Shenitzer, Abe
Overview
Works:  56 works in 217 publications in 4 languages and 4,876 library holdings 

Genres:  History Biography Sources 
Roles:  Translator, Editor, Other, Author, Contributor, tra, Creator 
Classifications:  QA685, B 
Publication Timeline
.
Most widely held works by
Abe Shenitzer
Felix Klein and Sophus Lie : evolution of the idea of symmetry in the Nineteenth Century by
I. M I︠A︡glom(
Book
)
8 editions published in 1988 in English and Spanish and held by 528 WorldCat member libraries worldwide
8 editions published in 1988 in English and Spanish and held by 528 WorldCat member libraries worldwide
NonEuclidean geometry in the theory of automorphic functions by
Jacques Hadamard(
Book
)
6 editions published in 1999 in English and held by 268 WorldCat member libraries worldwide
"This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts."Jacket
6 editions published in 1999 in English and held by 268 WorldCat member libraries worldwide
"This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts."Jacket
Mathematical evolutions(
Book
)
6 editions published in 2002 in English and held by 256 WorldCat member libraries worldwide
6 editions published in 2002 in English and held by 256 WorldCat member libraries worldwide
Geometric transformations III by
I. M I︠A︡glom(
Book
)
22 editions published between 1973 and 2014 in English and held by 188 WorldCat member libraries worldwide
Deals with the fundamental transformations of plane geometry, and introduces the reader to some important group theoretic concepts
22 editions published between 1973 and 2014 in English and held by 188 WorldCat member libraries worldwide
Deals with the fundamental transformations of plane geometry, and introduces the reader to some important group theoretic concepts
Lectures on partial differential equations by
I. G Petrovskiĭ(
Book
)
9 editions published between 1954 and 1991 in English and held by 106 WorldCat member libraries worldwide
DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; FOREWORD; TRANSLATOR'S NOTE; PREFACE; Table of Contents; CHAPTER I  INTRODUCTION. CLASSIFICATION OF EQUATIONS; 1. Definitions. Examples; 2. The Cauchy problem. The CauchyKowalewski theorem; 3. The generalized Cauchy problem. Characteristics.; 4. Uniqueness of the solution of the Cauchy problem in the class of nonanalytic functions.; 5. Reduction to canonical form at a point and classification of equations of the second order in one unknown function
9 editions published between 1954 and 1991 in English and held by 106 WorldCat member libraries worldwide
DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; FOREWORD; TRANSLATOR'S NOTE; PREFACE; Table of Contents; CHAPTER I  INTRODUCTION. CLASSIFICATION OF EQUATIONS; 1. Definitions. Examples; 2. The Cauchy problem. The CauchyKowalewski theorem; 3. The generalized Cauchy problem. Characteristics.; 4. Uniqueness of the solution of the Cauchy problem in the class of nonanalytic functions.; 5. Reduction to canonical form at a point and classification of equations of the second order in one unknown function
Entropy and information by
M. V Volʹkenshteĭn(
Book
)
9 editions published in 2009 in English and held by 80 WorldCat member libraries worldwide
"This treasure of popular science by the Russian biophysicist Mikhail V. Volkenstein is at last, more than twenty years after its appearance in Russian, available in English translation. As its title Entropy and Information suggests, the book deals with the thermodynamical concept of entropy and its interpretation in terms of information theory. The author shows how entropy is not to be considered a mere shadow of the central physical concept of energy, but more appropriately as a leading player in all of the major natural processes: physical, chemical, biological, evolutionary, and even cultural. The theory of entropy is thoroughly developed from its beginnings in the foundational work of Sadi Carnot and Clausius in the context of heat engines, including expositions of much of the necessary physics and mathematics, and illustrations from everyday life of the importance of entropy."Back cover
9 editions published in 2009 in English and held by 80 WorldCat member libraries worldwide
"This treasure of popular science by the Russian biophysicist Mikhail V. Volkenstein is at last, more than twenty years after its appearance in Russian, available in English translation. As its title Entropy and Information suggests, the book deals with the thermodynamical concept of entropy and its interpretation in terms of information theory. The author shows how entropy is not to be considered a mere shadow of the central physical concept of energy, but more appropriately as a leading player in all of the major natural processes: physical, chemical, biological, evolutionary, and even cultural. The theory of entropy is thoroughly developed from its beginnings in the foundational work of Sadi Carnot and Clausius in the context of heat engines, including expositions of much of the necessary physics and mathematics, and illustrations from everyday life of the importance of entropy."Back cover
Lectures on linear algebra by
I. M Gelʹfand(
Book
)
17 editions published between 1961 and 1989 in 3 languages and held by 61 WorldCat member libraries worldwide
17 editions published between 1961 and 1989 in 3 languages and held by 61 WorldCat member libraries worldwide
