{"title":"Encyclopaedia Of Mathematical Sciences","description":"\u003cp\u003eDelve into the depths of mathematical understanding with this comprehensive collection. From algebra to geometry, discover essential theories and applications, perfect for students and researchers alike.\u003c\/p\u003e","products":[{"product_id":"topology-ii-book-db-fuchs-9783540519966","title":"Topology II","description":"to Homotopy Theory O. Ya. Viro, D. B. Fuchs Translated from the Russian by C. J. Shaddock Contents Chapter 1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 § 1. Terminology and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 1. Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. Logical Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 3. Topological Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 4. Operations on Topological Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5. Operations on Pointed Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 §2. Homotopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2. 1. Homotopies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 10 2. 2. Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2. 3. Homotopy as a Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2. 4. Homotopy Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2. 5. Retractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2. 6. Deformation Retractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2. 7. Relative Homotopies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2. 8. k-connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2. 9. Borsuk Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2. 10. CNRS Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2. 11. Homotopy Properties of Topological Constructions . . . . . . . . . . . 15 2. 12. Natural Group Structures on Sets of Homotopy Classes . . . . . . . . 16 §3. Homotopy Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3. 1. Absolute Homotopy Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 O. Ya. Viro, D. B. Fuchs 3. 2. Digression: Local Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3. 3. Local Systems of Homotopy Groups of a Topological Space . . . . 23 3. 4. Relative Homotopy Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3. 5. The Homotopy Sequence of a Pair . . . . . . . . . . . . . . . . . . . . . . . . . 28 3. 6. Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3. 7. The Homotopy Sequence of a Triple . . . . . . . . . . . . . . . . . . . . . . . 32 Chapter 2. Bundle Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 33 §4. Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4. 1. General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4. 2. Locally Trivial Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4. 3. Serre Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4. 4. Bundles of Spaces of Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 §5. Bundles and Homotopy Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5. 1. The Local System of Homotopy Groups of the Fibres of a Serre Bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51060978974993,"sku":"NIN9783540519966","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52487239106833,"sku":"NLS9783540519966","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540519963.jpg?v=1751096381"},{"product_id":"topology-i-book-sp-novikov-9783540170075","title":"Topology I","description":"Introduction In the present essay, we attempt to convey some idea of the skeleton of topology, and of various topological concepts. It must be said at once that, apart from the necessary minimum, the subject-matter of this survey does not indude that subdiscipline known as \"general topology\" - the theory of general spaces and maps considered in the context of set theory and general category theory. (Doubtless this subject will be surveyed in detail by others. ) With this qualification, it may be daimed that the \"topology\" dealt with in the present survey is that mathematieal subject whieh in the late 19th century was called Analysis Situs, and at various later periods separated out into various subdisciplines: \"Combinatorial topology\", \"Algebraic topology\", \"Differential (or smooth) topology\", \"Homotopy theory\", \"Geometrie topology\". With the growth, over a long period of time, in applications of topology to other areas of mathematics, the following further subdisciplines crystallizedout: the global calculus of variations, global geometry, the topology of Lie groups and homogeneous spaces, the topology of complex manifolds and alge­ braic varieties, the qualitative (topologieal) theory of dynamical systems and foliations, the topology of elliptic and hyperbolic partial differential equations. Finally, in the 1970s and 80s, a whole complex of applications of topologie al methods was made to problems of modern physiesj in fact in several instances it would have been impossible to understand the essence of the real physical phenomena in question without the aid of concepts from topology.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061024555281,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061027143953,"sku":"NIN9783540170075","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333468680465,"sku":"NLS9783540170075","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540170073.jpg?v=1751189939"},{"product_id":"general-topology-ii-book-a-v-arhangel-skii-9783642770326","title":"General Topology II","description":"Compactness is related to a number of fundamental concepts of mathemat­ ics. Particularly important are compact Hausdorff spaces or compacta. Com­ pactness appeared in mathematics for the first time as one of the main topo­ logical properties of an interval, a square, a sphere and any closed, bounded subset of a finite dimensional Euclidean space. Once it was realized that pre­ cisely this property was responsible for a series of fundamental facts related to those sets such as boundedness and uniform continuity of continuous func­ tions defined on them, compactness was given an abstract definition in the language of general topology reaching far beyond the class of metric