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.
