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 relationshipbetween 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.
