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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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