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## An Introduction to Gilbreath Numbers

*Robert W. Vallin*

### in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164038
- eISBN:
- 9781400881338
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164038.003.0012
- Subject:
- Mathematics, History of Mathematics

This chapter mathematically analyzes the behavior of a card trick described by an undergraduate math major at the University of California, Los Angeles, named Norman Gilbreath. Stated succinctly, ... More

## Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier

*Laura Capuano, Peter Jossen, Christina Karolus, and Francesco Veneziano*

### in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter details Umberto Zannier's minicourse on hyperelliptic continued fractions and generalized Jacobians. It begins by presenting the Pell equation, which was studied by Indian, and later by ... More

## A Language That Can Express Its Own Truth Theory

*Tim Maudlin*

### in Truth and Paradox: Solving the Riddles

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199247295
- eISBN:
- 9780191601781
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199247293.003.0004
- Subject:
- Philosophy, Philosophy of Language

The semantic theory developed for a formal language in the previous chapters is now formulated in the language itself. Applying the semantic theory to this formulation, one finds that the theory of ... More

## Matching Moments and Model Reduction View

*Jörg Liesen and Zdenek Strakos*

### in Krylov Subspace Methods: Principles and Analysis

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199655410
- eISBN:
- 9780191744174
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655410.003.0003
- Subject:
- Mathematics, Applied Mathematics, Algebra

The projected system matrix in Krylov subspace methods consists of moments of the original system matrix with respect to the initial residual(s). This hints that Krylov subspace methods can be viewed ... More

## Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

*Gisbert Wüstholz and Clemens Fuchs (eds)*

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More

## Introduction

*Gisbert Wüstholz and Clemens Fuchs (eds)*

### in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.003.0001
- Subject:
- Mathematics, Geometry / Topology

This introductory chapter provides an overview of the three topics discussed in this book: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and ... More

## Continued Fractions

*Christophe Reutenauer*

### in From Christoffel Words to Markoff Numbers

- Published in print:
- 2018
- Published Online:
- January 2019
- ISBN:
- 9780198827542
- eISBN:
- 9780191866418
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198827542.003.0006
- Subject:
- Mathematics, Pure Mathematics

Basic theory of continued fractions: finite continued fractions (for rational numbers) and infinite continued fractions (for irrational numbers). This also includes computation of the quadratic ... More

## The Plaid Model: (AMS-198)

*Richard Evan Schwartz*

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.001.0001
- Subject:
- Mathematics, Educational Mathematics

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane ... More

## From Christoffel Words to Markoff Numbers

*Christophe Reutenauer*

- Published in print:
- 2018
- Published Online:
- January 2019
- ISBN:
- 9780198827542
- eISBN:
- 9780191866418
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198827542.001.0001
- Subject:
- Mathematics, Pure Mathematics

Christoffel introduced in 1875 a special class of words on a binary alphabet, linked to continued fractions. Some years laterMarkoff published his famous theory, called nowMarkoff theory. It ... More

## Euler: The Mathematics of Musical Sadness

*Peter Pesic*

### in Music and the Making of Modern Science

- Published in print:
- 2014
- Published Online:
- May 2017
- ISBN:
- 9780262027274
- eISBN:
- 9780262324380
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027274.003.0010
- Subject:
- Music, History, Western

Throughout his life, the great mathematician Leonhard Euler spent most of his free time on music, to which he devoted his first book. This chapter discusses how he reformulated the ordering of ... More

## Krylov Subspace Methods: Principles and Analysis

*Jörg Liesen and Zdenek Strakos*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199655410
- eISBN:
- 9780191744174
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655410.001.0001
- Subject:
- Mathematics, Applied Mathematics, Algebra

This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations. Starting from the idea of projections, Krylov ... More

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