Algebra Books
Cambridge University Press Designs and their Codes 103 Cambridge Tracts in Mathematics Series Number 103
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£145.35
Cambridge University Press Schur Algebras and Representation Theory Cambridge Tracts in Mathematics
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£105.45
Cambridge University Press LMS 163 Topics in Varieties Group London Mathematical Society Lecture Note Series Series Number 163
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£47.63
Cambridge University Press LMS 168 Reprsntn Algbras Rltd Tpcs London Mathematical Society Lecture Note Series Series Number 168
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£65.86
Cambridge University Press LMS 171 CR Squares London Mathematical Society Lecture Note Series Series Number 171
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£55.09
Cambridge University Press LMS 178 Lower K and L Theory London Mathematical Society Lecture Note Series Series Number 178
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£50.95
Cambridge University Press Handbook of Categorical Algebra Volume 1 Basic Category Theory Encyclopedia of Mathematics and its Applications Series Number 50
Book SynopsisA Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various 'refinements' of the fundamental concepts of category and functor.Trade Review"...Not only is this the most comprehensive book ever written on category theory, it is by far the best written...What the author has understood is that one cannot understand this subject without lots of examples..." Gian-Carlo Rota, The Bulletin of Mathematics Books"...these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical ReviewsTable of ContentsIntroduction; 1. The language of categories; 2. Limits; 3. Adjoint functors; 4. Generators and projectives; 5. Categories of fractions; 6. Flat functors and Cauchy completeness; 7. Bicategories and distributors; 8. Internal category theory; Bibliography; Index.
£152.95
Cambridge University Press Handbook of Categorical Algebra Volume 2 Categories and Structures Encyclopedia of Mathematics and its Applications Series Number 51
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£173.85
Cambridge University Press Handbook of Categorical Algebra Volume 3 Sheaf Theory Encyclopedia of Mathematics and its Applications Series Number 52
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£185.25
Cambridge University Press Theory of Algebraic Invariants
Book SynopsisAn English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.Trade Review"...Highly recommended for college libraries, undergraduate through faculty..." D.V. Feldman, Choice"...a skillful, readable, coherent presentation, with a contemporary flavor..." The American Mathematical MonthlyTable of ContentsPreface; Introduction; Part I. The Elements of Invariant Theory: 1. The forms; 2. The linear transformation; 3. The concept of an invariant; 4. Properties of invariants and covariants; 5. The operation symbols D and D; 6. The smallest system of conditions for the determination of the invariants and covariants; 7. The number of invariants of degree g; 8. The invariants and covariants of degree two and three; 9. Simultaneous invariants and covariants; 10. Covariants of covariants; 11. The invariants and covariants as functions of the roots; 12. The invariants and covariants as functions of the one-sided derivatives; 13. The symbolic representation of invariants and covariants; Part II. The Theory of Invariant Fields: 14. Proof of the finitenesss of the full invariant system via representation by root differences; 15. A generalizable proof for the finiteness of the full invariant system; 16. The system of invariants I; I1, I2, …, Ik; 17. The vanishing of the invariants; 18. The ternary nullform; 19. The finiteness of the number of irreducible syzygies and of the syzygy chain; 20. The inflection point problem for plane curves of order three; 21. The generalization of invariant theory; 22. Observations about new types of coordinates.
£34.19
Cambridge University Press LMS 195 Arithmetic Blowup Algebras London Mathematical Society Lecture Note Series Series Number 195
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£50.99
Cambridge University Press Designs and their Codes 103 Cambridge Tracts in Mathematics Series Number 103
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£72.19
Cambridge University Press Algebraic Graph Theory
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£51.29
Cambridge University Press Explicit Brauer Induction With Applications to Algebra and Number Theory 40 Cambridge Studies in Advanced Mathematics Series Number 40
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£122.55
Cambridge University Press Basic Abstract Algebra
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£107.35
Cambridge University Press Introduction to Finite Fields and their Applications
Book SynopsisThe theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of switching circuits. The first part of this updated edition presents an introduction to this theory, emphasising those aspects that are relevant for application. The second part is devoted to a discussion of the most important applications of finite fields, especially to information theory, algebraic coding theory and cryptology. There is also a chapter on applications within mathematics, such as finite geometries, combinatorics and pseudo-random sequences. The book is meant to be used as a textbook: worked examples and copious exercises that range from the routine, to those giving alternative proofs of key theorems, to extensions of material covered in the text, are provided throughout. It will appeal to advanced undergraduates and graduate students taking courses oTrade Review' … a model of how a text book should be written; it is clear, unfussy and contains lots of examples … of particular interest to anybody wishing to teach a course in concrete algebra' Mathematika' … a very useful and highly readable introduction to the classical theory and the standard applications of finite fields. It has a clear and precise presentation with many examples and a large selection of exercises.' The Mathematical GazetteTable of Contents1. Algebraic foundations; 2. Structure of finite fields; 3. Polynomials over finite fields; 4. Factorization of polynomials; 5. Exponential sums; 6. Linear recurring sequences; 7. Theoretical applications of finite fields; 8. Algebraic coding theory; 9. Cryptology; 10. Tables.
