Algebra Books
Taylor & Francis Ltd Modules and the Structure of Rings
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Taylor & Francis Ltd Characterizations of C Algebras the Gelfand Naimark Theorems
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Taylor & Francis Ltd Linear Algebra over Commutative Rings
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Taylor & Francis Ltd Linear Algebra With Machine Learning and Data
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Taylor & Francis Ltd 3D Rotations
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Taylor & Francis Ltd Linear Algebra and Its Applications with R
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Taylor & Francis Ltd Functional Linear Algebra Textbooks in Mathematics
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Taylor & Francis Ltd 3D Rotations
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Taylor & Francis Ltd Practical Linear Algebra
Book SynopsisLinear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book's geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topTable of Contents1. Descartes' Discovery. 1.1. Local and Global Coordinates: 2D. 1.2. Going from Global to Local. 1.3. Local and Global Coordinates: 3D. 1.4. Stepping Outside the Box. 1.5. Application: Creating Coordinates. 1.6. Exercises. 2. Here and There: Points and Vectors in 2D. 2.1. Points and Vectors. 2.2. What's the Difference? 2.3. Vector Fields. 2.4. Length of a Vector. 2.5. Combining Points. 2.6. Independence. 2.7. Dot Product. 2.8. Application: Lighting Model. 2.9. Orthogonal Projections. 2.10. Inequalities. 2.11. Exercises. 3. Lining Up: 2D Lines. 3.1. Defining a Line. 3.2. Parametric Equation of a Line. 3.3. Implicit Equation of a Line. 3.4. Explicit Equation of a Line. 3.5. Converting Between Line Forms. 3.6. Distance of a Point to a Line. 3.7. The Foot of a Point. 3.8. A Meeting Place: Computing Intersections. 3.9. Application: Closest Point of Approach. 3.10. Exercises. 4. Changing Shapes: Linear Maps in 2D. 4.1. Skew Target Boxes. 4.2. The Matrix Form. 4.3. Linear Spaces. 4.4. Scalings. 4.5 Reflections. 4.6. Rotations. 4.7. Shears. 4.8. Projections. 4.9. Application: Free-form Deformations. 4.10. Areas and Linear Maps: Determinants. 4.11. Composing Linear Maps. 4.12. More on Matrix Multiplication. 4.13. Matrix Arithmetic Rules. 4.14. Exercises. 5. 2 x 2 Linear Systems. 5.1. Skew Target Boxes Revisited. 5.2. The Matrix Form. 5.3. A Direct Approach: Cramer's Rule. 5.4. Gauss Elimination. 5.5. Pivoting. 5.6. Unsolvable Systems. 5.7. Underdetermined Systems. 5.8. Homogeneous Systems. 5.9. Kernel. 5.10. Undoing Maps: Inverse Matrices. 5.11. Defining a Map. 5.12. Change of Basis. 5.13. Application: Intersecting Lines. 5.14. Exercises. 6. Moving Things Around: Affine Maps in 2D. 6.1. Coordinate Transformations. 6.2. Affine and Linear Maps. 6.3. Translations. 6.4. Application: Animation. 6.5. Mapping Triangles to Triangles. 6.6. Composing Affine Maps. 6.7. Exercises. 7. Eigen Things. 7.1. Fixed Directions. 7.2. Eigenvalues. 7.3. Eigenvectors. 7.4. Striving for More Generality. 7.5. The Geometry of Symmetric Matrices and the Eigendecomposition. 7.6. Quadratic Forms. 7.7. Repeating Maps. 7.8. Exercises. 8. 3D Geometry. 8.1. From 2D to 3D. 8.2. Cross Product. 8.3. Lines. 8.4. Planes. 8.5. Scalar Triple Product. 8.6. Application: Lighting and Shading. 