Lagarias, Jeffrey C. 1949
Overview
Works:  62 works in 121 publications in 1 language and 1,427 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Contributor, Other, Musician 
Classifications:  QA241, 512.7 
Publication Timeline
.
Most widely held works by
Jeffrey C Lagarias
The Kepler conjecture : the HalesFerguson proof by Thomas Hales, Samuel Ferguson by
Thomas Callister Hales(
)
13 editions published in 2011 in English and held by 433 WorldCat member libraries worldwide
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of threedimensional Euclidean space by equal spheres is attained by the ""cannonball"" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published
13 editions published in 2011 in English and held by 433 WorldCat member libraries worldwide
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of threedimensional Euclidean space by equal spheres is attained by the ""cannonball"" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published
The ultimate challenge : the 3x+1 problem(
Book
)
18 editions published between 2010 and 2012 in English and held by 424 WorldCat member libraries worldwide
The 3x+1 problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer x is odd then "multiply by three and add one", while if it is even then "divide by two." The 3x+1 problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite this simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving the history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem. Finally, the book reprints six early papers on the problem and related questions.  from Back Cover
18 editions published between 2010 and 2012 in English and held by 424 WorldCat member libraries worldwide
The 3x+1 problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer x is odd then "multiply by three and add one", while if it is even then "divide by two." The 3x+1 problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite this simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving the history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem. Finally, the book reprints six early papers on the problem and related questions.  from Back Cover
Mathematical developments arising from linear programming : proceedings of a joint summer research conference held at Bowdoin
College, June 25July 1, 1988 by
AMSIMSSIAM Joint Summer Research Conference on Mathematical Developments Arising from Linear Programming(
Book
)
16 editions published between 1990 and 2012 in English and held by 292 WorldCat member libraries worldwide
16 editions published between 1990 and 2012 in English and held by 292 WorldCat member libraries worldwide
Combinatorial number theory : proceedings of the "Integers Conference 2005" in celebration of the 70th birthday of Ronald
Graham, Carrollton, Georgia, USA, October 2730, 2005 by
Bruce M Landman(
)
2 editions published in 2013 in English and held by 56 WorldCat member libraries worldwide
Annotation
2 editions published in 2013 in English and held by 56 WorldCat member libraries worldwide
Annotation
Cryptology and computational number theory by
Carl Pomerance(
)
1 edition published in 1990 in English and held by 46 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 46 WorldCat member libraries worldwide
The Kepler conjecture the HalesFerguson proof by
Jeffrey C Lagarias(
)
5 editions published in 2011 in English and held by 27 WorldCat member libraries worldwide
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of threedimensional Euclidean space by equal spheres is attained by the "cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry . Further supporting material is also presented : a followup paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work. Thomas C. Hales , Mellon Professor of Mathematics at the University of Pittsburgh, began his efforts to solve the Kepler conjecture before 1992. He is a pioneer in the use of computer proof techniques, and he continues work on a formal proof of the Kepler conjecture as the aim of the Flyspeck Project (F, P and K standing for Formal Proof of Kepler). Samuel P. Ferguson completed his doctorate in 1997 under the direction of Hales at the University of Michigan. In 1995, Ferguson began to work with Hales and made significant contributions to the proof of the Kepler conjecture. His doctoral work established one crucial case of the proof, which appeared as a singly authored paper in the detailed proof. Jeffrey C. Lagarias , Professor of Mathematics at the University of Michigan, Ann Arbor, was a coguest editor, with Gábor FejesTóth, of the special issue of Discrete & Computational Geometry that originally published the proof
5 editions published in 2011 in English and held by 27 WorldCat member libraries worldwide
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of threedimensional Euclidean space by equal spheres is attained by the "cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry . Further supporting material is also presented : a followup paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work. Thomas C. Hales , Mellon Professor of Mathematics at the University of Pittsburgh, began his efforts to solve the Kepler conjecture before 1992. He is a pioneer in the use of computer proof techniques, and he continues work on a formal proof of the Kepler conjecture as the aim of the Flyspeck Project (F, P and K standing for Formal Proof of Kepler). Samuel P. Ferguson completed his doctorate in 1997 under the direction of Hales at the University of Michigan. In 1995, Ferguson began to work with Hales and made significant contributions to the proof of the Kepler conjecture. His doctoral work established one crucial case of the proof, which appeared as a singly authored paper in the detailed proof. Jeffrey C. Lagarias , Professor of Mathematics at the University of Michigan, Ann Arbor, was a coguest editor, with Gábor FejesTóth, of the special issue of Discrete & Computational Geometry that originally published the proof
