Algebra Books
Cambridge University Press Elements of the Representation Theory of Associative Algebras Volume 3 RepresentationInfinite Tilted Algebras London Mathematical Society Student Texts Series Number 72
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£55.09
Cambridge University Press Groups and Analysis The Legacy of Hermann Weyl 354 London Mathematical Society Lecture Note Series Series Number 354
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£79.10
Cambridge University Press conceptualmathematics
Book SynopsisConceptual Mathematics introduces the concept of category to beginning students and practising mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems. The expanded second edition approaches more advanced topics via historical sketches and a concise introduction to adjoint functors.Trade Review'This text, written by two experts in Category Theory and tried out carefully in courses at SUNY Buffalo, provides a simple and effective first course on conceptual mathematics.' American Mathematical Monthly'… every mathematician should know the basic ideas and techniques explained in this book …' Monatshefte für Mathematik'Conceptual Mathematics provides an excellent introductory account to categories for those who are starting from scratch. It treats material which will appear simple and familiar to many philosophers, but in an unfamiliar way.' Studies in History and Philosophy of Modern Physics'Category Theory slices across the artificial boundaries dividing algebra, arithmetic, calculus, geometry, logic, topology. If you have students you wish to introduce to the subject, I suggest this delightfully elementary book . Lawvere is one of the greatest visionaries of mathematics in the last half of the twentieth century. He characteristically digs down beneath the foundations of a concept in order to simplify its understanding. Schanuel has published research in diverse areas of Algebra, Topology, and Number Theory and is known as a great teacher. I have recommended this book to motivated high school students. I certainly suggest it for undergraduates. I even suggest it for the mathematician who needs a refresher on modern concepts.' National Association of Mathematicians Newsletter'Conceptual Mathematics is the first book to serve both as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguists, etc … The fundamental ideas are illuminated in an engaging way.' L'Enseignment MathématiqueTable of ContentsForeword; Note to the reader; Preview; Part I. The Category of Sets: 1. Sets, maps, composition; Part II. The Algebra of Composition: 2. Isomorphisms; Part III. Categories of Structured Sets: 3. Examples of categories; Part IV. Elementary Universal Mapping Properties: 4. Universal mapping properties; Part V. Higher Universal Mapping Properties: 5. Map objects; 6. The contravariant parts functor; 7. The components functor; Appendix 1. Geometry of figures and algebra of functions; Appendix 2. Adjoint functors; Appendix 3. The emergence of category theory within mathematics; Appendix 4. Annotated bibliography.
£44.64
Cambridge University Press Analysis on Lie Groups An Introduction Cambridge Studies in Advanced Mathematics Series Number 110
Book SynopsisA self-contained and elementary presentation of Lie group theory, concentrating on analysis on Lie groups. The author describes in detail many interesting examples with topics ranging from Haar measure to harmonic functions. With numerous exercises and worked examples, it's ideal for a graduate course on analysis on Lie groups.Trade Review"The main themes are carefully explained and illustrated by well-chosen examples. He succeeds in putting a remarkable wealth of material into a 300-page book which will certainly serve as a basis for many courses on the subject." Joachim Hilgert, Mathematical ReviewsTable of ContentsPreface; 1. The linear group; 2. The exponential map; 3. Linear Lie groups; 4. Lie algebras; 5. Haar measure; 6. Representations of compact groups; 7. The groups SU(2) and SO(3), Haar measure; 8. Analysis on the group SU(2); 9. Analysis on the sphere; 10. Analysis on the spaces of symmetric and Hermitian matrices; 11. Irreducible representations of the unitary group; 12. Analysis on the unitary group; Bibliography; Index.
£76.94
Cambridge University Press An Introduction to Galois Cohomology and its Applications 377 London Mathematical Society Lecture Note Series Series Number 377
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£66.68
Cambridge University Press Words Notes on Verbal Width in Groups
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£55.91
Cambridge University Press Differential Tensor Algebras and their Module Categories 362 London Mathematical Society Lecture Note Series Series Number 362
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£65.02
Cambridge University Press How to Fold It The Mathematics of Linkages Origami and Polyhedra
Book SynopsisDiscover and understand mathematical theorems through paper folding, starting with high school algebra and geometry through to more advanced concepts.Trade Review'The major theorems presented are remarkable - results that may surprise the reader include the fact that, with the right folds, any shape or collection of shapes (even ones with holes in) … composed of straight lines may be cut out from a sheet of paper with just a single cut.' London Mathematical Society Newsletter'In this beautiful and inspiring book with many colour figures the reader can find a fascinating mathematical approach to linkages, foldings and unfoldings. Many exercises with detailed solutions give the reader the chance to control the acquired skills.' Hansueli Hosli, Zentralblatt MATH'… a great book for someone who wants to learn about the mathematics behind origami without being overwhelmed by the mathematics itself. This is a great book for a high school or undergraduate student to get introduced to the open problems in computational origami.' Brittany Terese Fasy and David L. Millman, SIGACT NewsTable of ContentsPart I. Linkages: 1. Robot arms; 2. Straight-line linkages and the pantograph; 3. Protein folding and pop-up cards; Part II. Origami: 4. Flat vertex folds; 5. Fold and one-cut; 6. The shopping bag theorem; Part III. Polyhedra: 7. Durer's problem: edge unfolding; 8. Unfolding orthogonal polyhedra; 9. Folding polygons to convex polyhedra; 10. Further reading; 11. Glossary; 12. Answers to exercises; 13. Permissions and acknowledgments.