8.7. Exercises. 9. Linear Maps in 3D. 9.1. Matrices and Linear Maps. 9.2. Linear Spaces. 9.3. Scalings. 9.4. Reflections. 9.5 Shears. 9.6. Rotations. 9.7. Projections. 9.8. Volumes and Linear Maps: Determinants. 9.9. Combining Linear Maps. 9.10. Inverse Matrices. 9.11. Application: Mapping Normals. 9.12. More on Matrices. 9.13. Exercises. 10. Affine Maps in 3D. 10.1. Affine Maps. 10.2. Translations. 10.3. Mapping Tetrahedra. 10.4. Parallel Projections. 10.5. Homogeneous Coordinates and Perspective Maps. 10.6. Application: Building Instance Models. 10.7. Exercises. 11. Interactions in 3D. 11.1. Distance Between a Point and a Plane. 11.2. Distance Between Two Lines. 11.3. Lines and Planes: Intersections. 11.4. Intersecting a Triangle and a Line. 11.5. Reflections. 11.6. Intersecting Three Planes. 11.7. Intersecting Two Planes. 11.8. Creating Orthonormal Coordinate Systems. 11.9. Application: Camera Model. 11.10. Exercises. 12. Gauss for Linear Systems. 12.1. The Problem. 12.2. The Solution via Gauss Elimination. 12.3. Homogeneous Linear Systems. 12.4. Inverse Matrices. 12.5. LU Decomposition. 12.6. Determinants. 12.7. Least Squares. 12.8. Application: Fitting Data from a Femoral Head. 12.9. Exercises. 13. Alternative System Solvers. 13.1. The Householder Method. 13.2. Vector Norms. 13.3. Matrix Norms. 13.4. The Condition Number. 13.5. Vector Sequences. 13.6. Iterative Methods: Gauss-Jacobi and Gauss-Seidel. 13.7. Application: Mesh Smoothing. 13.8. Exercises. 14. General Linear Spaces. 14.1. Basic Properties of Linear Spaces. 14.2. Linear Maps. 14.3. Inner Products. 14.4. Gram-Schmidt Orthonormalization. 14.5. QR Decompositon. 14.6. A Gallery of Spaces. 14.7. Least Squares. 14.8. Application: Music Analysis. 14.9. Exercises. 15. Eigen Things Revisited. 15.1. The Basics Revisited. 15.2. Similarity and Diagonalization. 15.3. Quadratic Forms. 15.4. The Power Method. 15.5. Application: Google Eigenvector. 15.6. QR Algorithm. 15.7. Eigenfunctions. 15.8. Application: Inuenza Modelling. 15.9. Exercises. 16. The Singular Value Decomposition. 16.1. The Geometry of the 2 x 2 Case. 16.2. The General Case. 16.3. SVD Steps. 16.4. Singular Values and Volumes. 16.5. The Pseudoinverse. 16.6. Least Squares. 16.7. Application: Image Compression. 16.8. Principal Components Analysis. 16.9. Application: Face Authentication. 16.10. Exercises. 17. Breaking It Up: Triangles. 17.1. Barycentric Coordinates. 17.2. Affine Invariance. 17.3. Some Special Points. 17.4. 2D Triangulations. 17.5. A Data Structure. 17.6. Application: Point Location. 17.7. 3D Triangulations. 17.8. Exercises. 18. Putting Lines Together: Polylines and Polygons. 18.1 Polylines. 18.2. Polygons. 18.3. Convexity. 18.4. Types of Polygons. 18.5. Unusual Polygons. 18.6. Turning Angles and Winding Numbers. 18.7. Area. 18.8. Application: Planarity Test. 18.9. Application: Inside or Outside? 18.10. Exercises. 19. Conics. 19.1. The General Conic. 19.2. Analyzing Conics. 19.3. General Conic to Standard Position. 19.4. The Action Ellipse. 19.5. Exercises. 20. Curves. 20.1. Parametric Curves. 20.2. Properties of Bézier Curves. 20.3. The Matrix Form. 20.4. Derivatives. 20.5. Composite Curves. 20.6. The Geometry of Planar Curves. 20.7. Application: Moving along a Curve. 20.8. Exercises. A. Applications. B. Glossary. C. Selected Exercises Solutions. Bibliography.
