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Operator Algebras and Their Modules: An operator space approach

David P. Blecher and Christian Le Merdy

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.001.0001
Subject:
Mathematics, Pure Mathematics

This book presents the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles ... More


Set Theory: Boolean-Valued Models and Independence Proofs

John L. Bell

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This is the third edition of a well-known graduate textbook on Boolean-valued models of set theory. The aim of the first and second editions was to provide a systematic and adequately motivated ... More


Visual Thinking in Mathematics

Marcus Giaquinto

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Visual thinking — visual imagination or perception of diagrams and symbol arrays, and mental operations on them — is omnipresent in mathematics. Is this visual thinking merely a psychological aid, ... More


Interpolation and Definability: Modal and Intuitionistic Logics

Dov M. Gabbay and Larisa Maksimova

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This book focuses on interpolation and definability. This notion is not only central in pure logic, but has significant meaning and applicability in all areas where logic itself is applied, ... More


The Fourth Janko Group

Alexander A. Ivanov

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198527596
eISBN:
9780191713163
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527596.001.0001
Subject:
Mathematics, Pure Mathematics

This book illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory, and local analysis, are combined to construct one of ... More


The Greate Invention of Algebra: Thomas Harriot's Treatise on equations

Jacqueline A. Stedall

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198526025
eISBN:
9780191712364
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526025.001.0001
Subject:
Mathematics, History of Mathematics

This book casts new light on the work of Thomas Harriot (c.1560-1621), an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, ... More


Tensor products of operator algebras

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0006
Subject:
Mathematics, Pure Mathematics

Tensor products and C*-norms play a prominent role in the theory of C*-algebras, in particular in the study of nuclear C*-algebras and semidiscrete (or injective) von Neumann algebras. This chapter ... More


Group Problem Solving

Patrick R. Laughlin

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147918
eISBN:
9781400836673
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147918.001.0001
Subject:
Psychology, Social Psychology

Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of ... More


3-fold flips after Shokurov

Alessio Corti

in Flips for 3-folds and 4-folds

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198570615
eISBN:
9780191717703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570615.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter gives a concise, complete, and pedagogical proof of existence of 3-fold flips according to Shokurov. In particular, the foundation of the theory of b-divisors, algebras of rational ... More


A Discourse Concerning Algebra: English Algebra to 1685

Jacqueline A. Stedall

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198524953
eISBN:
9780191711886
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198524953.001.0001
Subject:
Mathematics, History of Mathematics

This book provides an accessible account of the rise of algebra in England from the medieval period to the later years of the 17th century. The book includes new research and is the most detailed ... More


Completely isomorphic theory of operator algebras

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0005
Subject:
Mathematics, Pure Mathematics

This chapter studies operator algebras ‘up to isomorphism’ or ‘up to complete isomorphism’. Topics covered include homomorphisms of operator algebras, completely bounded characterizations, examples ... More


MODAL AND SUPERINTUITIONISTIC LOGICS: BASIC CONCEPTS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0002
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents basic definitions and known results related to modal and superintuitionistic logics. Well-known Hilbert-style axiomatizations of the most known modal systems K, D, T, K4, D4, ... More


SUPERINTUITIONISTIC LOGICS AND NORMAL EXTENSIONS OF THE MODAL LOGICS S4

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0003
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

It is well known that the intuitionistic logic Int may be translated into S4. This translation was introduced by Gödel to give an interpretation of Int in the classical logic with an additional ... More


How algebra was entertained and cultivated in Europe

Jacqueline A. Stedall

in A Discourse Concerning Algebra: English Algebra to 1685

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198524953
eISBN:
9780191711886
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198524953.003.0002
Subject:
Mathematics, History of Mathematics

This chapter discusses the development of algebra in Europe. Topics covered include the origins from which European algebra began to evolve and from which it took its name; The Liber abbaci (1202) of ... More


‘Many pretty things worth looking into’

Jacqueline A. Stedall

in A Discourse Concerning Algebra: English Algebra to 1685

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198524953
eISBN:
9780191711886
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198524953.003.0008
Subject:
Mathematics, History of Mathematics

This final chapter looks at some of the reactions to A treatise of algebra immediately after its publication and since, and draws together a few observations on Wallis' perspective on algebra and on ... More


BOOLEAN AND HEYTING ALGEBRAS: THE ESSENTIALS

John L. Bell

in Set Theory: Boolean-Valued Models and Independence Proofs

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides a brief account of the theory of Boolean and Heyting algebras, including the basic representation theorems and their connections with logic.


BOOLEAN-VALUED ANALYSIS

John L. Bell

in Set Theory: Boolean-Valued Models and Independence Proofs

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter gives a brief account of real analysis in Boolean-valued models arising from measure algebras and algebras of projections on Hilbert space. The latter is applied, following Martin Davis, ... More


Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Victor J. Katz and Karen Hunger Parshall

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.001.0001
Subject:
Mathematics, History of Mathematics

What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and ... More


Deductive Narrative and the Epistemological Function of Belief in Mathematics: On Bombelli and Imaginary Numbers

Federica La Nave

in Circles Disturbed: The Interplay of Mathematics and Narrative

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.003.0003
Subject:
Mathematics, History of Mathematics

This chapter explores the epistemological function of belief in mathematical thinking by considering Rafael Bombelli's contribution to the creation of imaginary numbers. The discussion focuses on ... More


The Emergence of Modern Algebra

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0014
Subject:
Mathematics, History of Mathematics

This chapter explores how the topography of algebra had changed significantly by the first decade of the twentieth century. It studies the progress made since the developments described in the last ... More


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