£100.70
Cambridge University Press Representations of Groups A Computational Approach 124 Cambridge Studies in Advanced Mathematics Series Number 124
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£48.44
Cambridge University Press Information Theory and Coding by Example
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£117.00
Cambridge University Press orientedmatroids
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£88.21
Cambridge University Press An Introduction to KTheory for CAlgebras 49 London Mathematical Society Student Texts Series Number 49
Book SynopsisOver the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C*-algebra. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.Trade Review'The textbook is a nice introduction to the subject preparing the ground for the study of more advanced texts.' H. Schröder, Zentralblatt für MathematikTable of ContentsPreface; 1. C*-algebra theory; 2. Projections and unitary elements; 3. The K0-group of a unital C*-algebra; 4. The functor K0; 5. The ordered Abelian group K0(A); 6. Inductive limit C*-algebras; 7. Classification of AF-algebras; 8. The functor K1; 9. The index map; 10. The higher K-functors; 11. Bott periodicity; 12. The six-term exact sequence; 13. Inductive limits of dimension drop algebras; References; Table of K-groups; Index of symbols; General index.
£111.15
Cambridge University Press Finite Group Theory Cambridge Studies in Advanced Mathematics Series Number 10
Book SynopsisFinite Group Theory develops the foundations of the theory of finite groups with an emphasis on the finite simple groups. It can serve as a text for advanced undergraduates or graduate students in mathematics and as a basic reference for research mathematicians.Trade Review'I consider this book as an extremely valuable source and help for anyone interested in a serious study of finite groups.' U. Dempwolff, Zentralblatt MATHTable of Contents1. Preliminary results; 2. Permutation representations; 3. Representations of groups on groups; 4. Linear representations; 5. Permutation groups; 6. Extensions of groups and modules; 7. Spaces with forms; 8. p-Groups; 9. Change of field of a linear representation; 10. Presentations of groups; 11. The generalized Fitting subgroup; 12. Linear representations of finite groups; 13. Transfer and fusion; 14. The geometry of groups of Lie type; 15. Signalizer functors; 16. Finite simple groups.
£41.79
Cambridge University Press Computational and Geometric Aspects of Modern Algebra 275 London Mathematical Society Lecture Note Series Series Number 275
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£61.71
Cambridge University Press Topics in Symbolic Dynamics and Applications 279 London Mathematical Society Lecture Note Series Series Number 279
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£58.40
Cambridge University Press AuslanderBuchweitz Approximations of Equivariant Modules 282 London Mathematical Society Lecture Note Series Series Number 282
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£61.71
Cambridge University Press Random Matrix Models and their Applications
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£122.55
Cambridge University Press Galois Theories 72 Cambridge Studies in Advanced Mathematics Series Number 72
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£122.55
Cambridge University Press Continuous Lattices and Domains 93 Encyclopedia of Mathematics and its Applications Series Number 93
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£194.75
Cambridge University Press Matrix Calculus and ZeroOne Matrices
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£95.00
Cambridge University Press Galois Groups and Fundamental Groups
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£133.95
Cambridge University Press Algebraic Combinatorics on Words 90 Encyclopedia of Mathematics and its Applications Series Number 90
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£133.95
Cambridge University Press Algebra and Geometry
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£90.24
Cambridge University Press New Directions in Hopf Algebras
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£133.95
Cambridge University Press QuasiFrobenius Rings 158 Cambridge Tracts in Mathematics Series Number 158
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£105.45
Cambridge University Press Codes Cryptology and Curves with Computer Algebra
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£145.35
Cambridge University Press Concrete Abstract Algebra
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£104.50
Cambridge University Press Trends in Commutative Algebra
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£105.45
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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£105.45
Cambridge University Press Exploratory Galois Theory
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£94.99
Cambridge University Press Lévy Processes in Lie Groups
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£90.99
Cambridge University Press Spectral Generalizations of Line Graphs On Graphs with Least Eigenvalue 2 314 London Mathematical Society Lecture Note Series Series Number 314
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£65.86
Cambridge University Press An Introduction to Noncommutative Noetherian Rings 61 London Mathematical Society Student Texts Series Number 61
An Introduction to Noncommutative Noetherian | BookCurl
£93.09
Cambridge University Press Linear and Projective Representations of Symmetric Groups 163 Cambridge Tracts in Mathematics Series Number 163
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£105.45
Cambridge University Press Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings 161 Cambridge Tracts in Mathematics Series Number 161
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£105.45
Cambridge University Press Symmetry Studies An Introduction to the Analysis of Structured Data in Applications 26 Cambridge Series in Statistical and Probabilistic Mathematics Series Number 26