£78.84
Taylor & Francis Ltd Methods for the Summation of Series
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£199.50
Taylor & Francis Ltd Abstract Algebra
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£87.39
Taylor & Francis Ltd Polynomials Dynamics and Choice
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Taylor & Francis Ltd Polynomials Dynamics and Choice
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Taylor & Francis Ltd Linear Models and the Relevant Distributions and Matrix Algebra
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£39.99
Taylor & Francis Ltd Multivariable Calculus with Mathematica
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Taylor & Francis Ltd The Power of Geometric Algebra Computing
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Taylor & Francis Ltd Infinite Groups
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Taylor & Francis Ltd Introduction to Traveling Waves
Book SynopsisThis book focuses on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. Table of Contents1. Nonlinear Traveling Waves. 1.1. Traveling Waves. 1.2. Reaction-Diffusion Equations. 1.3. Traveling Waves as Solutions of Reaction-Diffusion Equations. 1.4. Planar Waves. 1.5. Examples of Reaction-Diffusion Equations. 1.6. Other Partial Differential Equations that Support Waves. 2. Systems of Reaction-Diffusion Equations posed on Infinite Domains. 2.1. Systems of Reaction-Diffusion Equations. 2.2. Examples of Reaction-Diffusion Systems. 3. Existence of Fronts, Pulses, and Wavetrains. 3.1. Traveling Waves as Orbits in the Associated Dynamical Systems. 3.2. Dynamical Systems Approach: Equilibrium Points. 3.3. Existence of Fronts in Fisher-KPP Equation: Trapping Region Technique. 3.4. Existence of Fronts in Solid Fuel Combustion Model. 3.5. Wavetrains. 4. Stability of Fronts and Pulses. 4.1. Stability: Introduction. 4.2. A Heuristic Presentation of Spectral Stability for Front and Pulse Traveling Wave Solutions. 4.3. Location of the Point Spectrum. 4.4. Beyond Spectral Stability.
£87.39
Taylor & Francis Ltd Introduction to Lattice Algebra
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£99.75
Taylor & Francis Ltd An Invitation to Abstract Algebra
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£80.74
Taylor & Francis Ltd Teaching Early Algebra through ExampleBased Problem Solving
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Taylor & Francis Ltd FourDimensional Manifolds and Projective Structure
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Taylor & Francis Ltd Linear Algebra A Geometric Approach 7 Chapman HallCRC Mathematics Series
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£104.50
Taylor & Francis Ltd GammaLines On the Geometry of Real and Complex Functions Modern Analysis Series
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Taylor & Francis Ltd The Geometry of Vector Fields Routledge Revivals
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Taylor & Francis Ltd The Geometry of Vector Fields Routledge Revivals
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Taylor & Francis Ltd Extending Modules 313 Chapman HallCRC Research Notes in Mathematics Series
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Taylor & Francis Ltd A Survey of Preconditioned Iterative Methods 328 Chapman HallCRC Research Notes in Mathematics Series
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Taylor & Francis Ltd Practical Linear Algebra
Book SynopsisLinear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book's geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each top
£54.14
Taylor & Francis Ltd Invitation to Linear Algebra
Book SynopsisInvitation to Linear Algebra is an informative, clearly written, flexible textbook for instructors and students. Based on over 30 years of experience as a mathematics professor, the author invites students to develop a more informed understanding of complex algebraic concepts using innovative, easy-to-follow methods. The book is organized into lessons rather than chapters. This limits the size of the mathematical morsels that students must digest, making it easier for instructors to budget class time. Each definition is carefully explained with detailed proofs of key theorems, including motivation for each step. This makes the book more flexible, allowing instructors to choose material that reflects their and their students' interests. A larger than normal amount of exercises illustrate how linear and nonlinear algebra apply in the students' areas of study. Features<Table of ContentsMatrices and Linear Systems. Introduction to Matrices. Matrix Multiplication. Additional Topics in Matrix Algebra. Introduction to Linear Systems. The Inverse of a Matrix. Determinants. Introduction to Determinants. Properties of Determinants. Applications of Determinants. A First Look at Vector Spaces. Introduction to Vector Spaces. Subspaces of Vector Spaces. Linear Dependence and Independence. Basis and Dimension. The Rank of a Matrix. Linear Systems Revisited. More About Vector Spaces. Sums and Direct Sums of Subspaces. Quotient Spaces. Change of Basis. Euclidean Spaces. Orthonormal Bases. Linear Transformations. Introduction to Linear Transformations. Isomorphisms of Vector Spaces. The Kernel and Range of a Linear Transformation. Matrices of Linear Transformations. Similar Matrices. Matrix Diagonalization. Eigenvalues and Eigenvectors. Diagonalization of Square Matrices. Diagonalization of Symmetric Matrices. Complex Vector Spaces. Complex Vector Spaces. Unitary and Hermitian Matrices. Advanced Topics. Powers of Matrices. Functions of a Square Matrix. Matrix Power Series. Minimal Polynomials. Direct Sum Decompositions. Jordan Canonical Form. Applications. Systems of First Order Differential Equations. Stability Analysis of First Order Systems. Coupled Oscillations. Appendix. Solutions and Hints to Selected Exercises.
