Wermer, John
Overview
Works:  41 works in 227 publications in 4 languages and 4,122 library holdings 

Genres:  Mathematical formulae Tables (Data) 
Roles:  Author, Translator, Editor, Contributor 
Classifications:  QA41, 512.55 
Publication Timeline
.
Most widely held works by
John Wermer
Linear algebra through geometry by
Thomas Banchoff(
Book
)
34 editions published between 1983 and 1996 in English and Undetermined and held by 1,106 WorldCat member libraries worldwide
In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a nontrivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of twodimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.02.7. Then the very same outline is used in Chapters 3.03.7 to present the linear algebra of threedimensional space, so that the former ideas are reinforced while new concepts are being introduced
34 editions published between 1983 and 1996 in English and Undetermined and held by 1,106 WorldCat member libraries worldwide
In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a nontrivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of twodimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.02.7. Then the very same outline is used in Chapters 3.03.7 to present the linear algebra of threedimensional space, so that the former ideas are reinforced while new concepts are being introduced
Potential theory by
John Wermer(
Book
)
43 editions published between 1972 and 1981 in 4 languages and held by 906 WorldCat member libraries worldwide
Potential theory grew out of mathematical physics, in particular out of the theory of gravitation and the theory of electrostatics. Mathematical physicists such as Poisson and Green introduced some of the central ideas of the subject. A mathematician with a general knowledge of analysis may find it useful to begin his study of classical potential theory by looking at its physical origins. Sections 2, 5 and 6 of these Notes give in part heuristic arguments based on physical considerations. These heuristic arguments suggest mathematical theorems and provide the mathematician with the problem of finding the proper hypotheses and mathematical proofs. These Notes are based on a onesemester course given by the author at Brown University in 1971. On the part of the reader, they assume a knowledge of Real Function Theory to the extent of a first year graduate course. In addition some elementary facts regarding harmonic functions are aS$umed as known. For convenience we have listed these facts in the Appendix. Some notation is also explained there. Essentially all the proofs we give in the Notes are for Euclidean 3space R3 and Newtonian potentials ~
43 editions published between 1972 and 1981 in 4 languages and held by 906 WorldCat member libraries worldwide
Potential theory grew out of mathematical physics, in particular out of the theory of gravitation and the theory of electrostatics. Mathematical physicists such as Poisson and Green introduced some of the central ideas of the subject. A mathematician with a general knowledge of analysis may find it useful to begin his study of classical potential theory by looking at its physical origins. Sections 2, 5 and 6 of these Notes give in part heuristic arguments based on physical considerations. These heuristic arguments suggest mathematical theorems and provide the mathematician with the problem of finding the proper hypotheses and mathematical proofs. These Notes are based on a onesemester course given by the author at Brown University in 1971. On the part of the reader, they assume a knowledge of Real Function Theory to the extent of a first year graduate course. In addition some elementary facts regarding harmonic functions are aS$umed as known. For convenience we have listed these facts in the Appendix. Some notation is also explained there. Essentially all the proofs we give in the Notes are for Euclidean 3space R3 and Newtonian potentials ~
Banach algebras and several complex variables by
John Wermer(
Book
)
16 editions published between 1975 and 1976 in English and held by 539 WorldCat member libraries worldwide
During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n> I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and selfcontained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas
16 editions published between 1975 and 1976 in English and held by 539 WorldCat member libraries worldwide
During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n> I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and selfcontained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas
Several complex variables and Banach algebras by
Herbert Alexander(
Book
)
24 editions published between 1899 and 2005 in English and held by 521 WorldCat member libraries worldwide
Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts arising from the study of Banach algebras including the maximal ideal space, the Silov boundary, and Gleason parts, have led to new questions and to new methods of proofs in function theory. This book is concerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. The third edition of this book contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the StoneWeierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter containing commentaries on history and recent developments and an updated and expanded list of references
24 editions published between 1899 and 2005 in English and held by 521 WorldCat member libraries worldwide
Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts arising from the study of Banach algebras including the maximal ideal space, the Silov boundary, and Gleason parts, have led to new questions and to new methods of proofs in function theory. This book is concerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. The third edition of this book contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the StoneWeierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter containing commentaries on history and recent developments and an updated and expanded list of references
Seminar über FunktionenAlgebren, Eidg. Technische Hochschule, Zürich, Forschungsinstitut für Mathematik, wintersemester,
1963/64 by
John Wermer(
Book
)
18 editions published in 1964 in 4 languages and held by 416 WorldCat member libraries worldwide
18 editions published in 1964 in 4 languages and held by 416 WorldCat member libraries worldwide
Banach algebras and several complex variables by
John Wermer(
Book
)
18 editions published between 1971 and 1976 in English and held by 236 WorldCat member libraries worldwide
18 editions published between 1971 and 1976 in English and held by 236 WorldCat member libraries worldwide
Seminar über FunktionenAlgebren by
John Wermer(
Book
)
25 editions published in 1964 in German and Undetermined and held by 123 WorldCat member libraries worldwide
25 editions published in 1964 in German and Undetermined and held by 123 WorldCat member libraries worldwide
Lectures in modern analysis and applications by
Michael Francis Atiyah(
Book
)
6 editions published between 1969 and 2006 in English and held by 66 WorldCat member libraries worldwide
6 editions published between 1969 and 2006 in English and held by 66 WorldCat member libraries worldwide
Seminar über FunktionenAlgebren Eidg. Technische Hochschule, Zürich Forschungsinstitut für Mathematik by
John Wermer(
)
1 edition published in 1964 in German and held by 31 WorldCat member libraries worldwide
1 edition published in 1964 in German and held by 31 WorldCat member libraries worldwide
Lectures in Modern Analysis and Applications I by
Stephen Smale(
)
2 editions published in 1969 in English and held by 30 WorldCat member libraries worldwide
2 editions published in 1969 in English and held by 30 WorldCat member libraries worldwide
Potential theory by
John Wermer(
)
2 editions published between 1974 and 1981 in English and held by 24 WorldCat member libraries worldwide
2 editions published between 1974 and 1981 in English and held by 24 WorldCat member libraries worldwide
Linear algebra through geometry by
Sheldon Jay Axler(
Book
)
2 editions published in 1992 in English and held by 17 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 17 WorldCat member libraries worldwide
Recent development in the theory of connections and holonomy groups (Nomizu); Banach algebras and analytic functions (Wermer) by
Katsumi Nomizu(
Book
)
1 edition published in 1961 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 1961 in English and held by 16 WorldCat member libraries worldwide
Formulas and theorems for the special functions of mathematical physics by
Wilhelm Magnus(
Book
)
2 editions published in 1949 in English and held by 15 WorldCat member libraries worldwide
This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical publis hed by the American Mathematical Society; "Handbook of Mathe matical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, AddisonWesley, Reading, Mass.) . There is a list of symbols and abbreviations at the end of the book
2 editions published in 1949 in English and held by 15 WorldCat member libraries worldwide
This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical publis hed by the American Mathematical Society; "Handbook of Mathe matical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, AddisonWesley, Reading, Mass.) . There is a list of symbols and abbreviations at the end of the book
Seminar über FunktionenAlgebren by
John Wermer(
Book
)
1 edition published in 1964 in German and held by 14 WorldCat member libraries worldwide
1 edition published in 1964 in German and held by 14 WorldCat member libraries worldwide
Potential Theory by
John Wermer(
)
3 editions published between 1981 and 2008 in English and Undetermined and held by 8 WorldCat member libraries worldwide
3 editions published between 1981 and 2008 in English and Undetermined and held by 8 WorldCat member libraries worldwide
The Collected works by
Arne Beurling(
Book
)
1 edition published in 1989 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 8 WorldCat member libraries worldwide
Formulas and theorems for the functions of mathematical physics by
Wilhelm Magnus(
Book
)
4 editions published between 1949 and 1954 in English and held by 8 WorldCat member libraries worldwide
4 editions published between 1949 and 1954 in English and held by 8 WorldCat member libraries worldwide
Seminar über FunktioenAlgebren by Seminar Über FunktionenAlgebren(
Book
)
1 edition published in 1964 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1964 in English and held by 7 WorldCat member libraries worldwide
The Collected works by
Arne Beurling(
Book
)
1 edition published in 1989 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 5 WorldCat member libraries worldwide
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Algebraic functions Algebraic topology Algebras, Linear Banach algebras Connections (Mathematics) EducationCurricula Functional analysis Functions Functions of several complex variables Geometry Global analysis (Mathematics) Harvard University Holonomy groups Mathematical analysis Mathematics Physics Potential theory (Mathematics) Topology Transcendental functions