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  • Connected Sets in Global Bifurcation Theory

    Series series Mathematics and Statistics (R0)
    This book explores the topological properties of connected and path-connected solution sets for nonlinear equations in Banach spaces, focusing on the distinction between these concepts. Building on Rabinowitz's dichotomy and classical results on Peano continua, the authors introduce "congestion points"—where connected sets fail to be weakly locally connected—and examine the extent to which their ... Read more

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  • A Course in Mathematical Analysis: Volume 2, Metric and Topological Spaces, Functions of a Vector Variable

    The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 ... Read more

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  • Analysis on Polish Spaces and an Introduction to Optimal Transportation

    Series Book 89 - London Mathematical Society Student Texts
    A large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces ... Read more

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  • Computation with Linear Algebraic Groups

    Series series Chapman & Hall/CRC Monographs and Research Notes in Mathematics
    Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms.Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in ... Read more

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  • A Course in Point Set Topology

    Series series Mathematics and Statistics (R0)
    This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other ... Read more

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  • Certain Number-Theoretic Episodes In Algebra, Second Edition

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  • Ridge Functions

    by Allan Pinkus ...
    Series Book 205 - Cambridge Tracts in Mathematics
    Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory ... Read more

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  • Representations of the Infinite Symmetric Group

    Series Book 160 - Cambridge Studies in Advanced Mathematics
    Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to ... Read more

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  • Theory Of Multiple Zeta Values With Applications In Combinatorics, The

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    This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations ... Read more

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  • Modern General Topology

    by J.-I. Nagata ...
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    This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first edition appeared. The reader will find many new topics in chapters IV ... Read more

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  • Representation Theory of the Symmetric Groups

    The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

    Series Book 121 - Cambridge Studies in Advanced Mathematics
    The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur ... Read more

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