Cooke, Roger 1942
Overview
Works:  37 works in 200 publications in 3 languages and 6,688 library holdings 

Genres:  History Biography Conference papers and proceedings 
Roles:  Author, Translator, Editor, Other 
Classifications:  QA372, 510.9 
Publication Timeline
.
Most widely held works by
Roger Cooke
The history of mathematics : a brief course by
Roger Cooke(
Book
)
37 editions published between 1997 and 2013 in English and held by 1,400 WorldCat member libraries worldwide
"The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society."Jacket
37 editions published between 1997 and 2013 in English and held by 1,400 WorldCat member libraries worldwide
"The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society."Jacket
The mathematics of Sonya Kovalevskaya by
Roger Cooke(
Book
)
19 editions published between 1984 and 2012 in English and held by 635 WorldCat member libraries worldwide
This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc
19 editions published between 1984 and 2012 in English and held by 635 WorldCat member libraries worldwide
This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc
Classical algebra : its nature, origins, and uses by
Roger Cooke(
Book
)
14 editions published in 2008 in English and held by 450 WorldCat member libraries worldwide
"Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra orginally developed from classical algebraic precursors." "Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, this book is excellent for mathematics courses of the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics."Jacket
14 editions published in 2008 in English and held by 450 WorldCat member libraries worldwide
"Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra orginally developed from classical algebraic precursors." "Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, this book is excellent for mathematics courses of the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics."Jacket
Mathematical analysis by
V. A Zorich(
Book
)
19 editions published between 2004 and 2015 in English and held by 396 WorldCat member libraries worldwide
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions
19 editions published between 2004 and 2015 in English and held by 396 WorldCat member libraries worldwide
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions
Landmark writings in Western mathematics 16401940 by
I GrattanGuinness(
Book
)
10 editions published between 2005 and 2008 in English and held by 366 WorldCat member libraries worldwide
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 16401940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field
10 editions published between 2005 and 2008 in English and held by 366 WorldCat member libraries worldwide
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 16401940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field
Statistics in science : the foundations of statistical methods in biology, physics, and economics by
Roger Cooke(
Book
)
9 editions published in 1990 in English and held by 306 WorldCat member libraries worldwide
An inference may be defined as a passage of thought according to some method. In the theory of knowledge it is customary to distinguish deductive and nondeductive inferences. Deductive inferences are truth preserving, that is, the truth of the premises is preserved in the con clusion. As a result, the conclusion of a deductive inference is already 'contained' in the premises, although we may not know this fact until the inference is performed. Standard examples of deductive inferences are taken from logic and mathematics. Nondeductive inferences need not preserve truth, that is, 'thought may pass' from true premises to false conclusions. Such inferences can be expansive, or, ampliative in the sense that the performances of such inferences actually increases our putative knowledge. Standard nondeductive inferences do not really exist, but one may think of elementary inductive inferences in which conclusions regarding the future are drawn from knowledge of the past. Since the body of scientific knowledge is increasing, it is obvious that the method of science must allow nondeductive as well as deductive inferences. Indeed, the explosive growth of science in recent times points to a prominent role for the former. Philosophers of science have long tried to isolate and study the nondeductive inferences in science. The inevitability of such inferences one the one hand, juxtaposed with the poverty of all efforts to identify them, constitutes one of the major cognitive embarrassments of our time
9 editions published in 1990 in English and held by 306 WorldCat member libraries worldwide
An inference may be defined as a passage of thought according to some method. In the theory of knowledge it is customary to distinguish deductive and nondeductive inferences. Deductive inferences are truth preserving, that is, the truth of the premises is preserved in the con clusion. As a result, the conclusion of a deductive inference is already 'contained' in the premises, although we may not know this fact until the inference is performed. Standard examples of deductive inferences are taken from logic and mathematics. Nondeductive inferences need not preserve truth, that is, 'thought may pass' from true premises to false conclusions. Such inferences can be expansive, or, ampliative in the sense that the performances of such inferences actually increases our putative knowledge. Standard nondeductive inferences do not really exist, but one may think of elementary inductive inferences in which conclusions regarding the future are drawn from knowledge of the past. Since the body of scientific knowledge is increasing, it is obvious that the method of science must allow nondeductive as well as deductive inferences. Indeed, the explosive growth of science in recent times points to a prominent role for the former. Philosophers of science have long tried to isolate and study the nondeductive inferences in science. The inevitability of such inferences one the one hand, juxtaposed with the poverty of all efforts to identify them, constitutes one of the major cognitive embarrassments of our time
Uncertainty analysis with high dimensional dependence modelling by
Dorota Kurowicka(
Book
)
12 editions published between 2005 and 2006 in English and held by 169 WorldCat member libraries worldwide
