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Softcover ISBN:  9780821869048 
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Softcover ISBN:  9780821869048 
Product Code:  HMATH/32.S 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470418083 
Product Code:  HMATH/32.E 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 
Softcover ISBN:  9780821869048 
eBook ISBN:  9781470418083 
Product Code:  HMATH/32.S.B 
List Price:  $245.00 $185.00 
MAA Member Price:  $220.50 $166.50 
AMS Member Price:  $196.00 $148.00 

Book DetailsHistory of MathematicsVolume: 32; 2007; 336 ppMSC: Primary 01;
Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still.
The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenthcentury work of Charles Babbage on functional equations to Alexandre Grothendieck's midtwentiethcentury metaphor of a “rising sea” in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of noncommutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century.
The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.ReadershipGraduate students and research mathematicians interested in the history of mathematics and algebra.

Table of Contents

Chapters

Acknowledgments

Introduction

Babbage and French Idéologie: Functional equations, language, and the analytical method

“Very full of symbols”: Duncan F. Gregory, the calculus of operations, and the Cambridge Mathematical Journal

Divisibility theories in the early history of commutative algebra and the foundations of algebraic geometry

Kronecker’s fundamental theorem of general arithmetic

Developments in the theory of algebras over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory

Minkowski, Hensel, and Hasse: On the beginnings of the localglobal principle

Research in algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert

Emmy Noether’s 1932 ICM lecture on noncommutative methods in algebraic number theory

From Algebra (1895) to Moderne Algebra (1930): Changing conceptions of a discipline—A guided tour using the Jahrbuch über die Fortschritte der Mathematik

A historical sketch of B. L. van der Waerden’s work in algebraic geometry: 1926–1946

On the arithmetization of algebraic geometry

The rising sea: Grothendieck on simplicity and generality


Additional Material

Reviews

This book offers new light on the development and history of modern algebra.
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Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still.
The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenthcentury work of Charles Babbage on functional equations to Alexandre Grothendieck's midtwentiethcentury metaphor of a “rising sea” in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of noncommutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century.
The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.
Graduate students and research mathematicians interested in the history of mathematics and algebra.

Chapters

Acknowledgments

Introduction

Babbage and French Idéologie: Functional equations, language, and the analytical method

“Very full of symbols”: Duncan F. Gregory, the calculus of operations, and the Cambridge Mathematical Journal

Divisibility theories in the early history of commutative algebra and the foundations of algebraic geometry

Kronecker’s fundamental theorem of general arithmetic

Developments in the theory of algebras over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory

Minkowski, Hensel, and Hasse: On the beginnings of the localglobal principle

Research in algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert

Emmy Noether’s 1932 ICM lecture on noncommutative methods in algebraic number theory

From Algebra (1895) to Moderne Algebra (1930): Changing conceptions of a discipline—A guided tour using the Jahrbuch über die Fortschritte der Mathematik

A historical sketch of B. L. van der Waerden’s work in algebraic geometry: 1926–1946

On the arithmetization of algebraic geometry

The rising sea: Grothendieck on simplicity and generality

This book offers new light on the development and history of modern algebra.
EMS Newsletter