"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."
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.
Keywords: Modern / Abstract Algebra, algebra, modern algebra, math history, RSA algorithm, logic, proof, sets, functions, equivalence relations, prime factorizations, Sylow theory, complex numbers, solutions of equations, modular arithmetic, binomial theorem, modular powers, rings and fields, polynomials, Galois, galois fields, permutations, groups, quotient groups, elementary group theory