Bernhard Riemann, 18261866 : turning points in the conception of mathematics by
Detlef Laugwitz(
Book
)
9 editions published between 1999 and 2008 in English and held by 46 WorldCat member libraries worldwide
This book, originally written in German and presented here in an Englishlanguage translation, is the first attempt to examine Riemann's scientific work from a single unifying perspective. Laugwitz describes Riemann's development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle  for mathematics and physics alike  to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann's work and to the development of them in their historical context. This illuminating Englishlanguage version of the original German edition will be an important contribution to the literature of the history of mathematics
9 editions published between 1999 and 2008 in English and held by 46 WorldCat member libraries worldwide
This book, originally written in German and presented here in an Englishlanguage translation, is the first attempt to examine Riemann's scientific work from a single unifying perspective. Laugwitz describes Riemann's development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle  for mathematics and physics alike  to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann's work and to the development of them in their historical context. This illuminating Englishlanguage version of the original German edition will be an important contribution to the literature of the history of mathematics
A simple nonEuclidean geometry and its physical basis : an elementary account of Galilean geometry and the Galilean principle
of relativity by
I. M I︠A︡glom(
Book
)
4 editions published in 1979 in English and held by 39 WorldCat member libraries worldwide
There are many technical and popular accounts, both in Russian and in other languages, of the nonEuclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' collegesa reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "nonuniqueness" of geometry; of the existence of many geometric systems
4 editions published in 1979 in English and held by 39 WorldCat member libraries worldwide
There are many technical and popular accounts, both in Russian and in other languages, of the nonEuclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' collegesa reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "nonuniqueness" of geometry; of the existence of many geometric systems
Topics in complex function theory by
C. L Siegel(
Book
)
5 editions published between 1969 and 1988 in English and held by 36 WorldCat member libraries worldwide
5 editions published between 1969 and 1988 in English and held by 36 WorldCat member libraries worldwide
A history of nonEuclidean geometry : evolution of the concept of a geometric space by
B. A Rozenfelʹd(
Book
)
3 editions published between 1987 and 1988 in English and held by 29 WorldCat member libraries worldwide
This book is an investigation of the mathematical and philosophical factors underlying the discovery of the concept of noneuclidean geometries, and the subsequent extension of the concept of space. Chapters one through five are devoted to the evolution of the concept of space, leading up to chapter six which describes the discovery of noneuclidean geometry, and the corresponding broadening of the concept of space. The author goes on to discuss concepts such as multidimensional spaces and curvature, and transformation groups. The book ends with a chapter describing the applications of nonassociative algebras to geometry
3 editions published between 1987 and 1988 in English and held by 29 WorldCat member libraries worldwide
This book is an investigation of the mathematical and philosophical factors underlying the discovery of the concept of noneuclidean geometries, and the subsequent extension of the concept of space. Chapters one through five are devoted to the evolution of the concept of space, leading up to chapter six which describes the discovery of noneuclidean geometry, and the corresponding broadening of the concept of space. The author goes on to discuss concepts such as multidimensional spaces and curvature, and transformation groups. The book ends with a chapter describing the applications of nonassociative algebras to geometry
In search of infinity by
N. I︠A︡ Vilenkin(
Book
)
6 editions published in 1995 in English and held by 24 WorldCat member libraries worldwide
The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of paradoxes that have led many scholars to doubt the soundness of it foundations. The author of this book presents a popularlevel account of the roads followed by human thought in attempts to understand the idea of the infinite in mathematics and physics. In doing so, he brings to the general reader a deep insight into the nature of the problem and its importance to an understanding of our world. "When I read the first edition of the book, about 20 years ago, I was carried away by Vilenkins storytelling and his ability to bring subtle mathematical ideas down to earth. He stretches our imagination and educates our intuitionThe second edition improves on the first by omission of some routine material about finite properties of sets, and increased attention to infinity. There is a wealth of new material on the position of infinity in human thought, from philosophy to physics, and also on its role in the history of mathematics. In particular, there are now biographical notes on over 100 mathematicians. Abe Shenitzers elegant translation makes this a rare work of literaturea serious mathematical book that will be read from over to cover."John Stillwell, Monash University, Australia
