## 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