spaces. This immensely extended the realm of application of this concept (including in particular, function spaces of quite general nature). The fact, that general topology provided an adequate language for a description of the concept of compactness and secured a natural medium for its harmonious development is a major credit to this area of mathematics. The final formulation of a general definition of compactness and the creation of the foundations of the theory of compact topological spaces are due to P.S. Aleksandrov and Urysohn (see Aleksandrov and Urysohn (1971)).","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51061030682897,"sku":"NIN9783642770326","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52622618525969,"sku":"NLS9783642770326","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642770320.jpg?v=1751221993"},{"product_id":"general-topology-i-book-av-arkhangel-skii-9783642647673","title":"General Topology I","description":"First encyclopedia volume on topology, based on a highly successful Russian edition. The book is both nov- el enough to appeal to the professional mathematician and accessible enough for students to use as an introductory textbook.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51061125710097,"sku":"NIN9783642647673","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52617503539473,"sku":"NLS9783642647673","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642647677.jpg?v=1751350781"},{"product_id":"algebraic-geometry-v-book-an-parshin-9783642082603","title":"Algebraic Geometry V","description":"The aim of this survey, written by V.A. Iskovskikh and Yu.G. Prokhorov, is to provide an exposition of the structure theory of Fano varieties, i.e. algebraic vareties with an ample anticanonical divisor. Such varieties naturally appear in the birational classification of varieties of negative Kodaira dimension, and they are very close to rational ones. This EMS volume covers different approaches to the classification of Fano varieties such as the classical Fano-Iskovskikh \"double projection\" method and its modifications, the vector bundles method due to S. Mukai, and the method of extremal rays. The authors discuss uniruledness and rational connectedness as well as recent progress in rationality problems of Fano varieties. The appendix contains tables of some classes of Fano varieties.    This book will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51067289043217,"sku":"NIN9783642082603","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481144062225,"sku":"NLS9783642082603","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642082602.jpg?v=1751000255"},{"product_id":"geometry-i-book-rv-gamkrelidze-9783540519997","title":"Geometry I","description":"Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes. In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geomerty. The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators. Several of the topics are approaches which are now enjoying a resurgence, e.g. G-structures and contact geometry. As an overview of the major current methods of differential geometry, EMS 28 is a map of these different ideas which explains the interesting points at every stop. The authors' intention is that the reader should gain a new understanding of geometry from the process of reading this survey.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51630514176273,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51630516470033,"sku":"NGR9783540519997","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52410017546513,"sku":"NLS9783540519997","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761657966865,"sku":"NIN9783540519997","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540519998.jpg?v=1751221355"},{"product_id":"modular-invariant-theory-book-hea-eddy-campbell-9783642266805","title":"Modular Invariant Theory","description":"This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers-an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52120827265297,"sku":"NLS9783642266805","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642266805.jpg?v=1757427457"},{"product_id":"analysis-iv-book-vg-maz-ya-9783642634918","title":"Analysis IV","description":"A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integralequations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52124849013009,"sku":"NLS9783642634918","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642634918.jpg?v=1757459708"},{"product_id":"dynamical-systems-x-book-victor-v-kozlov-9783540422075","title":"Dynamical Systems X","description":"The English teach mechanics as an experimental science, while on the Continent, it has always been considered a more deductive and a priori science. Unquestionably, the English are right. * H. Poincare, Science and Hypothesis Descartes, Leibnitz, and Newton As is well known, the basic principles of dynamics were stated by New­ ton in his famous work Philosophiae Naturalis Principia Mathematica, whose publication in 1687 was paid for by his friend, the astronomer Halley. In essence, this book was written with a single purpose: to prove the equivalence of Kepler's laws and the assumption, suggested to Newton by Hooke, that the acceleration of a planet is directed toward the center of the Sun and decreases in inverse proportion to the square of the distance between the planet and the Sun. For this, Newton needed to systematize the principles of dynamics (which is how Newton's famous laws appeared) and to state the \"theory of fluxes\" (analysis of functions of one variable). The principle of the equality of an action and a counteraction and the inverse square law led Newton to the theory of gravitation, the interaction at a distance. In addition, New­ ton discussed a large number of problems in mechanics and mathematics in his book, such as the laws of similarity, the theory of impact, special vari­ ational problems, and algebraicity conditions for Abelian integrals. Almost everything in the Principia subsequently became classic. In this connection, A. N.