£128.25
Cambridge University Press Matrices and Graphs in Geometry 139 Encyclopedia of Mathematics and its Applications Series Number 139
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£105.45
Cambridge University Press Modules and Rings
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£133.95
Cambridge University Press Basic Abstract Algebra
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£54.14
Cambridge University Press InfiniteDimensional Lie Algebras
Book SynopsisThis is the third, substantially revised edition of this important monograph and graduate text. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems. The theory has applications in many areas of mathematics and mathematical physics and these are discussed in relation to the basic theory where appropriate.Trade Review'A clear account of Kac–Moody algebras by one of the founders … Eminently suitable as an introduction … with a surprising number of exercises.' American Mathematical Monthly' … a useful contribution. All the basic elements of the subject are covered … Many results which were previously scattered about in the literature are collected here … The book also contains many exercises and useful comments …' Physics in CanadaTable of ContentsIntroduction; Notational conventions; 1. Basic definitions; 2. The invariant bilinear form and the generalized casimir operator; 3. Integrable representations of Kac-Moody algebras and the weyl group; 4. A classification of generalized cartan matrices; 5. Real and imaginary roots; 6. Affine algebras: the normalized cartan invariant form, the root system, and the weyl group; 7. Affine algebras as central extensions of loop algebras; 8. Twisted affine algebras and finite order automorphisms; 9. Highest-weight modules over Kac-Moody algebras; 10. Integrable highest-weight modules: the character formula; 11. Integrable highest-weight modules: the weight system and the unitarizability; 12. Integrable highest-weight modules over affine algebras; 13. Affine algebras, theta functions, and modular forms; 14. The principal and homogeneous vertex operator constructions of the basic representation; Index of notations and definitions; References; Conference proceedings and collections of paper.
£52.24
Cambridge University Press Topics in Matrix Analysis
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£71.24
Cambridge University Press LMS 217 Quadratic Forms Appllctns London Mathematical Society Lecture Note Series Series Number 217
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£50.95
Cambridge University Press Cohomology of Drinfeld Modular Varieties Part 1 Geometry Counting of Points and Local Harmonic Analysis Cambridge Studies in Advanced Mathematics Series Number 41
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£122.55
Cambridge University Press Cohomology of Drinfeld Modular Varieties Part 2 Automorphic Forms Trace Formulas and Langlands Correspondence Cambridge Studies in Advanced Mathematics Series Number 56
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£122.55
Cambridge University Press Multiplicities and Chern Classes in Local Algebra
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£105.45
Cambridge University Press The Grothendieck Theory of Dessins dEnfants 0200 London Mathematical Society Lecture Note Series Series Number 200
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£94.01
Cambridge University Press LMS 203 Hochschild Cohomology London Mathematical Society Lecture Note Series Series Number 203
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£47.63
Cambridge University Press LMS 210 Hilbert CModules A Toolkit for Operator Algebraists London Mathematical Society Lecture Note Series Series Number 210
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£39.36
Cambridge University Press Matrices of SignSolvable Linear Systems
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£105.45
Cambridge University Press Affine Lie Algebras and Quantum Groups
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£72.19
Cambridge University Press Lectures on Lie Groups and Lie Algebras 32 London Mathematical Society Student Texts Series Number 32
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£44.64
Cambridge University Press A Computational Introduction to Number Theory and Algebra World Trade Organization
Book SynopsisThis introductory book emphasizes algorithms and applications, and is accessible to a broad audience. The author alternates between theory and applications in order to illustrate the mathematics. This second edition includes many new exercises and worked examples, and has been reorganized to improve presentation and clarity of exposition.Trade Review'The subject matter is presented in a very thorough way … The material is very well organized: definitions, results and their interrelations fit together perfectly … The book is especially attractive to students with a background or interest in computer science … The suitability of the book for self-study is greatly enhanced by a wealth of exercises and examples that are provided … the book is very well-written, and it is a pleasure to read.' Mathematics of Computation'… the book could serve as a course of discrete mathematics for computer science students.' EMS NewsletterTable of ContentsPreface; Preliminaries; 1. Basic properties of the integers; 2. Congruences; 3. Computing with large integers; 4. Euclid's algorithm; 5. The distribution of primes; 6. Abelian groups; 7. Rings; 8. Finite and discrete probability distributions; 9. Probabilistic algorithms; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Z*p; 12. Quadratic reciprocity and computing modular square roots; 13. Modules and vector spaces; 14. Matrices; 15. Subexponential-time discrete logarithms and factoring; 16. More rings; 17. Polynomial arithmetic and applications; 18. Linearly generated sequences and applications; 19. Finite fields; 20. Algorithms for finite fields; 21. Deterministic primality testing; Appendix: some useful facts; Bibliography; Index of notation; Index.
