## 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