A History of Abstract Algebra : From Algebraic Equations to Modern Algebra

Resource Information

The work A History of Abstract Algebra : From Algebraic Equations to Modern Algebra represents a distinct intellectual or artistic creation found in European University Institute. This resource is a combination of several types including: Work, Language Material, Books.

Label

A History of Abstract Algebra : From Algebraic Equations to Modern Algebra

Title remainder

From Algebraic Equations to Modern Algebra

Statement of responsibility

by Jeremy Gray

Creator

• Gray, Jeremy

Subject

• Algebra
• History
• Mathematics
• Number theory

Language

eng

Summary

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.--

Member of

• Springer Undergraduate Mathematics Series,

Assigning source

Provided by publisher

Image bit depth

0

Literary form

non fiction

Nature of contents

dictionaries

Series statement

• Springer eBooks.
• Springer eBooks
• Springer Undergraduate Mathematics Series,