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52125536878865,"sku":"NLS9783540422075","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540422075.jpg?v=1757466290"},{"product_id":"partial-differential-equations-iv-book-yuv-egorov-9783540533634","title":"Partial Differential Equations IV","description":"In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52125694591249,"sku":"NLS9783540533634","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540533634.jpg?v=1757467768"},{"product_id":"invariants-of-homology-3-spheres-book-nikolai-saveliev-9783540437963","title":"Invariants of Homology 3-Spheres","description":"Homology 3-sphere is a closed 3-dimensional manifold whose homology equals that of the 3-sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered are constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, including invariants of Walker and Lescop, Herald and Lin invariants of knots, and equivariant Casson invariants, Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. It will be appealing to both graduate students and researchers in mathematics and theoretical physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52127311692049,"sku":"NLS9783540437963","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540437963.jpg?v=1757485492"},{"product_id":"introduction-to-complex-analysis-book-em-chirka-9783540630050","title":"Introduction to Complex Analysis","description":"In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. it will be an invaluable reference and a companion to modern courses on several complex variables.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52130155954449,"sku":"NLS9783540630050","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540630050.jpg?v=1757502413"},{"product_id":"partial-differential-equations-ix-book-ms-agranovich-9783540570448","title":"Partial Differential Equations IX","description":"This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS  63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered.  The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52130277032209,"sku":"NLS9783540570448","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540570448.jpg?v=1757503185"},{"product_id":"functional-analysis-i-book-yui-lyubich-9783540505846","title":"Functional Analysis I","description":"Up to a certain time the attention of mathematicians was concentrated on the study of individual objects, for example, specific elementary functions or curves defined by special equations. With the creation of the method of Fourier series, which allowed mathematicians to work with 'arbitrary' functions, the individual approach was replaced by the 'class' approach, in which a particular function is considered only as an element of some 'function space'. More or less simultane- ously the development of geometry and algebra led to the general concept of a linear space, while in analysis the basic forms of convergence for series of functions were identified: uniform, mean square, pointwise and so on. It turns out, moreover, that a specific type of convergence is associated with each linear function space, for example, uniform convergence in the case of the space of continuous functions on a closed interval. It was only comparatively recently that in this connection the general idea of a linear topological space (L TS)l was formed; here the algebraic structure is compatible with the topological structure in the sense that the basic operations (addition and multiplication by a scalar) are continuous.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52131533062417,"sku":"NLS9783540505846","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540505846.jpg?v=1757510944"},{"product_id":"algebraic-transformation-groups-and-algebraic-varieties-book-vladimir-leonidovich-popov-9783540208389","title":"Algebraic Transformation Groups and Algebraic Varieties","description":"The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52131946266897,"sku":"NLS9783540208389","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540208389.jpg?v=1757513869"},{"product_id":"basic-notions-of-algebra-book-igor-r-shafarevich-9783642425165","title":"Basic Notions of Algebra","description":"§22. K-theory 230 A. Topological X-theory 230 Vector bundles and the functor Vec(X). Periodicity and the functors KJX). K(X) and t the infinite-dimensional linear group. The symbol of an elliptic differential operator. The index theorem. B. Algebraic K-theory 234 The group of classes of projective modules. K , K and K of a ring. K of a field and o l n 2 its relations with the Brauer group. K-theory and arithmetic. Comments on the Literature 239 References 244 Index of Names 249 Subject Index 251 Preface This book aims to present a general survey of algebra, of its basic notions and main branches. Now what language should we choose for this? In reply to the question 'What does mathematics study?', it is hardly acceptable to answer 'structures' or 'sets with specified relations'; for among the myriad conceivable structures or sets with specified relations, only a very small discrete subset is of real interest to mathematicians, and the whole point of the question is to understand the special value of this infinitesimal fraction dotted among the amorphous masses. In the same way, the meaning of a mathematical notion is by no means confined to its formal definition; in fact, it may be rather better expressed by a (generally fairly small) sample of the basic examples, which serve the mathematician as the motivation and the substantive definition, and at the same time as the real meaning of the notion.