The Theory of Classical Valuations, Paulo Ribenboim

Автор: Alexander J. Hahn; J. Dieudonne; O.Timothy O`Meara
Название: The Classical Groups and K-Theory
ISBN: 3642057373 ISBN-13(EAN): 9783642057373
Издательство: Springer
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Описание: It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups," foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E - However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).

Автор: Melvyn B. Nathanson
Название: Additive Number Theory The Classical Bases
ISBN: 1441928480 ISBN-13(EAN): 9781441928481
Издательство: Springer
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Автор: Kenneth Ireland; Michael Rosen
Название: A Classical Introduction to Modern Number Theory
ISBN: 038797329X ISBN-13(EAN): 9780387973296
Издательство: Springer
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Описание: Details the historical development of the modern number theory. This text provides wide-ranging coverage of significant results with comparatively elementary proofs. It contains chapters that provide a proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of progress on the arithmetic of elliptic curves.

Автор: Alexander Kechris
Название: Classical Descriptive Set Theory
ISBN: 1461286921 ISBN-13(EAN): 9781461286929
Издательство: Springer
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Описание: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory.
This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.

Автор: John Stillwell
Название: Classical Topology and Combinatorial Group Theory
ISBN: 1461287499 ISBN-13(EAN): 9781461287490
Издательство: Springer
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