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The Central Binomial Coefficient Revisited

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/9780195334548.003.0003
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter continues to investigate the central binomial coefficient in much greater detail. Topics explained include Wallis' product, Lucas numbers, Fermat's little theorem, Carlitz's formula, ... More


Introduction

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This introductory chapter explores the concept of large numbers, showing why large numbers appear in thermal physics and explaining how to handle them. Large numbers arise in thermal physics because ... More


Bannockburn: The Scottish War and the British Isles 1307-1323

Michael Brown

Published in print:
2008
Published Online:
September 2012
ISBN:
9780748633326
eISBN:
9780748672127
Item type:
book
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748633326.001.0001
Subject:
History, British and Irish Medieval History

The battle of Bannockburn, fought on the fields south of Stirling at midsummer 1314, is the best-known event in the history of Medieval Scotland. It was a unique event. The clash of two armies, each ... More


The Battle and its Story

Michael Brown

in Bannockburn: The Scottish War and the British Isles 1307-1323

Published in print:
2008
Published Online:
September 2012
ISBN:
9780748633326
eISBN:
9780748672127
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748633326.003.0002
Subject:
History, British and Irish Medieval History

Two armies numbering in total tens of thousands of men were camped in the lands south of Stirling in central Scotland. The battle that was about to break was the first full-scale clash between the ... More


The Campaign (October 1313–Midsummer 1314)

Michael Brown

in Bannockburn: The Scottish War and the British Isles 1307-1323

Published in print:
2008
Published Online:
September 2012
ISBN:
9780748633326
eISBN:
9780748672127
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748633326.003.0006
Subject:
History, British and Irish Medieval History

The Scottish wars had seen no clash on the scale of Bannockburn since the battle of Falkirk sixteen years earlier. While many leaders, like Edward I, engaged aggressive campaigns which exhibited ... More


Two Kinds of War

G.W.S. Barrow

in Robert Bruce: And the Community of the Realm of Scotland

Published in print:
2005
Published Online:
September 2012
ISBN:
9780748620227
eISBN:
9780748672189
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748620227.003.0005
Subject:
History, European Medieval History

Edward's response to these developments was to besiege and sack Berwick in the spring of 1296, defeat the Scottish army at Dunbar and lead his invasion force as far north as Elgin, removing ... More


The King over the Water

G.W.S. Barrow

in Robert Bruce: And the Community of the Realm of Scotland

Published in print:
2005
Published Online:
September 2012
ISBN:
9780748620227
eISBN:
9780748672189
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748620227.003.0007
Subject:
History, European Medieval History

At the turn of 1299-1300 Robert Bruce may have tried to make a bid for pre-eminent leadership in Scotland; the possibility of the restoration of Balliol and hostility to the Comyns would have ... More


Practical heat engines

Andrew M. Steane

in Thermodynamics: A complete undergraduate course

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198788560
eISBN:
9780191830426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198788560.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Heat engines used for power generation and other purposes are introduced. The Stirling engine and the internal combustion engine are described, and the Otto cycle explained. The maximum work theorem ... More


The Turn of the Tide

G.W.S. Barrow

in Robert Bruce: And the Community of the Realm of Scotland

Published in print:
2005
Published Online:
September 2012
ISBN:
9780748620227
eISBN:
9780748672189
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748620227.003.0011
Subject:
History, European Medieval History

This chapter traces events in Scotland 1309-14. For most of this period Lothian and the Merse with their castles of Edinburgh, Roxburgh and Berwick were in English hands. Bruce forced the inhabitants ... More


Bannockburn

G.W.S. Barrow

in Robert Bruce: And the Community of the Realm of Scotland

Published in print:
2005
Published Online:
September 2012
ISBN:
9780748620227
eISBN:
9780748672189
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748620227.003.0012
Subject:
History, European Medieval History

To relieve Stirling and to ‘suppress the wicked rebellion of Robert Bruce’, Edward II planned a major campaign with forces of perhaps 15000 infantry and 2-3000 cavalry; against this, the forces ... More


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