Episodes in the History of Modern Algebra (1800-1950) (History of Mathematics)

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 Nineteenth-century Work Of Charles Babbage On Functional Equations To Alexandre Grothendieck's Mid-twentieth-century 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 Non-commutative 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. Co-published With The London Mathematical Society Beginning With Volume 4. Members Of The Lms May Order Directly From The Ams At The Ams Member Price. The Lms Is Registered With The Charity Commissioners. Introduction / Jeremy J. Gray, Karen Hunger Parshall -- Babbage And French Ideologie: Functional Equations, Language, And The Analytical Method / Eduardo L. Ortiz -- Very Full Of Symbols: Duncan F. Gregory, The Calculus Of Operations, And The Cambridge Mathematical Journal / Sloan Evans Despeaux -- Divisibility Theories In The Early History Of Commutative Algebra And The Foundations Of The Algebraic Geometry / Olaf Neumann -- Kronecker's Fundamental Theorem Of General Arithmetic / Harold M. Edwards -- 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 / Gunther Frei -- Minkowski, Hensel, And Hasse: On The Beginnings Of The Local-global Principle / Joachim Schwermer -- Research In Algebra At The University Of Chicago: Leonard Eugene Dickson And A. Adrian Albert / Della Dumbaugh Fenster -- Emmy Noether's 1932 Icm Lecture On Noncommutative Methods In Algebraic Number Theory / Charles W. Curtis -- From Algebra (1895) To Moderne Algebra (1930): Changing Conceptions Of A Discipline: A Guided Tour Using The Jahrbuch Uber Die Fortschritte Der Mathematik / Leo Corry -- A Historical Sketch Of B.l Van Der Waedern's Work In Algebraic Geometry: 1926-1946 / Norbert Schappacher -- On The Arithmetization Of Algebraic Geometry / Silke Slembek -- The Rising Sea: Grothendieck On Simplicity And Generality / Colin Mclarty. Jeremy J. Gray And Karen Hunger Parshall, Editors. Includes Bibliographical References And Index.