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52132003643665,"sku":"NLS9783642425165","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642425165.jpg?v=1757514334"},{"product_id":"theory-of-operator-algebras-ii-book-masamichi-takesaki-9783540429142","title":"Theory of Operator Algebras II","description":"Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52132127965457,"sku":"NLS9783540429142","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540429142.jpg?v=1757515207"},{"product_id":"graphs-on-surfaces-and-their-applications-book-sergei-k-lando-9783540002031","title":"Graphs on Surfaces and Their Applications","description":"Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of \"dessins d'enfants\"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52134946242833,"sku":"NLS9783540002031","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540002031.jpg?v=1757546135"},{"product_id":"homological-algebra-book-si-gelfand-9783540653783","title":"Homological Algebra","description":"This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52136917795089,"sku":"NLS9783540653783","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":53609882845457,"sku":"GOR014979746","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540653783.jpg?v=1757555717"},{"product_id":"computational-invariant-theory-book-harm-derksen-9783662569214","title":"Computational Invariant Theory","description":"Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision.The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52137115779345,"sku":"NLS9783662569214","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662569214.jpg?v=1757556805"},{"product_id":"theory-of-operator-algebras-i-book-m-takesaki-9783540422488","title":"Theory of Operator Algebras I","description":"Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects. The book's unifying theme is the Banach space duality for operator algebras. This allows the reader to recognize the affinity between operator algebras and measure theory on locally compact spaces. Very technical sections are clearly labeled and there are extensive comments by the author, a good historical background and excercises. This book is part of the subseries of the EMS on Operator Algebras and Non-Commutative Geometry.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52138681630993,"sku":"NLS9783540422488","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540422488.jpg?v=1757564430"},{"product_id":"geometry-ii-book-eb-vinberg-9783642080869","title":"Geometry II","description":"A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory - a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52142130495761,"sku":"NLS9783642080869","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642080869.jpg?v=1757579356"},{"product_id":"commutative-harmonic-analysis-i-book-vp-khavin-9783540181804","title":"Commutative Harmonic Analysis I","description":"This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics. The fundamental nature of this subject, however, has been determined so long ago, that unlike in other volumes of this publication, we have to start with simple notions which have been in constant use in mathematics and physics. Planning the series as a whole, we have assumed that harmonic analysis is based on a small number of axioms, simply and clearly formulated in terms of group theory which illustrate its sources of ideas. However, our subject cannot be completely reduced to those axioms. This part of mathematics is so well developed and has so many different sides to it that no abstract scheme is able to cover its immense concreteness completely. In particular, it relates to an enormous stock of facts accumulated by the classical trigonometric harmonic analysis. Moreover, subjected to a general mathematical tendency of integration and diffusion of conventional intersubject borders, harmonic analysis, in its modem form, more and more rests on non-translation invariant constructions. For example, one ofthe most signifi- cant achievements of latter decades, which has substantially changed the whole shape of harmonic analysis, is the penetration in this subject of subtle techniques of singular integral operators.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52143088501009,"sku":"NLS9783540181804","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540181804.jpg?v=1757582932"},{"product_id":"lie-groups-and-lie-algebras-i-book-vv-gorbatsevich-9783540612223","title":"Lie Groups and Lie Algebras I","description":"Its first part, which is written by Onishchik and Vinberg, is an introduction to the theory of Lie groups and Lie algebras. The second more advanced part by Gorbatsevich and Onishchik deals with Lie transformation groups and covers the work of the last decades including the most recent research results. The book is written for graduate students and researchers in mathematics and theoretical physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52147356533009,"sku":"NLS9783540612223","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540612223.jpg?v=1757600270"},{"product_id":"dynamical-systems-v-book-vi-arnold-9783540181736","title":"Dynamical Systems V","description":"Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to hot topics, such as the characterization of personalities and the difference between a genius and a maniac. Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52147487211793,"sku":"NLS9783540181736","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540181736.jpg?v=1757600679"},{"product_id":"surfaces-in-4-space-book-scott-carter-9783540210405","title":"Surfaces in 4-Space","description":"Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included.      This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case.      As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52148217151761,"sku":"NLS9783540210405","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540210405.jpg?v=1757602951"},{"product_id":"dynamical-systems-vii-book-vi-arnol-d-9783540181767","title":"Dynamical Systems VII","description":"This book is another volume in the successful subseries \"Dynamical Systems\" of the Encyclopaedia of Mathematical Sciences. It focuses on new developments in the field of integrable systems and it provides a unique and comprehensive survey on new differential geometric and Lie-algebraic methods. Since other literature on these topics is often rather unreadable, this volume will be an indispensable guide to the current research which no mathematician or theoretical physicist who is interested in this field can do without.