Rosen, Michael I. (Michael Ira) 1938
Overview
Works:  21 works in 122 publications in 3 languages and 3,116 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Publication Timeline
.
Most widely held works by
Michael I Rosen
A classical introduction to modern number theory by
Kenneth F Ireland(
Book
)
47 editions published between 1972 and 2011 in 3 languages and held by 1,236 WorldCat member libraries worldwide
This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 111 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time
47 editions published between 1972 and 2011 in 3 languages and held by 1,236 WorldCat member libraries worldwide
This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 111 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time
Number theory in function fields by
Michael I Rosen(
Book
)
15 editions published between 2001 and 2011 in English and held by 426 WorldCat member libraries worldwide
Elementary number theory is concerned with arithmetic properties of the ring of integers. Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting, for example, analogues of the theorems of Fermat and Euler, Wilsons theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlets theorem on primes in an arithmetic progression. After presenting the required foundational material on function fields, the later chapters explore the analogy between global function fields and algebraic number fields. A variety of topics are presented, including: the ABCconjecture, Artins conjecture on primitive roots, the BrumerStark conjecture, Drinfeld modules, class number formulae, and average value theorems. The first few chapters of this book are accessible to advanced undergraduates. The later chapters are designed for graduate students and professionals in mathematics and related fields who want to learn more about the very fruitful relationship between number theory in algebraic number fields and algebraic function fields. In this book many paths are set forth for future learning and exploration. Michael Rosen is Professor of Mathematics at Brown University, where hes been since 1962. He has published over 40 research papers and he is the coauthor of A Classical Introduction to Modern Number Theory, with Kenneth Ireland. He received the Chauvenet Prize of the Mathematical Association of America in 1999 and the Philip J. Bray Teaching Award in 2001
15 editions published between 2001 and 2011 in English and held by 426 WorldCat member libraries worldwide
Elementary number theory is concerned with arithmetic properties of the ring of integers. Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting, for example, analogues of the theorems of Fermat and Euler, Wilsons theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlets theorem on primes in an arithmetic progression. After presenting the required foundational material on function fields, the later chapters explore the analogy between global function fields and algebraic number fields. A variety of topics are presented, including: the ABCconjecture, Artins conjecture on primitive roots, the BrumerStark conjecture, Drinfeld modules, class number formulae, and average value theorems. The first few chapters of this book are accessible to advanced undergraduates. The later chapters are designed for graduate students and professionals in mathematics and related fields who want to learn more about the very fruitful relationship between number theory in algebraic number fields and algebraic function fields. In this book many paths are set forth for future learning and exploration. Michael Rosen is Professor of Mathematics at Brown University, where hes been since 1962. He has published over 40 research papers and he is the coauthor of A Classical Introduction to Modern Number Theory, with Kenneth Ireland. He received the Chauvenet Prize of the Mathematical Association of America in 1999 and the Philip J. Bray Teaching Award in 2001
Elements of number theory; including an introduction to equations over finite fields by
Kenneth F Ireland(
Book
)
6 editions published in 1972 in English and held by 384 WorldCat member libraries worldwide
6 editions published in 1972 in English and held by 384 WorldCat member libraries worldwide
Exposition by Emil Artin : a selection by
Emil Artin(
Book
)
9 editions published in 2007 in English and held by 221 WorldCat member libraries worldwide
"Emil Artin was one of the great mathematicians of the twentieth century. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching and expository writing. In this volume we gather together in one place a selection of his writings wherein the reader can learn some mathematics as seen through the eyes of a true master."Jacket
9 editions published in 2007 in English and held by 221 WorldCat member libraries worldwide
"Emil Artin was one of the great mathematicians of the twentieth century. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching and expository writing. In this volume we gather together in one place a selection of his writings wherein the reader can learn some mathematics as seen through the eyes of a true master."Jacket