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£56.99
Cambridge University Press Free Ideal Rings and Localization in General Rings
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£151.05
Cambridge University Press Algebraic Statistics for Computational Biology
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£75.04
Cambridge University Press Symmetric Generation of Groups With Applications to many of the Sporadic Finite Simple Groups 111 Encyclopedia of Mathematics and its Applications Series Number 111
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£105.45
Cambridge University Press Combinatorial Matrix Classes
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£151.05
Cambridge University Press Purity Spectra and Localisation 121 Encyclopedia of Mathematics and its Applications Series Number 121
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£175.75
Cambridge University Press Forcing Idealized 174 Cambridge Tracts in Mathematics Series Number 174
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£105.45
Cambridge University Press Enumeration of Finite Groups 173 Cambridge Tracts in Mathematics Series Number 173
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£105.45
Cambridge University Press Kazhdans Property T 11 New Mathematical Monographs Series Number 11
Book SynopsisProperty (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).Table of ContentsIntroduction; Part I. Kazhdan's Property (T): 1. Property (T); 2. Property (FH); 3. Reduced Cohomology; 4. Bounded generation; 5. A spectral criterion for Property (T); 6. Some applications of Property (T); 7. A short list of open questions; Part II. Background on Unitary Representations: A. Unitary group representations; B. Measures on homogeneous spaces; C. Functions of positive type; D. Representations of abelian groups; E. Induced representations; F. Weak containment and Fell topology; G. Amenability; Appendix; Bibliography; List of symbols; Index.
£133.95
Cambridge University Press An Introduction to Lie Groups and Lie Algebras Cambridge Studies in Advanced Mathematics Series Number 113
Book SynopsisWith roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York, Stony Brook, the book includes numerous exercises and worked examples, and is ideal for graduate courses on Lie groups and Lie algebras.Trade Review'… the exposition is very clear and logical. It has the advantage of giving the basic facts about Lie algebra theory with enough arguments but skipping the tedious technical details of proofs. Another excellent feature of the book is that many of the basic notions, properties and results are illustrated by a great number of exercises and examples. In my opinion this book is a nice addition to the landmarks in the field … I strongly recommend it to anyone wishing to enter into the beautiful and exciting field of Lie algebras and their applications.' Journal of Geometry and Symmetry in Physics'… very readable … I strongly recommend this book as a possible selection for graduate courses, as well as for independent study, or individual reading.' MAA Reviews'There are many exercises … The last appendix contains a useful detailed sample syllabus for a one-semester graduate course (two lectures a week).' EMS Newsletter'The book is a very concise and nice introduction to Lie groups and Lie algebras. It seems to be well suited for a course on the subject.' Mathematical ReviewsTable of ContentsPreface; 1. Introduction; 2. Lie groups: basic definitions; 3. Lie groups and Lie algebras; 4. Representations of Lie groups and Lie algebras; 5. Structure theory of Lie algebras; 6. Complex semisimple Lie algebras; 7. Root systems; 8. Representations of semisimple Lie Algebras; Overview of the literature; A. Root systems and simple Lie algebras; B. Sample syllabus; List of notation; Index; Bibliography.
£71.24
Cambridge University Press Stable Domination and Independence in Algebraically Closed Valued Fields 30 Lecture Notes in Logic Series Number 30
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£95.95
Cambridge University Press Group Theory
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£71.24
Cambridge University Press Algebraic Number Theory for Beginners
Book SynopsisThis book introduces algebraic number theory through the problem of generalizing ''unique prime factorization'' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind''s concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.Trade Review'In Algebraic Number Theory for Beginners, John Stillwell once again displays his remarkable talent for using the history of mathematics to motivate and explore even the most abstract mathematical concepts at an accessible, undergraduate level. This book is another gem of the genre Stillwell has done so much to enhance.' Karen Hunger Parshall, University of Virginia'Stillwell, more than any author I know, helps us understand mathematics from its roots. In this book, he leads us into algebraic number theory along a historical route from concrete to abstract. In doing so, Stillwell makes a strong pedagogical case for flipping a typical algebraic number theory course — that students will understand number theory better if questions about numbers come before and throughout the abstract theory of rings and ideals. The treatments of mathematics and its history are crystal clear and meticulous. Stillwell's text is particularly well-suited for an advanced undergraduate or early graduate-level course in number theory. Experts also will find this text to be an incredible resource for its historical approach and well-motivated exercises. Stillwell has written another gem, this time for readers interested in number theory, abstract algebra, and their intertwined history.' Martin Weissman, University of California, Santa CruzTable of ContentsPreface; 1. Euclidean arithmetic; 2. Diophantine arithmetic; 3. Quadratic forms; 4. Rings and fields; 5. Ideals; 6. Vector spaces; 7. Determinant theory; 8. Modules; 9. Ideals and prime factorization; References; Index.
£29.99