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52148700217617,"sku":"NLS9783540181767","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540181767.jpg?v=1757604378"},{"product_id":"mathematical-aspects-of-classical-and-celestial-mechanics-book-vladimir-i-arnold-9783540282464","title":"Mathematical Aspects of Classical and Celestial Mechanics","description":"In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the working apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52151339974929,"sku":"NLS9783540282464","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540282464.jpg?v=1757613013"},{"product_id":"geometry-v-book-robert-osserman-9783540605232","title":"Geometry V","description":"Few people outside of mathematics are aware of the varieties of mathemat- ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas- ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52151423205649,"sku":"NLS9783540605232","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540605232.jpg?v=1757613295"},{"product_id":"operator-algebras-book-bruce-blackadar-9783540284864","title":"Operator Algebras","description":"This volume attempts to give a comprehensive discussion of the theory of operator algebras (C*-algebras and von Neumann algebras. ) The volume is intended to serve two purposes: to record the standard theory in the Encyc- pedia of Mathematics, and to serve as an introduction and standard reference for the specialized volumes in the series on current research topics in the subject. Since there are already numerous excellent treatises on various aspects of thesubject,howdoesthisvolumemakeasigni?cantadditiontotheliterature, and how does it di?er from the other books in the subject? In short, why another book on operator algebras? The answer lies partly in the ?rst paragraph above. More importantly, no other single reference covers all or even almost all of the material in this volume. I have tried to cover all of the main aspects of “standard” or “clas- cal” operator algebra theory; the goal has been to be, well, encyclopedic. Of course, in a subject as vast as this one, authors must make highly subjective judgments as to what to include and what to omit, as well as what level of detail to include, and I have been guided as much by my own interests and prejudices as by the needs of the authors of the more specialized volumes.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52151674536209,"sku":"NLS9783540284864","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761648988433,"sku":"NIN9783540284864","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540284864.jpg?v=1757614148"},{"product_id":"projective-duality-and-homogeneous-spaces-book-evgueni-a-tevelev-9783540228981","title":"Projective Duality and Homogeneous Spaces","description":"Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event.   Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry.    This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52327412891921,"sku":"NLS9783540228981","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761654165777,"sku":"NIN9783540228981","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540228981.jpg?v=1758062415"},{"product_id":"several-complex-variables-ii-book-gm-khenkin-9783642633911","title":"Several Complex Variables II","description":"Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten- tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52331019370769,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52331019862289,"sku":"NLS9783642633911","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642633911.jpg?v=1758147109"},{"product_id":"commutative-harmonic-analysis-iii-book-vp-havin-9783642633805","title":"Commutative Harmonic Analysis III","description":"The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis. Such operations are widely used in mathematical physics and the theory of differential equations, where the ideas of generalized func- tions first arose, in other areas of analysis and beyond. The point of departure for this theory is to regard a function not as a mapping of point sets, but as a linear functional defined on smooth densi- ties. This route leads to the loss of the concept of the value of function at a point, and also the possibility of multiplying functions, but it makes it pos- sible to perform differentiation an unlimited number of times. The space of generalized functions of finite order is the minimal extension of the space of continuous functions in which coordinate differentiations are defined every- where. In this sense the theory of generalized functions is a development of all of classical analysis, in particular harmonic analysis, and is to some extent the perfection of it. The more general theories of ultradistributions or gener- alized functions of infinite order make it possible to consider infinite series of generalized derivatives of continuous functions.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52331053875473,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52331054563601,"sku":"NLS9783642633805","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642633805.jpg?v=1758147210"},{"product_id":"several-complex-variables-v-book-gm-khenkin-9783642634338","title":"Several Complex Variables V","description":"This volume of the Encyclopaedia contains three contributions in the field of complex analysis. The topics treated are mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. The latter two have strong links with quantum field theory and the theory of general relativity. In fact, the mathematical results described inthe book arose from the need of physicists to find a sound mathematical basis for their theories. The authors present their material in the formof surveys which provide up-to-date accounts of current research. The book will be immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theoryand general relativity.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52331244978449,"sku":"NLS9783642634338","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761837928721,"sku":"NIN9783642634338","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642634338.jpg?v=1758147800"},{"product_id":"partial-differential-equations-v-book-mv-fedoryuk-9783642635861","title":"Partial Differential Equations V","description":"In this paper we shall discuss the construction of formal short-wave asymp- totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to surmise what the correct ansiitze are for the general solution.