£43.99
Taylor & Francis Ltd Topological Methods for Differential Equations
Book SynopsisTopological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis. Table of ContentsIntroduction. 1 Background in Multi-valued Analysis. 2 Hausdor□-Pompeiu Metric Topology. 3 Measurable Multifunctions. Measurable selection. 4 Continuous Selection Theorems. 5 Linear Multivalued Operators. 6 Fixed Point Theorems. 7 Generalized Metric and Banach Spaces. 8 Fixed Point Theorems in Vector Metric and Banach Spaces. 9 Random □xed point theorem. 10 Semigroups. 11 Systems of Impulsive Di□erential Equations on the Half-line. 12 Di□erential Inclusions. 13 Random Systems of Di□erential Equations. 14 Random Fractional Di□erential Equations via Hadamard Fractional Derivatives. 15 Existence Theory for Systems of Discrete Equations. 16 Discrete Inclusions. 17 Semilinear System of Discrete Equations. 18 Discrete Boundary Value Problems. 19 Appendix.
£147.25
Taylor & Francis Ltd Introduction to Abstract Algebra Third Edition
Book SynopsisThe first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.Table of ContentsChapter One SETS AND LOGIC -- 1. Some very general remarks -- 2. Introductory remarks on sets -- 3. Statements and conditions; quantifiers -- 4. The implies sign () -- 5. Proof by contradiction -- 6. Subsets -- 7. Unions and intersections -- 8. Cartesian product of sets -- EXERCISES -- Chapter Two SOME PROPERTIES OF -- 9. Introduction -- 10. The well-ordering principle -- I I. The division algorithm -- 12. Highest common factors and Euclid’s algorithm -- 13. The fundamental theorem of arithmetic -- 14. Congruence modulo m (mE f4J) -- EXERCISES -- Chapter Three EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES -- 15. Relations in general -- 16. Equivalence relations -- 17. Equivalence classes -- 18. Congruence classes -- 19. Properties of l,, as an algebraic system -- EXERCISES -- Chapter Four MAPPINGS -- 20. Introduction -- 21. The image of a subset of the domain; surjcctions -- 22. Injections; bijections; inverse of a bijection -- 23. Restriction of a mapping -- 24. Composition of mappings -- 25. Some further results and examples on mappings -- EXERCISES -- Chapter Five SEMIGROUPS -- 26. Introduction -- 27. Binary operations -- 28. Associativity and commutativity -- 29. Semigroups: definition and examples -- 30. Powers of an element in a semigroup -- 31. Identity elements and inverses -- 32. Subsemigroups -- EXERCISES -- Chapter Six AN INTRODUCTION TO GROUPS -- 33. The definition of a group -- 34. Examples of groups -- 35. Elementary consequences of the group axioms -- 36. Subgroups -- 37. Some important general examples of subgroups -- 38. Period of an element -- 39. Cyclic groups -- EXERCISES -- Chapter Seven COSETS AND LAGRANGE’S THEOREM ON FINITE GROUPS -- 40. Introduction -- 41. Multiplication of subsets of a group -- 42. Another approach to cosets -- 43. Lagrange’s theorem -- 44. Some consequences of Lagrange’s theorem -- EXERCISES -- Chapter Eight HOMOMORPHISMS, NORMAL SUBGROUPS, AND QUOTIENT GROUPS -- 45. Introduction -- 46. Isomorphic groups -- 47. Homomorphisms and their elementary properties -- 48. Conjugacy -- 49. Normal subgroups -- 50. Quotient groups -- 51. The quotient group G/Z -- 52. The first isomorphism theorem -- EXERCISES -- Chapter Nine THE SYMMETRIC GROUP S -- 53. Introduction -- 54. Cycles -- 55. Products of disjoint cycles -- 56. Periods of elements of Sft -- 57. Conjugacy in S1 -- 58. Arrangement of the objects 1,2,...,n -- 59. The alternating character, and alternating groups -- 60. The simplicity of A5 -- EXERCISES -- Chapter Ten THE FUNDAMENTALS OF RING THEORY -- 61. Introduction -- 62. The definition of a ring and its elementary consequences -- 63. Special types of ring and ring elements -- 64. Subrings and subtIelds -- 65. Ring homomorphisms -- 66. Ideals -- 67. Principal ideals in a commutative ring with a one -- 68. Factor rings -- 69. Characteristic of an integral domain or field -- 70. The field of fractions of an integral domain -- EXERCISES -- Chapter Eleven POLYNOMIALS AND FIELDS -- 71. Introduction -- 72. Polynomial rings -- 73. Some properties of F[X], where F is a field -- 74 Generalities on factorization -- 75. Further properties of F[XJ, where F is a field -- 76. Some matters of notation -- 77. Minimal polynomials and the structure of F(c) -- 78. Some elementary properties of finite fields -- 79. Construction of fields by root adjunction -- 80. Degrees of field extensions -- 81. Epilogue -- EXERCISES -- BIBLIOGRAPHY -- APPENDIX TO EXERCISES -- INDEX.
£171.00
Taylor & Francis Ltd An Introduction to Linear Algebra
Book SynopsisThe techniques of linear algebra are used extensively across the applied sciences, and in many different areas of algebra such as group theory, module theory, representation theory, ring theory, and Galois theory. Written by experienced researchers with a decades of teaching experience, Introduction to Linear Algebra is a clear and rigorous introductory text on this key topic for students of both applied sciences and pure mathematics. Table of ContentsLinear Vector Spaces. Matrices. Determinants. Invertible Matrices. Linear Systems. LU Factorization. Linear Dependence and Independence. Bases and Dimension. Coordinates and Isomorphisms. Rank of a Matrix. Linear Mappings. Matrix Representation of Linear Mappings. Inner Products and Orthogonality. Linear Functionals. Eigenvalues and Eigenvectors. Normed Linear Spaces. Diagonalization. Singular Value Decomposition. Differential and Difference Systems. Least Squares Approximation. Quadratic Forms. Positive Definite Matrices. Moore–Penrose Inverse.Special Matrices.
£80.74
Taylor & Francis Ltd Factoring Groups into Subsets
Book SynopsisDecomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs.EncompassTrade ReviewThe book under review was written by two leading experts in this field.… The exposition is clear and detailed—it is enriched with examples and exercises—making the book, as envisioned by the authors, readily accessible to non-experts in the field.—Mathematical Reviews, Issue 2010hTable of ContentsIntroduction. New Factorizations from Old Ones. Nonperiodic Factorizations. Periodic Factorizations. Various Factorizations. Factoring by Many Factors. Group of Integers. Infinite Groups. Combinatorics. Codes. Some Classical Problems. References. Index.