The Kepler Conjecture : the HalesFerguson Proof by
Jeffrey C Lagarias(
)
1 edition published in 2011 in English and held by 25 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 25 WorldCat member libraries worldwide
Aperiodic order by
Michael Baake(
Book
)
2 editions published in 2017 in English and held by 15 WorldCat member libraries worldwide
Quasicrystals are nonperiodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multivolume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field
2 editions published in 2017 in English and held by 15 WorldCat member libraries worldwide
Quasicrystals are nonperiodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multivolume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field
Mathematical developments arising from linear programming by
Jeffrey C Lagarias(
)
3 editions published between 1990 and 1991 in English and held by 11 WorldCat member libraries worldwide
3 editions published between 1990 and 1991 in English and held by 11 WorldCat member libraries worldwide
The Kepler conjecture the HalesFerguson proof ; including a special issue of Discrete & computational geometry(
Book
)
3 editions published in 2011 in English and held by 11 WorldCat member libraries worldwide
3 editions published in 2011 in English and held by 11 WorldCat member libraries worldwide
Linear congruential generators do not produce random sequences by
A. M Frieze(
Book
)
3 editions published between 1983 and 1984 in English and Undetermined and held by 5 WorldCat member libraries worldwide
3 editions published between 1983 and 1984 in English and Undetermined and held by 5 WorldCat member libraries worldwide
Mathematical developments : proceedings of a Joint Summer Research Conference held at Bowdoin College, June 25  July, 1,1988(
Book
)
1 edition published in 1990 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 5 WorldCat member libraries worldwide
The Unreasonable effectiveness of number theory by
Stefan A Burr(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Cubetilings of ℝ n and nonlinear codesand nonlinear codes by
Jeffrey C Lagarias(
)
2 editions published between 1992 and 1994 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1992 and 1994 in English and held by 3 WorldCat member libraries worldwide
A walk along the branches of the extended Farey tree by
Jeffrey C Lagarias(
Book
)
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
Abstract: "The rational numbers can be presented as the set of vertices of a degreethree tree. If p/q and p/́q ́are two rational numbers written in lowest terms, the difference pq ́ pq́ depends only on the shape of the path joining p/q to p/́q ́on this tree."
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
Abstract: "The rational numbers can be presented as the set of vertices of a degreethree tree. If p/q and p/́q ́are two rational numbers written in lowest terms, the difference pq ́ pq́ depends only on the shape of the path joining p/q to p/́q ́on this tree."
The dStep Conjecture and Gaussian Elimination by
Jeffrey C Lagarias(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Optimal pairs of score vectors for positional scoring rules by
William V Gehrlein(
)
1 edition published in 1982 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1982 in English and held by 2 WorldCat member libraries worldwide
Geometric Models for Quasicrystals II. Local Rules Under Isometries by
Jeffrey C Lagarias(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Counting d Step Paths in Extremal Dantzig Figures by
Jeffrey C Lagarias(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions by
Ronald L Graham(
)
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Hales, Thomas Callister Other Author
 Ferguson, Samuel (Samuel P.)
 Todd, Michael J. 1947 Other Editor
 Pomerance, Carl Editor
 Kurlberg, Pär Contributor Editor Author
 Hindman, Neil Contributor Editor
 Tanny, Yuval Contributor Editor
 Savage, Carla D. Contributor Editor
 Johnson, John H. Contributor Editor
 Odlyzko, A. M.
Useful Links
Associated Subjects
Aperiodicity Aperiodic tilings Combinatorial number theory Combinatorial packing and covering ComputersAccess control Convex geometry Cryptography Crystallography Crystallography, Mathematical Cycles Discrete geometry Discrete groups Harmonic analysis Kepler's conjecture Linear programming Mathematical physics Mathematics Number theory Polynomials Programming (Mathematics) Sequences (Mathematics) Sphere packings Trees (Graph theory)
Covers
Alternative Names
Jeffrey Lagarias American mathematician
Jeffrey Lagarias Amerikaans wiskundige
Jeffrey Lagarias amerikai matematikus, egyetemi tanár, 1949
Jeffrey Lagarias Amerikalı matematikçi, üniversite profesörü
Jeffrey Lagarias amerikansk datavetare och matematiker
Jeffrey Lagarias amerikansk informatikar og matematikar
Jeffrey Lagarias amerikansk informatiker og matematiker
Jeffrey Lagarias matamaiticeoir Meiriceánach
Jeffrey Lagarias matemàtic estatunidenc
Jeffrey Lagarias matemático estadounidense
Jeffrey Lagarias matematico statunitense
Jeffrey Lagarias matemáticu estauxunidense
Jeffrey Lagarias matematikan amerikan
Jeffrey Lagarias mathématicien américain
Jeffrey Lagarias USamerikanischer Mathematiker
Lagarias, J. C
Lagarias, J. C., 1949
Lagarias, Jeffrey, 1949
Lagarias, Jeffrey Clark 1949
ジェフリー・ラガリアス
傑佛瑞·拉加里亞斯
Languages