ... All this material is beautifully covered in this book with many examples and exercises. The book is a joy to read, and must be read by all students of mathematics. It is specially welcome to have this book in softcover, relatively in-expensive, edition ... ." (Dipendra Prasad, Journal of the Indian Academy of Mathematics, Vol. 24 (1), 2002) "This book, an outgrowth of the author’s lectures at the University of Berkeley, is intended as a textbook for a one-semester course in basic ring theory. ... More than 400 exercises testing the understanding of the general theory in the text are included in this new edition." (L’Enseignement Mathematique, Vol. 47 (3-4), 2001) "The present book is a radical update. For the second edition the text was retyped, some proofs were rewritten and improvements in exposition have also taken place. ... It is well-written and consists of eight chapters. ... There is a very good reference section for further study and a name index consisting of four pages of closely-packed names. ... As always the standard of print and presentation by Springer is exemplary." (Brian Denton, The Mathematical Gazette, Vol. 86 (505), 2002)Table of Contents* Wedderburn-Artin Theory * Jacobson Radical Theory * Introduction to Representation Theory * Prime and Primitive Rings * Introduction to Division Rings * Local Rings, Semilocal Rings, and Idempotents * Perfect and Semiperfect Rings * References
£63.64
Springer Applied Abstract Algebra
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£68.40
Springer Disquisitiones Arithmeticae
Book SynopsisCongruent Numbers in General.- Congruences of the First Degree.- Residues of Powers.- Congruences of the Second Degree.- Forms and Indeterminate Equations of the Second Degree.- Various Applications of the Preceding Discussions.- Equations Defining Sections of a Circle.- Additional Notes.- Tables.- Gauss' Handwritten Notes.- List of Special Symbols.- Directory of Terms.Table of ContentsCongruent Numbers in General.- Congruences of the First Degree.- Residues of Powers.- Congruences of the Second Degree.- Forms and Indeterminate Equations of the Second Degree.- Various Applications of the Preceding Discussions.- Equations Defining Sections of a Circle.- Additional Notes.- Tables.- Gauss' Handwritten Notes.- List of Special Symbols.- Directory of Terms.
£170.99
Springer Representation Theory
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£75.99
Springer Linear Algebra Through Geometry
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£49.99