£204.25
Cambridge University Press LMS 286 Clifford Algebr Spinor 2ed London
Book SynopsisIn this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The initial chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This book also gives the first comprehensive survey of recent research on Clifford algebras. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the analytic side, Brauer-Wall groups and Witt rings are discussed, and Caucy's integral formula is Trade Review'The author gives a concise but thorough introduction to spinors and Clifford algebras extending from the very beginning to present research … A very recommendable book for everyone interested in this field.' G. Kowol, Monatschefte fur Mathematik'This book sets standards in the field of quality and careful notation, especially in the relation of several kinds of spinors. It is highly recommended to teachers and researchers active in this field.' B. Fauser, Zentralblatt für Mathematik'This book cannot be underestimated in its current influence.' B. Fauser, Zentralblatt für MathematikTable of ContentsPreface; Mathematical notation; 1. Vectors and linear spaces; 2. Complex numbers; 3. Bivectors and the exterior algebra; 4. Pauli spin matrices and spinors; 5. Quaternions; 6. The fourth dimension; 7. The cross product; 8. Electromagnetism; 9. Lorentz transformations; 10. The Dirac equation; 11. Fierz identities and boomerangs; 12. Flags, poles and dipoles; 13. Tilt to the opposite metric; 14. Definitions of the Clifford algebra; 15. Witt rings and Brauer groups; 16. Matrix representations and periodicity of 8; 17. Spin groups and spinor spaces; 18. Scalar products of spinors and the chessboard; 19. Möbius transformations and Vahlen matrices; 20. Hypercomplex analysis; 21. Binary index sets and Walsh functions; 22. Chevalley's construction and characteristic 2; 23. Octonions and triality; A history of Clifford algebras; Selected reading; Index.
£53.43
Cambridge University Press Tits Buildings and the Model Theory of Groups 291 London Mathematical Society Lecture Note Series Series Number 291
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Cambridge University Press Matrix Calculus and ZeroOne Matrices
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£29.44
Cambridge University Press Polycyclic Groups 82 Cambridge Tracts in Mathematics Series Number 82
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Cambridge University Press Symbols Impossible Numbers and Geometric Entanglements
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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.
£44.32
Cambridge University Press EOM 52 Handbk Categorcl Algebra v3 Volume 3 Sheaf Theory Encyclopedia of Mathematics and its Applications Series Number 52
Book SynopsisThe Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.Trade Review" . . . these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical ReviewsTable of ContentsPreface; Introduction to the handbook; 1. Locales; 2. Sheaves; 3. Grothendieck toposes; 4. The classifying topos; 5. Elementary toposes; 6. Internal logic of a topos; 7. The law of excluded middle; 8. The axiom of infinity; 9. Sheaves in a topos; Index.
£37.99
Cambridge University Press EOM 57 Skew Fields Theory of General Division Rings Encyclopedia of Mathematics and its Applications Series Number 57
Book SynopsisBased on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in a concise form. The notes and comments at the end of each chapter provide an historical background.Trade ReviewReview of the hardback: '… the first book on this theme and will be the basis of any future development in this field.' J. Schoissengeier, Monatshefte für MathematikReview of the hardback: 'While the material is quite technical, the book is very readable.' MathematikaReview of the hardback: '… an up-to-date account.' European Mathematical Society NewsletterReview of the hardback: 'This is a tremendous piece of work, whose importance will grow for many years.' Bulletin of the London Mathematic SocietyTable of ContentsPreface; From the preface to Skew Field Constructions; Note to the reader; Prologue; 1. Rings and their fields of fractions; 2. Skew polynomial rings and power series rings; 3. Finite skew field extensions and applications; 4. Localization; 5. Coproducts of fields; 6. General skew fields; 7. Rational relations and rational identities; 8. Equations and singularities; 9. Valuations and orderings on skew fields; Standard notations; List of special notations used throughout the text; Bibliography and author index; Subject index.
£72.48
Cambridge University Press Modules and Rings
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Cambridge University Press Groups as Galois Groups
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Cambridge University Press Finite Fields 20 Encyclopedia of Mathematics and its Applications Series Number 20
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Cambridge University Press Multiplicities and Chern Classes Cambridge Tracts in Mathematics Series Number 133
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Cambridge University Press Some Applications of Modular Forms Cambridge Tracts in Mathematics Series Number 99
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Cambridge University Press Galois Theories Cambridge Studies in Advanced Mathematics Series Number 72
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£61.74