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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


Sasakian Geometry

Charles Boyer and Krzysztof Galicki

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.001.0001
Subject:
Mathematics, Geometry / Topology

Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an ... 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


Random Geometric Graphs

Mathew Penrose

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.001.0001
Subject:
Mathematics, Probability / Statistics

This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability density, and edges added to connect ... 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


Chern-Simons Theory, Matrix Models, and Topological Strings

Marcos Mariño

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string ... More


New Perspectives in Stochastic Geometry

Wilfrid S. Kendall and Ilya Molchanov (eds)

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.001.0001
Subject:
Mathematics, Geometry / Topology

Stochastic geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, ... More


Space, Time, and Stuff

Frank Arntzenius

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199696604
eISBN:
9780191738333
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696604.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, ... More


Time, Space, and Metaphysics

Bede Rundle

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199575114
eISBN:
9780191722349
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575114.001.0001
Subject:
Philosophy, Metaphysics/Epistemology

This book engages with major philosophical questions concerning time and space — a framework for the investigation being provided by the debate between the absolutists and the relationists, so ... More


The grid

Louis A. Girifalco

in The Universal Force: Gravity - Creator of Worlds

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228966
eISBN:
9780191711183
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228966.003.0004
Subject:
Physics, History of Physics

Descartes believed he was meant to create the ultimate natural philosophy. He relied primarily on reason and philosophic principles, so most of the physics he developed was wrong. But he was a great ... More


Cartesian Method and the Problem of Reduction

Emily R. Grosholz

Published in print:
1991
Published Online:
October 2011
ISBN:
9780198242505
eISBN:
9780191680502
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198242505.001.0001
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

Cartesian method, construed as a way of organizing domains of knowledge according to the ‘order of reason’, was a powerful reductive tool. Descartes produced important ... More


A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

John P. Burgess and Gideon Rosen

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250128
eISBN:
9780191597138
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250126.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility ... More


The Many Facets of Geometry: A Tribute to Nigel Hitchin

Oscar Garcia-Prada, Jean Pierre Bourguignon, and Simon Salamon (eds)

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.001.0001
Subject:
Mathematics, Geometry / Topology

Few people have proved more influential in the field of differential and algebraic geometry, and in showing how this links with mathematical physics, than Nigel Hitchin. Oxford University's Savilian ... More


Logic and Revisability

Graham Priest

in Doubt Truth to be a Liar

Published in print:
2005
Published Online:
May 2006
ISBN:
9780199263288
eISBN:
9780191603631
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199263280.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter argues that logic is a theory, and can be revised as any other scientific theory. The comparison with geometry is helpful in this regard. It also discusses Quine’s views on the matter, ... More


The Vocabulary of the Liberal Arts

Philip Burton

in Language in the Confessions of Augustine

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199266227
eISBN:
9780191709098
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199266227.003.0003
Subject:
Religion, Early Christian Studies

This chapter considers Augustine's use of Greek and Latin terminology in the technical register of the Seven Liberal Arts (grammar, rhetoric, dialect, arithmetic, geometry, music, and philosophy). It ... More


Quaternionic Kähler and Hyperkähler Manifolds

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0013
Subject:
Mathematics, Geometry / Topology

This chapter gives an extensive overview of various quaternionic geometries. The main focus is on positive quaternionic Kähler manifolds (orbifolds) and on hyper Kähler manifolds (orbifolds). Various ... More


Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper ... More


Hertz on the Hamilton formalism

JESPER LÜTZEN

in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567370
eISBN:
9780191717925
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567370.003.0023
Subject:
Physics, History of Physics

In the introduction to his book Principles of Mechanics, Heinrich Hertz emphasised that one of the advantages of his geometric formulation of his mechanics is that it throws a bright light upon ... More


Variable Geometry, Multilevel Governance: European Integration and Subnational Government in the New Millennium

Mike Goldsmith

in The Politics of Europeanization

Published in print:
2003
Published Online:
November 2003
ISBN:
9780199252091
eISBN:
9780191599224
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199252092.003.0005
Subject:
Political Science, European Union

The creation of the European Union, and the associated process of economic, political, and social integration that has accompanied it, has changed the nature of nation state and subnational politics ... More


From Community to Diverse Union

Giandomenico Majone

in Dilemmas of European Integration: The Ambiguities and Pitfalls of Integration by Stealth

Published in print:
2005
Published Online:
February 2006
ISBN:
9780199274307
eISBN:
9780191603310
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199274304.003.0001
Subject:
Political Science, European Union

Since the Treaty on European Union, it has become clear that the process of European integration moves along several paths, of which the Community path is the best known, but not necessarily the most ... More


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