Introductory Modern Algebra (PDF)

Praise for the First Edition

"Stahl offers the solvability of equations from the historical
point of view...one of the best books available to support a
one-semester introduction to abstract algebra."

--CHOICE

Introductory Modern Algebra: A Historical Approach, Second
Edition presents the evolution of algebra and provides readers
with the opportunity to view modern algebra as a consistent
movement from concrete problems to abstract principles. With a few
pertinent excerpts from the writings of some of the greatest
mathematicians, the Second Edition uniquely facilitates the
understanding of pivotal algebraic ideas.

The author provides a clear, precise, and accessible
introduction to modern algebra and also helps to develop a more
immediate and well-grounded understanding of how equations lead to
permutation groups and what those groups can inform us about such
diverse items as multivariate functions and the 15-puzzle.
Featuring new sections on topics such as group homomorphisms, the
RSA algorithm, complex conjugation, the factorization of real
polynomials, and the fundamental theorem of algebra, the Second
Edition also includes:

* An in-depth explanation of the principles and practices of
modern algebra in terms of the historical development from the
Renaissance solution of the cubic equation to Dedekind's
ideals

* Historical discussions integrated with the development of
modern and abstract algebra in addition to many new explicit
statements of theorems, definitions, and terminology

* A new appendix on logic and proofs, sets, functions, and
equivalence relations

* Over 1,000 new examples and multi-level exercises at the end of
each section and chapter as well as updated chapter summaries

Introductory Modern Algebra: A Historical Approach, Second
Edition is an excellent textbook for upper-undergraduate
courses in modern and abstract algebra.