£54.14
Cambridge University Press Computational Algebraic Geometry
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£34.19
Cambridge University Press Corings and Comodules 309 London Mathematical Society Lecture Note Series Series Number 309
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£74.13
Cambridge University Press Elements of the Representation Theory of Associative Algebras Volume 2 Tubes and Concealed Algebras of Euclidean Type London Mathematical Society Student Texts Series Number 71
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£55.09
Cambridge University Press Exploratory Galois Theory
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£37.99
Cambridge University Press A Primer of Algebraic DModules 33 London Mathematical Society Student Texts Series Number 33
Book SynopsisThe theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.Trade Review'I truly recommend this book, both for its mathematical content and for its light reading.' Bulletin of the London Mathematic Society'A readable account.' MathematikaTable of Contents1. The Weyl algebra; 2. Ideal structure of the Weyl algebra; 3. Rings of differential operators; 4. Jacobian conjectures; 5. Modules over the Weyl algebra; 6. Differential equations; 7. Graded and filtered modules; 8. Noetherian rings and modules; 9. Dimension and multiplicity; 10. Holonomic modules; 11. Characteristic varieties; 12. Tensor products; 13. External products; 14. Inverse image; 15. Embeddings; 16. Direct images; 17. Kashiwara's theorem; 18. Preservation of holonomy; 19. Stability of differential equations; 20. Automatic proof of identities.
£116.85
Cambridge University Press Clifford Algebras and the Classical Groups
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£105.45
Cambridge University Press Classical Invariant Theory 44 London Mathematical Society Student Texts Series Number 44
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£100.70
Cambridge University Press Classical Invariant Theory
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£41.79
Cambridge University Press Guide to Quantum Groups
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£83.59
Cambridge University Press A Primer of Algebraic DModules 33 London Mathematical Society Student Texts Series Number 33
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£42.74
Cambridge University Press Introduction to Homological Algebra 38 Cambridge Studies in Advanced Mathematics Series Number 38
Book SynopsisThe landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these toTrade Review"It is...the ideal text for the working mathematician need- ing a detailed description of the fundamentals of the subject as it exists and is used today; the author has succeeded brilliantly in his avowed intention to break down 'the technological barriers between casual users and experts'." Kenneth A. Brown, Mathematical Reviews"By collecting, organizing, and presenting both the old and the new in homological algebra, Weibel has performed a valuable service. He has written a book that I am happy to have in my library." Joseph Rotman, Bulletin of the American Mathematical SocietyTable of Contents1. Chain complexes; 2. Derived functors; 3. Tor and Ext; 4. Homological dimensions; 5. Spectral sequences; 6. Group homology and cohomology; 7. Lie algebra homology and cohomology; 8. Simplicial methods in homological algebra; 9. Hothschild and cyclic homology; 10. The derived category; Appendix: category theory language.
£55.09
Cambridge University Press Solitons
Book SynopsisThis 1999 book investigates the high degree of symmetry that lies hidden in integrable systems. Differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems.Trade Review' ... this charming book can be recommended to anybody interested in the modern development in the mathematics arising from mathematical physics.' EMSTable of ContentsPreface; 1. The KdV equation and its symmetries; 2. The KdV hierarchy; 3. The Hirota equation and vertex operators; 4. The calculus of Fermions; 5. The Boson–Fermion correspondence; 6. Transformation groups and tau functions; 7. The transformation group of the KdV equation; 8. Finite dimensional Grassmannians and Plücker relations; 9. Infinite dimensional Grassmannians; 10. The bilinear identity revisited; Solutions to exercises; Bibliography; Index.
£71.24
Cambridge University Press Groups as Galois Groups
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£105.45
Cambridge University Press CohenMacaulay Rings 2ed Revised Edition 39
Book SynopsisIn the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy thTrade Review' … a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen–Macaulay rings … very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.' L'Enseignement Mathématique'This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic … A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.' Zentralblatt für MathematikTable of Contents1. Regular sequences and depth; 2. Cohen-Macaulay rings; 3. The canonical module. Gorenstein rings; 4. Hilbert functions and multiplicities; 5. Stanley-Reisner rings; 6. Semigroup rings and invariant theory; 7. Determinantal rings; 8. Big Cohen-Macaulay modules; 9. Homological theorems; 10. Tight closure.
£76.94
Cambridge University Press A Users Guide to Spectral Sequences Second Edition 58 Cambridge Studies in Advanced Mathematics Series Number 58
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£57.94
Cambridge University Press LMS 250 Characters Finite Groups London Mathematical Society Lecture Note Series Series Number 250
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£74.99