Manual L2-invariants: Theory and applications to geometry and K-theory

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Irrational l2 invariants arising from the lamplighter group

Language and concepts may be changed to fit modern tastes, or to better describe books cataloged. Hardcover First published in , Fibonacci's "Liber abaci" was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe.


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Its author, Leonardo Pisano, known today as Fibonacci, was a citizen of Pisa, an active maritime power, with trading outposts on the Barbary Coast and other points in the Muslim Empire. As a youth Fibonacci was instructed in mathematics in one of these outposts; he continued his study of mathematics while traveling extensively on business and developed contacts with scientists throughout the Mediterranean world. A member of the academic court around the Emperor Frederick II, Leonardo saw clearly the advantages for both commerce and scholarship of the Hindu positional number system and the algebraic methods developed by al-Khwarizmi and other Muslim scientists.

Though it is known as an introduction to the Hindu number system and the algorithms of arithmetic that children now learn in grade school, "Liber abaci" is much more: an encyclopaedia of thirteenth-century mathematics, both theoretical and practical. It develops the tools rigorously, establishing them with Euclidean geometric proofs, and then shows how to apply them to all kinds of situations in business and trade - conversion of measures and currency, allocations of profit, computation of interest, alloying of currencies, and so forth.

It is rigorous mathematics, well applied, and vividly described. As the first translation into a modern language of the "Liber abaci", this book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.


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  • L2-Invariants: Theory and Applications to Geometry and K-Theory | Wolfgang Lück | Springer.
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  • L2-Invariants: Theory and Applications to Geometry and K-Theory | Wolfgang Lück | Springer.
  • Contents: Introduction. Hardcover X This book contains a large amount of information not found in standard textbooks. Among its many particular features are: - fully worked-out examples - many carefully selected and formulated problems - fast Fourier transform methods - a thorough discussion of some important minimization methods - solution of stiff or implicit ordinary differential equations and of differential algebraic systems - modern shooting techniques for solving two-point boundary value problems - basics of multigrid methods.

    Included are numerous references to contemporary research literature. Contents: Prefaces.

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    Series: Texts in Applied Mathematics. XV, pp. Hardcover In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups.

    L2-Invariants: Theory and Applications to Geometry and K-Theory - Wolfgang Lück - Google книги

    These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. It is particularly these interactions with different fields that make L2-invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

    It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material. Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. Hardcover This book presents aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations.

    It contains results on Morse-Smale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms. Contents: Preface.