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Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.001.0001
Subject:
Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More


Cartoons

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0008
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces a method of marking up a short Gelfand-Tsetlin pattern based on inequalities between its entries, that encodes the effect of the involution t 7 → t′ and the boxing and ... More


Knowability

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0012
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces the Knowability Lemma, which explains when products of Gauss sums associated to elements of a preaccordion are explicitly evaluable as polynomials in q, the order of the ... More


PRO-SUBJECTIVE APPROACH LOSES AS SAMPLING THEORY GAINS GROUND

Shoutir Kishore Chatterjee

in Statistical Thought: A Perspective and History

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525318
eISBN:
9780191711657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525318.003.0008
Subject:
Mathematics, Probability / Statistics

In the first half of the 19th century, Laplace, Gauss, and a number of other contributors enriched statistical thought. The quest for a suitable model for the distribution of observational errors led ... More


Visions, Dreams, and Mathematics

Barry Mazur

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/9780691149042.003.0006
Subject:
Mathematics, History of Mathematics

This chapter considers the role of visions and dreams in mathematics by focusing on Leopold Kronecker's desire—or dream—to find solutions to a large and interesting collection of polynomial ... More


Riemann Surfaces, Coverings, and Hypergeometric Functions

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ... More


Outline of the Proof

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0006
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents the proof of the equivalence of the two definitions for the λ‎-parts in terms of Gelfand-Tsetlin patterns. The equivalence of these two descriptions is a deep fact that uses ... More


The Problem of Time In Quantum Geometrodynamics

Karel Kuchař

in The Arguments of Time

Published in print:
2006
Published Online:
January 2012
ISBN:
9780197263464
eISBN:
9780191734748
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197263464.003.0007
Subject:
Philosophy, General

This chapter describes the problem of time in quantum geometrodynamics in more detail. It first describes how the fundamental equation of general relativity can be written as an instantaneous law, ... More


Mathematicians on the geometrization of the Hamilton–Jacobi 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/9780198567370.003.0024
Subject:
Physics, History of Physics

It has long since been remarked by mathematicians that William Rowan Hamilton's method contains purely geometrical truths, and that a peculiar mode of expression, suitable to it, is required in order ... More


Channel Service

Markus Krajewski

in The Server: A Media History from the Present to the Baroque

Published in print:
2018
Published Online:
May 2019
ISBN:
9780300180817
eISBN:
9780300186802
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300180817.003.0005
Subject:
Society and Culture, Media Studies

This chapter turns to the servants of (tele)communication networks, particularly to their relation to the channel of information transmission. The central focus here is the transformation of the ... More


Contrasts in Riemann surface theory

Simon Donaldson

in Riemann Surfaces

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198526391
eISBN:
9780191774874
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526391.003.0011
Subject:
Mathematics, Geometry / Topology, Analysis

Section 4.2.3 showed how to associate a compact connected Riemann surface to any irreducible polynomial P(z,w) in two variables. This chapter first establishes the converse — any compact connected ... More


Ordinary differential equations

Simon Donaldson

in Riemann Surfaces

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198526391
eISBN:
9780191774874
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526391.003.0015
Subject:
Mathematics, Geometry / Topology, Analysis

Chapter 1 discussed ordinary differential equations and, in particular, the hypergeometric equation denoted by HGa,b,c (z). This chapter takes this discussion further, fitting it ... More


Regression Analysis

Quan Li

in Using R for Data Analysis in Social Sciences: A Research Project-Oriented Approach

Published in print:
2018
Published Online:
March 2019
ISBN:
9780190656218
eISBN:
9780190656256
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190656218.003.0005
Subject:
Political Science, Political Theory

This chapter teaches how to use R to conduct regression analysis to answer the question: Does trade promote economic growth? It demonstrates how to specify a statistical model from a theoretical ... More


The Riemann curvature tensor

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0016
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter first examines some fundamental examples where the Riemann curvature tensor has an especially simple form. It then discusses the ways in which the Riemann and Ricci curvatures are used ... More


Basic Theory

Walter Gautschi

in Orthogonal Polynomials: Computation and Approximation

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198506720
eISBN:
9780191916571
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198506720.003.0003
Subject:
Computer Science, Mathematical Theory of Computation

This introductory chapter is to present a quick review of material on orthogonal polynomials that is particularly relevant to computation. Proofs of most results are ... More


There’s Magic in the Air

Nicholas Mee

in Celestial Tapestry: The Warp and Weft of Art and Mathematics

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198851950
eISBN:
9780191886690
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851950.003.0010
Subject:
Physics, History of Physics

Carl Friedrich Gauss showed remarkable mathematical ability from a young age. As a child he found a formula for calculating the sum of sequences of consecutive numbers, a type of arithmetic ... More


The Perils of Parallels!

Nicholas Mee

in Celestial Tapestry: The Warp and Weft of Art and Mathematics

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198851950
eISBN:
9780191886690
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851950.003.0016
Subject:
Physics, History of Physics

In the nineteenth century, three mathematicians—Bolyai, Gauss, and Lobachevsky—almost simultaneously discovered the possibility of non-Euclidean or hyperbolic geometries. These geometries rest on ... More


The simple pendulum

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

The simple pendulum is a simple mechanical system with a surprising depth. It can be solved in terms of Jacobi elliptic functions. A simple physical argument shows that these functions are doubly ... More


Mapping Space

Rasmus Grønfeldt Winther

in When Maps Become the World

Published in print:
2020
Published Online:
January 2021
ISBN:
9780226669670
eISBN:
9780226674865
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226674865.003.0006
Subject:
Philosophy, Philosophy of Science

This chapter examines a selection of maps to show how ubiquitous map thinking is in science, matching up four fields of the physical sciences with map types introduced in chapter 2: (1) cosmology ... More


Arendt: To Have One’s Language for a Homeland

Barbara Cassin

in Nostalgia

Published in print:
2016
Published Online:
September 2016
ISBN:
9780823269501
eISBN:
9780823269549
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823269501.003.0004
Subject:
Philosophy, General

In this final chapter, Cassin shows that language is central to the experience of exile; those who have been exiled from their homeland seek to find a home in language, that is, for many, in a native ... More


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