Stahl's "example-abstract" approach emphasizes that modern algebra evolved as a response to concrete problems, primarily the solvability of equations.
Introductory Modern Algebra: A Historical Approach by Saul Stahl, published by Wiley , is a unique undergraduate textbook that deviates from the standard axiomatic "group-then-ring-then-field" teaching method. Instead, it uses the historical quest to solve polynomial equations by radicals as a motivating narrative to introduce abstract concepts. Core Philosophy and Structure Introductory Modern Algebra: A Historical Appro...
: The second edition contains over 1,000 exercises, many of which focus on non-routine computations and verifications rather than just abstract proofs. Critical Reception Core Philosophy and Structure : The second edition
: Chapters 1–3 focus on formalizing what it means to solve an equation by radicals. : Chapters 4–7 explore fields, centered on the
: Includes classic topics like the Euclidean algorithm, Fermat’s Theorem, and RSA Encryption .
: Chapters 4–7 explore fields, centered on the Primitive Element Theorem as a unifying concept.
Much of modern algebra has its roots in the solvability of equations by radicals. Most introductory modern algebra texts, however, Amazon.com Introductory Modern Algebra A Historical Approach