6 editions published in 1995 in English and held by 24 WorldCat member libraries worldwide
The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of paradoxes that have led many scholars to doubt the soundness of it foundations. The author of this book presents a popularlevel account of the roads followed by human thought in attempts to understand the idea of the infinite in mathematics and physics. In doing so, he brings to the general reader a deep insight into the nature of the problem and its importance to an understanding of our world. "When I read the first edition of the book, about 20 years ago, I was carried away by Vilenkins storytelling and his ability to bring subtle mathematical ideas down to earth. He stretches our imagination and educates our intuitionThe second edition improves on the first by omission of some routine material about finite properties of sets, and increased attention to infinity. There is a wealth of new material on the position of infinity in human thought, from philosophy to physics, and also on its role in the history of mathematics. In particular, there are now biographical notes on over 100 mathematicians. Abe Shenitzers elegant translation makes this a rare work of literaturea serious mathematical book that will be read from over to cover."John Stillwell, Monash University, Australia
Combinatorics by
N. I︠A︡ Vilenkin(
Book
)
6 editions published in 1971 in English and Undetermined and held by 23 WorldCat member libraries worldwide
Populární formou vysvětluje autor obecná pravidla kombinatoriky, variace, permutace a kombinace, kombinatorické úlohy s omezujícími podmínkami, dále kombinatoriku rozkladů, rekurentní vzorce aj. Výklad ilustruje zajímavýmipříklady z různých oborů a uvádí několik set kombinatorických úloh
6 editions published in 1971 in English and Undetermined and held by 23 WorldCat member libraries worldwide
Populární formou vysvětluje autor obecná pravidla kombinatoriky, variace, permutace a kombinace, kombinatorické úlohy s omezujícími podmínkami, dále kombinatoriku rozkladů, rekurentní vzorce aj. Výklad ilustruje zajímavýmipříklady z různých oborů a uvádí několik set kombinatorických úloh
Stories about maxima and minima by
V. M Tikhomirov(
Book
)
4 editions published between 1990 and 1995 in English and held by 22 WorldCat member libraries worldwide
Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of the pastEuclid, Archimedes, Heron, the Bernoullis, Newton, and many otherstook part in seeking solutions to these concrete problems. The solutions stimulated the development of the theory, and, as a result, techniques were elaborated that made possible the solution of a tremendous variety of prob
4 editions published between 1990 and 1995 in English and held by 22 WorldCat member libraries worldwide
Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of the pastEuclid, Archimedes, Heron, the Bernoullis, Newton, and many otherstook part in seeking solutions to these concrete problems. The solutions stimulated the development of the theory, and, as a result, techniques were elaborated that made possible the solution of a tremendous variety of prob
Noneuclidean geometry by
Herbert Meschkowski(
Book
)
11 editions published between 1964 and 1965 in 3 languages and held by 21 WorldCat member libraries worldwide
11 editions published between 1964 and 1965 in 3 languages and held by 21 WorldCat member libraries worldwide
Quadratic forms and matrices, an introductory approach by
N. V Efimov(
Book
)
7 editions published in 1964 in English and held by 21 WorldCat member libraries worldwide
7 editions published in 1964 in English and held by 21 WorldCat member libraries worldwide
Mathematician for all seasons : recollections and notes, vol. 1 (18871945) by
Hugo Steinhaus(
Book
)
8 editions published in 2015 in English and held by 18 WorldCat member libraries worldwide
This book presents, in his own words, the life of Hugo Steinhaus (1887@0394@03BC1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who @0394@03C6discovered@0394@03C7 the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus@0394@03C3s personal story of the turbulent times he survived @0394@03BC including two world wars and life postwar under the Soviet heel @0394@03BC cannot but be of consuming interest. His recounting of the fearful years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th century, but also to anyone wishing to read a firsthand account of the history of those unquiet times in Europe @0394@03BC and indeed worldwide @0394@03BC by someone of uncommon intelligence and forthrightness situated near an eye of the storm
8 editions published in 2015 in English and held by 18 WorldCat member libraries worldwide