"Uncertainty Analysis with High Dimensional Dependence Modeling offers a comprehensive exploration of a new emerging field. It will prove an invaluable text for researchers, practitioners and graduate students in areas ranging from statistics and engineering to reliability and environmetrics."Jacket
12 editions published between 2005 and 2006 in English and held by 169 WorldCat member libraries worldwide
"Uncertainty Analysis with High Dimensional Dependence Modeling offers a comprehensive exploration of a new emerging field. It will prove an invaluable text for researchers, practitioners and graduate students in areas ranging from statistics and engineering to reliability and environmetrics."Jacket
Ordinary differential equations by
V. I Arnolʹd(
Book
)
9 editions published between 1992 and 2006 in English and held by 66 WorldCat member libraries worldwide
Although there is no lack of other books on this subject, even with the same title, the appearance of this new one is fully justified on at least two grounds: its approach makes full use of modern mathematical concepts and terminology of considerable sophistication and abstraction, going well beyond the traditional presentation of the subject; and, at the same time, the resulting enhancement of mathematical abstractness is counterbalanced by a constant appeal to geometrical and physical considerations, presented in the main text and in numerous problems and exercises. In the terms of mathematical approach, the text is dominated by two central ideas: the theorem on rectifiability of a vector field (which is equivalent to the usual theorems on existence, uniqueness, and differentiability of solutions) and the theory of oneparameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental conceptslike phase space and phase flows, smooth manifolds and tangent bundles, vector fields and oneparameter groups of diffeomorphismsthat remain in the shadows in the traditional coordinatebased approach. All of these concepts are presented in some detail, but without assuming any background on the part of the reader beyond the scope of the standard elementary courses on analysis and linear algebra
9 editions published between 1992 and 2006 in English and held by 66 WorldCat member libraries worldwide
Although there is no lack of other books on this subject, even with the same title, the appearance of this new one is fully justified on at least two grounds: its approach makes full use of modern mathematical concepts and terminology of considerable sophistication and abstraction, going well beyond the traditional presentation of the subject; and, at the same time, the resulting enhancement of mathematical abstractness is counterbalanced by a constant appeal to geometrical and physical considerations, presented in the main text and in numerous problems and exercises. In the terms of mathematical approach, the text is dominated by two central ideas: the theorem on rectifiability of a vector field (which is equivalent to the usual theorems on existence, uniqueness, and differentiability of solutions) and the theory of oneparameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental conceptslike phase space and phase flows, smooth manifolds and tangent bundles, vector fields and oneparameter groups of diffeomorphismsthat remain in the shadows in the traditional coordinatebased approach. All of these concepts are presented in some detail, but without assuming any background on the part of the reader beyond the scope of the standard elementary courses on analysis and linear algebra
Foundations of the classical theory of partial differential equations by
I︠U︡. V Egorov(
Book
)
3 editions published between 1992 and 1998 in English and held by 45 WorldCat member libraries worldwide
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: " ... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 " ... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 " ... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte fr Mathematik, 1993 " ... It is comparable in scope with the great CourantHilbert "Methods of Mathematical Physics", but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. The book gives a good and readable overview of the subject. ... carefully written, well translated, and well produced." The Mathematical Gazette, 1993
3 editions published between 1992 and 1998 in English and held by 45 WorldCat member libraries worldwide
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: " ... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 " ... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 " ... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte fr Mathematik, 1993 " ... It is comparable in scope with the great CourantHilbert "Methods of Mathematical Physics", but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. The book gives a good and readable overview of the subject. ... carefully written, well translated, and well produced." The Mathematical Gazette, 1993
Mathematics of the 19th century : geometry, analytic function theory by
A. N Kolmogorov(
Book
)
5 editions published in 1996 in English and held by 27 WorldCat member libraries worldwide
<Volume 2>
5 editions published in 1996 in English and held by 27 WorldCat member libraries worldwide
<Volume 2>
Mathematics of the 19th century : function theory according to Chebyshev, ordinary differential equations, calculus of variations,
theory of finite differences(
Book
)
5 editions published in 1998 in English and held by 25 WorldCat member libraries worldwide
5 editions published in 1998 in English and held by 25 WorldCat member libraries worldwide
Scenes from the history of real functions by
F. A Medvedev(
Book
)
5 editions published in 1991 in English and German and held by 23 WorldCat member libraries worldwide
To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt
5 editions published in 1991 in English and German and held by 23 WorldCat member libraries worldwide
To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt
A description of Weyer's Cave by
Roger Cooke(
Book
)
5 editions published between 1834 and 1860 in English and held by 15 WorldCat member libraries worldwide
5 editions published between 1834 and 1860 in English and held by 15 WorldCat member libraries worldwide
Manitoba Clinic, 19461996 by
I. I Mayba(
Book
)
2 editions published in 1996 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 1996 in English and held by 14 WorldCat member libraries worldwide
Riemann, topology, and physics by
