## 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

## 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

## 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

## 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

## Discontinuous Shifts: History Reading History

*Andrzej Warminski*

### in Ideology, Rhetoric, Aesthetics: For de Man

- Published in print:
- 2013
- Published Online:
- May 2014
- ISBN:
- 9780748681266
- eISBN:
- 9780748693764
- Item type:
- chapter

- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9780748681266.003.0009
- Subject:
- Literature, Criticism/Theory

This chapter presents a reading of two of de Man's 1967 Gauss lectures — one on Heidegger's interpretation of Hölderlin as an ‘apocalyptic’ poet and one on Wordsworth and Geoffrey Hartman's also ... More

## | 1827–8 | 1827–8 Family Life and Conferences Abroad

*Dan C. Christensen*

### in Hans Christian Ørsted: Reading Nature's Mind

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199669264
- eISBN:
- 9780191748745
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199669264.003.0044
- Subject:
- Physics, History of Physics

H.C. Ørsted counsels his sister-in-law on marriage. The social life around the Ørsted family's dinner table is narrated. Hans Christian Andersen, Ørsted's protégé, becomes a friend of the family. ... More

## Quantization of gauge field theories

*Franco Strocchi*

### in An Introduction to Non-Perturbative Foundations of Quantum Field Theory

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199671571
- eISBN:
- 9780191751073
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199671571.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Gauge field theories exhibit structural properties which have no analog in ordinary QFT, and the chapter begins by tracing such peculiar properies back to the invariance under the ... More

## Yang–Mills theories

*Rodolfo Gambini and Jorge Pullin*

### in A First Course in Loop Quantum Gravity

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199590759
- eISBN:
- 9780191774980
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590759.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces Yang-Mills theories as a natural generalization of Maxwell's theory. It discusses covariant derivatives and the Yang-Mills equations, which it also considers in a Hamiltonian ... More

## At Least Squares

*Steven J. Osterlind*

### in The Error of Truth: How History and Mathematics Came Together to Form Our Character and Shape Our Worldview

- Published in print:
- 2019
- Published Online:
- January 2019
- ISBN:
- 9780198831600
- eISBN:
- 9780191869532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198831600.003.0007
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the next important mathematical invention: the method of least squares. First, it sets the historical context for its invention by describing the events in France and Germany ... More