This book presents, in his own words, the life of Hugo Steinhaus (1887@0394@03BC1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who @0394@03C6discovered@0394@03C7 the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus@0394@03C3s personal story of the turbulent times he survived @0394@03BC including two world wars and life postwar under the Soviet heel @0394@03BC cannot but be of consuming interest. His recounting of the fearful years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th century, but also to anyone wishing to read a firsthand account of the history of those unquiet times in Europe @0394@03BC and indeed worldwide @0394@03BC by someone of uncommon intelligence and forthrightness situated near an eye of the storm
Mathematician for all seasons : recollections and notes by
Hugo Steinhaus(
Book
)
6 editions published in 2016 in English and held by 9 WorldCat member libraries worldwide
This book presents, in his own words, the life of Hugo Steinhaus (1887@0394@03BC1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who @0394@03C6discovered@0394@03C7 the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus@0394@03C3s personal story of the turbulent times he survived @0394@03BC including two world wars and life postwar under the Soviet heel @0394@03BC cannot but be of consuming interest. His recounting of the fearful years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th@222B@03C2century, but also to anyone wishing to read a firsthand account of the history of those unquiet times in Europe @0394@03BC and indeed worldwide @0394@03BC by someone of uncommon intelligence and forthrightness situated near an eye of the storm
6 editions published in 2016 in English and held by 9 WorldCat member libraries worldwide
This book presents, in his own words, the life of Hugo Steinhaus (1887@0394@03BC1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who @0394@03C6discovered@0394@03C7 the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus@0394@03C3s personal story of the turbulent times he survived @0394@03BC including two world wars and life postwar under the Soviet heel @0394@03BC cannot but be of consuming interest. His recounting of the fearful years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th@222B@03C2century, but also to anyone wishing to read a firsthand account of the history of those unquiet times in Europe @0394@03BC and indeed worldwide @0394@03BC by someone of uncommon intelligence and forthrightness situated near an eye of the storm
Geometric transformations by
I. M I︠A︡glom(
Book
)
6 editions published between 2009 and 2011 in English and held by 5 WorldCat member libraries worldwide
6 editions published between 2009 and 2011 in English and held by 5 WorldCat member libraries worldwide
Geometric transformations II by
I. M I︠A︡glom(
)
4 editions published in 1968 in English and held by 0 WorldCat member libraries worldwide
"This book is the sequel to Geometric Transformations I which appeared in this series in 1962. Part I treats lengthpreserving transformations, this volume treats shapepreserving transformations; and Part III treats affine and protective transformations. These classes of transformations play a fundamental role in the grouptheoretic approach to geometry. As in the previous volume, the treatment is direct and simple. The introduction of each new idea is supplemented by problems whose solutions employ the idea just presented, and whose detailed solutions are given in the second half of the book."Publisher's description
4 editions published in 1968 in English and held by 0 WorldCat member libraries worldwide
"This book is the sequel to Geometric Transformations I which appeared in this series in 1962. Part I treats lengthpreserving transformations, this volume treats shapepreserving transformations; and Part III treats affine and protective transformations. These classes of transformations play a fundamental role in the grouptheoretic approach to geometry. As in the previous volume, the treatment is direct and simple. The introduction of each new idea is supplemented by problems whose solutions employ the idea just presented, and whose detailed solutions are given in the second half of the book."Publisher's description
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fewer
Audience Level
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Related Identities
 I︠A︡glom, I. M. (Isaak Moiseevich) 19211988 Author
 Burns, Robert G. Translator Editor
 Grant, Hardy Translator Editor
 Klein, Felix 18491925
 Lie, Sophus 18421899
 Volʹkenshteĭn, M. V. (Mikhail Vladimirovich) 19121992 Author
 Steinhaus, Hugo 18871972 Author
 Weron, A. Other Editor
 Szymaniec, Irena Other Editor
 Hadamard, Jacques 18651963 Author
Associated Subjects
Algebra Algebras, Linear Astronomy Automorphic functions Calculus of tensors Calculus of variations Combinatorial analysis Differential equations, Partial Elliptic functions Entropy Entropy (Information theory) Forms, Quadratic Functions, Entire Functions of complex variables Geometry Geometry, Modern Geometry, ModernPlane Geometry, NonEuclidean Germany History Infinite Inversions (Geometry) Isometrics (Mathematics) Jewish mathematicians Klein, Felix, Lie, Sophus, Linear operators Logic, Symbolic and mathematical Mathematical optimization Mathematical physics Mathematical statistics Mathematicians Mathematics Matrices Maxima and minima Physics Poland Relativity (Physics) Riemann, Bernhard, Set theory Statistical physics Steinhaus, Hugo, Substitutions, Linear Symmetry Thermodynamics Transformations (Mathematics)