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52331295605009,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52331296489745,"sku":"NLS9783642635861","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642635861.jpg?v=1758147961"},{"product_id":"partial-differential-equations-iii-book-youri-egorov-9783642634901","title":"Partial Differential Equations III","description":"The mathematics in this volume of the Encyclopaedia, the third in the subseries on PDEs, is more advanced than that in EMS 30 (PDE I). The reader should already be familiar with what is found in that volume. EMS 32 covers in detail two very important topics in PDE: the Cauchy problem and the qualitative theory of second order linear equations. It should be of interest to advanced students and researchers in mathematics and to scientists in neighboring fields with strong mathematical backgrounds.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52331296227601,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52331296686353,"sku":"NLS9783642634901","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642634901.jpg?v=1758147963"},{"product_id":"commutative-harmonic-analysis-ii-book-vp-havin-9783642638008","title":"Commutative Harmonic Analysis II","description":"Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52331685773585,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52331686330641,"sku":"NLS9783642638008","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642638008.jpg?v=1758149122"},{"product_id":"linear-algebraic-monoids-book-lex-e-renner-9783642063497","title":"Linear Algebraic Monoids","description":"This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52332741951761,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52332742639889,"sku":"NLS9783642063497","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642063497.jpg?v=1758152563"},{"product_id":"standard-monomial-theory-book-v-lakshmibai-9783642095436","title":"Standard Monomial Theory","description":"Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitous - they have been intensively studied over the last fifty years, from many different points of view.   This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory and standard monomial theory for Schubert varieties in certain special flag varieties. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52332880986385,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52332881379601,"sku":"NLS9783642095436","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642095436.jpg?v=1758152984"},{"product_id":"theory-of-operator-algebras-iii-book-masamichi-takesaki-9783540429135","title":"Theory of Operator Algebras III","description":"to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. A factor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52333617873169,"sku":"NLS9783540429135","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540429135.jpg?v=1758155320"},{"product_id":"lie-groups-and-lie-algebras-iii-book-a-l-onishchik-9783540546832","title":"Lie Groups and Lie Algebras III","description":"The book contains a comprehensive account of the structure and classification of Lie groups and finite-dimensional Lie algebras (including semisimple, solvable, and of general type). In particular, a modern approach to the description of automorphisms and gradings of semisimple Lie algebras is given. A special chapter is devoted to models of the exceptional Lie algebras. The book contains many tables and will serve as a reference. At the same time many results are accompanied by short proofs. Onishchik and Vinberg are internationally known specialists in their field and well-known for their monograph Lie Groups and Algebraic Groups (Springer-Verlag 1990). This Encyclopaedia volume will be immensely useful to graduate students in differential geometry, algebra and theoretical physics.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52333748617489,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333752058129,"sku":"NLS9783540546832","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540546832.jpg?v=1758155562"},{"product_id":"algebraic-quotients-torus-actions-and-cohomology-the-adjoint-representation-and-book-a-bialynicki-birula-9783540432111","title":"Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action","description":"This is the second volume of the new subseries Invariant Theory and Algebraic Transformation Groups. The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52333899972881,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333900988689,"sku":"NLS9783540432111","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540432111.jpg?v=1758155710"},{"product_id":"partial-differential-equations-vi-book-yuv-egorov-9783540546788","title":"Partial Differential Equations VI","description":"This volume of the EMS contains three contributions covering topics in the field of partial differential equations. All the authors are well-known researchers and they present their material as accessible surveys, enabling readers to find comprehensive coverage of results which are scattered throughout the literature. For this reason the book is a unique source of information. It forms part of a multi-volume subseries of the EMS devoted to partial differential equations and it will be very useful to graduate students and researchers in mathematics and theoretical physics as well as engineers who are interested in this subject.