The Arithmetic of function fields : proceedings of the workshop at the Ohio State University, June 1726, 1991(
Book
)
17 editions published between 1992 and 2011 in English and held by 158 WorldCat member libraries worldwide
17 editions published between 1992 and 2011 in English and held by 158 WorldCat member libraries worldwide
Two theorems on Galois cohomology by
Michael I Rosen(
Book
)
5 editions published between 1964 and 1968 in English and Undetermined and held by 21 WorldCat member libraries worldwide
5 editions published between 1964 and 1968 in English and Undetermined and held by 21 WorldCat member libraries worldwide
The Jacobson radical of a group algebra by
Michael I Rosen(
Book
)
4 editions published between 1963 and 1965 in English and held by 20 WorldCat member libraries worldwide
4 editions published between 1963 and 1965 in English and held by 20 WorldCat member libraries worldwide
A Classical Introduction to Modern Number Theory by
Kenneth F Ireland(
)
2 editions published between 1982 and 1990 in English and held by 6 WorldCat member libraries worldwide
2 editions published between 1982 and 1990 in English and held by 6 WorldCat member libraries worldwide
The vocal behaviour of the Spring Peeper, Hyla crucifer by
Michael I Rosen(
Book
)
3 editions published in 1974 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1974 in English and held by 4 WorldCat member libraries worldwide
Representations of twisted group rings by
Michael I Rosen(
)
2 editions published between 1963 and 1978 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1963 and 1978 in English and held by 3 WorldCat member libraries worldwide
Number Theory in Function Fields by
Michael I Rosen(
)
1 edition published in 2002 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 3 WorldCat member libraries worldwide
The class group of an absolutely Abelian lextension by
Gary Cornell(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
Studying links via closed braids by
Joan S Birman(
Book
)
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
Klassicheskoe vvedenie v sovremennuiu teoriiu chisel by Kenneth Ireland(
Book
)
1 edition published in 1987 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in Russian and held by 2 WorldCat member libraries worldwide
A note on the splitting of the Hilbert class field by
Gary Cornell(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
Exposition by Emil Artin : a selection by
Emil Artin(
Book
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Klassičeskoe vvedenie v sovremennuû teoriû čisel by
Kenneth F Ireland(
Book
)
1 edition published in 1987 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1987 in Russian and held by 1 WorldCat member library worldwide
Quality measures for the emergency services(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Klassičeskoe vvedenie v sovremennujo teoriju čisel : A classical introduction to modern number theory by K Ajerland(
Book
)
1 edition published in 1987 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1987 in Russian and held by 1 WorldCat member library worldwide
Exposition by Emil Artin by
Michael I Rosen(
)
1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide
Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. He also discovered and proved the Artin reciprocity law, the culmination of over a century and a half of progress in algebraic number theory. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching a
1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide
Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. He also discovered and proved the Artin reciprocity law, the culmination of over a century and a half of progress in algebraic number theory. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching a
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Related Identities
 Ireland, Kenneth F. Author
 Hayes, David (David R.) Editor
 Goss, David 1952 Editor
 Artin, Emil 18981962 Author
 International mathematical research institute (Columbus, Ohio) Editor
 Cornell, Gary Author
 Ohio State University
 Ireland, Kenneth Author
 Birman, Joan Author
 Ontario Hydro
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Associated Subjects
Algebraic fields Algebraic functions Braid theory Drinfeld modules Emergency medicineStandards Field theory (Physics) Finite fields (Algebra) Frogs Galois theory Gamma functions Geometry, Algebraic Group rings Group theory Homology theory Mathematics Number theory Rings (Algebra) Sexual behavior in animals
Alternative Names
Michael Rosen Amerikaans wiskundige
Michael Rosen amerikansk matematikar
Michael Rosen amerikansk matematiker
Michael Rosen mathématicien américain
Michael Rosen USamerikanischer Mathematiker
Rosen, Michael.
Rosen Michael 1938....
Rosen, Michael I.
Rosen, Michael Ira
Rouzen, M.
Rouzen, M. 1938
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