Mikhail Ilʹich Monastyrskiĭ(
Book
)
6 editions published between 1998 and 2008 in English and Italian and held by 9 WorldCat member libraries worldwide
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the RiemannHilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann's name appears prominently throughout the literature
6 editions published between 1998 and 2008 in English and Italian and held by 9 WorldCat member libraries worldwide
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the RiemannHilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann's name appears prominently throughout the literature
Statistical mechanics of magnetically ordered systems by
I︠U︡. A Izi︠u︡mov(
Book
)
1 edition published in 1988 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 8 WorldCat member libraries worldwide
Mirror symmetry by
Claire Voisin(
Book
)
2 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
Discussion of the merits of Noah Webster's orthography, and Lyman Cobb's school books in the "Society of Teachers and Friends
of Education" in the state of New Jersey in 18445 by
Samuel Irenæus Prime(
Book
)
1 edition published in 1845 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1845 in English and held by 4 WorldCat member libraries worldwide
Experts in uncertainty : opinion and subjective probability in science by
Roger Cooke(
Book
)
8 editions published between 1989 and 2011 in English and held by 3 WorldCat member libraries worldwide
This volume contains an extensive survey and critical examination of current views on the use of expert opinion in scientific inquiry and policymaking
8 editions published between 1989 and 2011 in English and held by 3 WorldCat member libraries worldwide
This volume contains an extensive survey and critical examination of current views on the use of expert opinion in scientific inquiry and policymaking
Mathematical analysis by
V. A Zorich(
Book
)
3 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
This second English edition of a very popular twovolume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions. zThe textbook of Zorich seems to me the most successful of the available comprehensive textbooks of analysis for mathematicians and physicists. It differs from the traditional exposition in two major ways: on the one hand in its closer relation to naturalscience applications (primarily to physics and mechanics) and on the other hand in a greaterthanusual use of the ideas and methods of modern mathematics, that is, algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems. Especially unusual is the second volume, which includes vector analysis, the theory of differential forms on manifolds, an introduction to the theory of generalized functions and potential theory, Fourier series and the Fourier transform, and the elements of the theory of asymptotic expansions. At present such a way of structuring the course must be considered innovative. It was normal in the time of Goursat, but the tendency toward specialized courses, noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere logical justifications. The need to return to more substantive courses of analysis now seems obvious, especially in connection with the applied character of the future activity of the majority of students. ...In my opinion, this course is the best of the existing modern courses of analysis.y From a review by V.I.Arnold VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences
3 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
This second English edition of a very popular twovolume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions. zThe textbook of Zorich seems to me the most successful of the available comprehensive textbooks of analysis for mathematicians and physicists. It differs from the traditional exposition in two major ways: on the one hand in its closer relation to naturalscience applications (primarily to physics and mechanics) and on the other hand in a greaterthanusual use of the ideas and methods of modern mathematics, that is, algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems. Especially unusual is the second volume, which includes vector analysis, the theory of differential forms on manifolds, an introduction to the theory of generalized functions and potential theory, Fourier series and the Fourier transform, and the elements of the theory of asymptotic expansions. At present such a way of structuring the course must be considered innovative. It was normal in the time of Goursat, but the tendency toward specialized courses, noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere logical justifications. The need to return to more substantive courses of analysis now seems obvious, especially in connection with the applied character of the future activity of the majority of students. ...In my opinion, this course is the best of the existing modern courses of analysis.y From a review by V.I.Arnold VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences
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Related Identities
 Zorich, V. A. (Vladimir Antonovich) Author
 Kovalevskai︠a︡, S. V. (Sofʹi︠a︡ Vasilʹevna) 18501891 Other
 GrattanGuinness, I.
 Costantini, Domenico Other Editor
 Kurowicka, Dorota 1967 Author
 Istituto Ludovico Geymonat Other
 Società italiana di logica e filosofia della scienza Other
 T., Octavio Paniagua Translator
 Wiley InterScience (Online service)
 Paniagua T., Octavio Translator
Associated Subjects
Algebra Algebraic logic Analytic functions BiologyPhilosophy CalabiYau manifolds Canada Caves Decision making Differential equations Differential equations, Partial English languageOrthography and spellingStudy and teaching Field theory (Physics) Functions of real variables Geometry Germany Global analysis (Mathematics) Global differential geometry History Hodge theory Kovalevskai︠a︡, S. V.(Sofʹi︠a︡ Vasilʹevna), Manifolds (Mathematics) Manitoba Clinic Mathematical analysis Mathematical physics Mathematicians Mathematics Mirror symmetry New Jersey Nuclear magnetismMathematical models Physics Probabilities Quantum field theory Research ResearchStatistical methods Riemann, Bernhard, Science ScienceMethodology SciencePhilosophy ScienceStatistical methods Scientists Soviet Union Spellers Statistical mechanicsMathematical models Symmetry (Physics) Topology Uncertainty Uncertainty (Information theory) United States VirginiaWeyers Cave Webster, Noah,