This exposition provides a comprehensive historical account of the
intellectual lineage behind the basic concepts, results, and
theories of abstract algebra. Prior to the 19th century, the
concept of "algebra" strictly referred to the study of the solution
of polynomial equations. By the 20th century it came to encompass
the study of abstract, axiomatic systems such as groups, rings, and
fields.
Abstract algebra came into existence largely because
mathematicians were unable to solve classical problems by classical
means. A major theme of this book is to demonstrate how abstract
algebra can illuminate the solution to some of these concrete
problems. By focusing on the history of the sources of the subject
and considering the context in which the originator of an idea was
operating, the reader can better comprehend the "burning problem"
that spurred the innovation, while gaining a deeper appreciation of
the mathematics involved.
Key features:
* Begins with a substantial discussion of the history of
classical algebra
* Contains separate chapters detailing the development of
groups, rings, and fields
* Examines the history of linear algebra and relates its
evolution to abstract algebra
* Highlights the lives and works of six notables: Cayley,
Dedekind, Galois, Gauss, Hamilton, and especially the pioneering
work of Noether
* Suggests a detailed outline for instructors on methods for
integrating the history of abstract algebra into their teaching
* Each chapter concludes with suggested project assignments and
extensive references to the relevant literature
The book may serve as a primary text for a course on the history
of modern algebra, or as a supplementaltext for an abstract algebra
course or a more general course on the history of mathematics.
Additionally, graduate students studying to become mathematics
instructors or existing math teachers will find the work
particularly useful as a guide for designing a course in abstract
algebra inspired by history. Finally, algebraists and historians of
science will find the book a valuable reference.
General
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