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Pascal' Triangle and Catalan Numbers

Thomas Koshy

in Catalan Numbers with Applications

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195334548
eISBN:
9780199868766
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195334548.003.0012
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter shows the various ways Catalan numbers can be extracted from Pascal's triangle. It includes discussion of nonisomorphic groups, Catalan polynomials, Touchard's recursive formula, and ... More


Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Christopher I. Beckwith

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.001.0001
Subject:
History, World Medieval History

This book tells how key cultural innovations from Central Asia revolutionized medieval Europe and gave rise to the culture of science in the West. Medieval scholars rarely performed scientific ... More


Conclusion

Christopher I. Beckwith

in Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.003.0008
Subject:
History, World Medieval History

This chapter raises three objections about the development of a full scientific culture and examines the modern descendants of the recursive argument method. It suggests that colleges and the ... More


CONTINUITY ON THE REAL LINE AND IN FORMAL SPACES

Erik Palmgren

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Brouwer introduced his axioms for intuitionism to regain central results on continuity. Special axioms were avoided instead in Bishop's development of constructive analysis. Bishop in fact modified ... More


On the application of the method of least squares to some cases, in which a combination of certain types of inhomogeneous random sources of errors gives these a ‘systematic’ character

T. N. Thiele

in Thiele: Pioneer in Statistics

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509721
eISBN:
9780191709197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509721.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter presents Thiele's first paper on the method of least squares. This paper was so far ahead of its time that only a few appreciated the results. Thiele's recursive algorithm developed in ... More


RECURSIVE CAUSALITY

Jon Williamson

in Bayesian Nets and Causality: Philosophical and Computational Foundations

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530794
eISBN:
9780191712982
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530794.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The framework developed thus far in the book is extended to cope with the situation in which causal relations themselves are causes or effects. Examples of this phenomenon are presented and the ... More


LOGIC

Jon Williamson

in Bayesian Nets and Causality: Philosophical and Computational Foundations

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530794
eISBN:
9780191712982
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530794.003.0011
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

It is shown how the approach of this book can be extended to deal with probabilities over logical languages and cases in which an agent has logical background knowledge. Bayesian nets can be applied ... More


Weighting for Reasons

Mark Schroeder

in Slaves of the Passions

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199299508
eISBN:
9780191714917
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199299508.003.0007
Subject:
Philosophy, Political Philosophy

This chapter advances a positive theory of the weight of reasons to replace Proportionalism, the thesis rejected in Chapters 5 and 6. First preliminary matters are set aside, in order to avoid an ... More


Alternative Decision Criteria

Christian Gollier

in Pricing the Planet's Future: The Economics of Discounting in an Uncertain World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691148762
eISBN:
9781400845408
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148762.003.0011
Subject:
Economics and Finance, Development, Growth, and Environmental

This chapter describes a sample of the alternative decision criteria that have features which are normatively attractive. A standard critique made to the discounted expected utility (DEU) model that ... More


Introduction

Christopher I. Beckwith

in Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.003.0001
Subject:
History, World Medieval History

This book investigates how the recursive argument method, the actual medieval “scientific method,” was transmitted along with the college to medieval Western Europe from Classical Arabic ... More


The Recursive Argument Method of Medieval Science

Christopher I. Beckwith

in Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.003.0002
Subject:
History, World Medieval History

This chapter examines the recursive argument method of medieval science. The distinctive argument method used in scientific literature from the High Middle Ages to the Enlightenment was the ... More


Buddhist Central Asian Invention of the Method

Christopher I. Beckwith

in Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.003.0004
Subject:
History, World Medieval History

This chapter examines Buddhist Central Asia's invention of the recursive argument method. Some Buddhist teachings, which are found in all Buddhist traditions—indicating that they may be inherited ... More


Islamization in Classical Arabic Central Asia

Christopher I. Beckwith

in Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.003.0005
Subject:
History, World Medieval History

This chapter examines Islamization in Classical Arabic Central Asia. The Arab Empire founded by the prophet Muhammad expanded rapidly, defeating the Byzantine Empire and capturing Syria (637) and ... More


Transmission to Medieval Western Europe

Christopher I. Beckwith

in Warriors of the Cloisters: The Central Asian Origins of Science in the Medieval World

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155319
eISBN:
9781400845170
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155319.003.0006
Subject:
History, World Medieval History

This chapter examines how the recursive argument method was transmitted to medieval Western Europe. The appearance of the recursive argument method in Latin texts was preceded by more than a century ... More


The multi-causality of injury – current concepts

Willem Meeuwisse and Brent Hagel

in Sports Injury Research

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199561629
eISBN:
9780191722479
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199561629.003.08
Subject:
Public Health and Epidemiology, Public Health, Epidemiology

A sports injury is not a solitary occurrence. Instead, it is the result of a complex pathway of various internal and external risk factors acting upon an athlete. This multi-causal pathway is the ... More


Econometric Tools and Techniques

David F. Hendry

in Dynamic Econometrics

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198283164
eISBN:
9780191596384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283164.003.0003
Subject:
Economics and Finance, Econometrics

Least squares and recursive methods for estimating the values of unknown parameters and the logic of testing in empirical modelling, are discussed. The tools needed for investigating the properties ... More


Linguistics and Moral Theorys 1

Erica Roedder and Gilbert Harman

in The Moral Psychology Handbook

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199582143
eISBN:
9780191594496
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199582143.003.0009
Subject:
Philosophy, Moral Philosophy, Philosophy of Mind

This chapter describes various issues suggested by the analogy between morality and linguistics. The first part discusses what might be involved in a generative “moral grammar”. The second part ... More


From Han d’Islande to Les Misérables and Beyond

Kathryn M. Grossman

in The Later Novels of Victor Hugo: Variations on the Politics and Poetics of Transcendence

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199642953
eISBN:
9780191739231
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199642953.003.0002
Subject:
Literature, European Literature, 19th-century Literature and Romanticism

This chapter illustrates the study’s critical methodology by reviewing the major findings of the author’s previous research on Hugo’s early fiction from Han d’Islande (1823) to Notre-Dame de Paris ... More


A Semantic Conception of Truthmaking

Stephen Yablo

in Aboutness

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691144955
eISBN:
9781400845989
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144955.003.0005
Subject:
Philosophy, Philosophy of Language

Truth for Aristotle was a metaphysical notion. Alfred Tarski showed how to conceive truth semantically, that is, in such a way that it could play a foundational role in semantics. David Armstrong, ... More


What Are the Uniquely Human Components of the Language Faculty?

Marc D. Hauser and W. Tecumseh Fitch

in Language Evolution

Published in print:
2003
Published Online:
January 2010
ISBN:
9780199244843
eISBN:
9780191715167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199244843.003.0009
Subject:
Linguistics, Historical Linguistics

Taking a biologist's perspective on language evolution, this chapter advocates the use of a comparative method for exploring the various other components that make up the human language ability. It ... More


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