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52401925030161,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52401925652753,"sku":"NLS9783540546788","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540546788.jpg?v=1758756205"},{"product_id":"several-complex-variables-iii-book-gm-khenkin-9783642647857","title":"Several Complex Variables III","description":"We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space  1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n\u0026gt; 1 there exist several different natural ways of exhausting the space","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52405283389713,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52405284241681,"sku":"NLS9783642647857","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642647857.jpg?v=1758766610"},{"product_id":"control-theory-from-the-geometric-viewpoint-book-andrei-a-agrachev-9783540210191","title":"Control Theory from the Geometric Viewpoint","description":"This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com- pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for free will in this fatalistic world, then we come to control systems. We do so by allowing certain param- eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems  Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi- nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52414520819985,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52414521639185,"sku":"NLS9783540210191","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540210191.jpg?v=1758842756"},{"product_id":"partial-differential-equations-ii-book-yuv-egorov-9783540520016","title":"Partial Differential Equations II","description":"This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52423690649873,"sku":"NLS9783540520016","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540520016.jpg?v=1759149480"},{"product_id":"complex-analysis-i-book-aa-gonchar-9783540547037","title":"Complex Analysis I","description":"This book contains two surveys on important topics in complex analysis. It addresses graduate students and researchers in complex analysis.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52423695171857,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52423695663377,"sku":"NLS9783540547037","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540547037.jpg?v=1759149497"},{"product_id":"dynamical-systems-ix-book-dv-anosov-9783540570431","title":"Dynamical Systems IX","description":"This volume is devoted to the hyperbolic theory of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra- jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less significant subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are sufficiently many such trajectories and the phase space is compact, then although they tend to diverge from one another as it were, they have nowhere to go and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about chaos in such situations. ) This type of be- haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter- 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52423961870609,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52423962525969,"sku":"NLS9783540570431","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540570431.jpg?v=1759150359"},{"product_id":"algebraic-theory-of-locally-nilpotent-derivations-book-gene-freudenburg-9783642067327","title":"Algebraic Theory of Locally Nilpotent Derivations","description":"But, in the further development of a branch of mathematics, the human mind, encouraged by the success of its solutions, becomes conscious of its independence. It evolves from itself alone, often without appreciable in?uence from without, by means of logical combination, generalization, specialization, by separating and collecting ideas in fortunate new ways, new and fruitful problems, and appears then itself as the real questioner. David Hilbert, Mathematical Problems Thestudyoflocallynipotentderivationsand G -actionshasrecentlyemerged a from the long shadows of other branches of mathematics, branches whose provenance is older and more distinguished. The subject grew out of the rich environment of Lie theory, invariant theory, and di?erential equations, and continues to draw inspiration from these and other ?elds. At the heart of the present exposition lie sixteen principles for locally nilpotent derivations, laid out in Chapter 1. These provide the foundation upon which the subsequent theory is built. As a rule, we would like to dist- guish which properties of a locally nilpotent derivation are due to its being a derivation, and which are special to the condition locally nilpotent. Thus, we ?rst consider general properties of derivations. The sixteen First Principles which follow can then be seen as belonging especially to the locally nilpotent derivations.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52424977580305,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52424978235665,"sku":"NLS9783642067327","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642067327.jpg?v=1759153493"},{"product_id":"analysis-iii-book-s-m-nikol-skii-9783540518662","title":"Analysis III","description":"In the Part at hand the authors undertake to give a presentation of the historical development of the theory of imbedding of function spaces, of the internal as well as the externals motives which have stimulated it, and of the current state of art in the field, in particular, what regards the methods employed today. The impossibility to cover all the enormous material connected with these questions inevitably forced on us the necessity to restrict ourselves to a limited circle of ideas which are both fundamental and of principal interest. Of course, such a choice had to some extent have a subjective character, being in the first place dictated by the personal interests of the authors. Thus, the Part does not constitute a survey of all contemporary questions in the theory of imbedding of function spaces. Therefore also the bibliographical references given do not pretend to be exhaustive; we only list works mentioned in the text, and a more complete bibliography can be found in appropriate other monographs. O.V. Besov, v.1. Burenkov, P.1. Lizorkin and V.G. Maz'ya have graciously read the Part in manuscript form. All their critical remarks, for which the authors hereby express their sincere thanks, were taken account of in the final editing of the manuscript.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52425018310929,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52425018933521,"sku":"NLS9783540518662","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540518662.jpg?v=1759153616"}],"url":"https:\/\/www.worldofbooks.com\/en-au\/collections\/encyclopaedia-of-mathematical-sciences-book-series.oembed?page=5","provider":"World of Books ","version":"1.0","type":"link"}