Topics in Algebra (2nd Edition)

Topics in Algebra (2nd Edition) by I. N. Herstein is a world-renowned, classic textbook widely regarded as a cornerstone of modern abstract algebra literature. Published by John Wiley & Sons, this 2nd Edition is celebrated for its clear exposition, deep mathematical rigor, and Herstein's distinctive, engaging commentary that guides students through abstract algebraic structures.

This textbook is extensively prescribed across BS Mathematics, MS Mathematics, M.Phil, PhD coursework, and theoretical physics programs at leading Pakistani universities and institutes.

The book thoroughly covers the core foundational areas of abstract algebra:

- Group Theory: Subgroups, normal subgroups, quotient groups, homomorphisms, Cayley's Theorem, permutation groups, direct products, and the Sylow Theorems.

- Ring Theory: Ring homomorphisms, ideals, quotient rings, maximal and prime ideals, Euclidean rings, polynomial rings, and unique factorization domains (UFDs).

- Vector Spaces & Modules: Vector spaces, dual spaces, inner product spaces, and modules over principal ideal domains.

- Fields & Galois Theory: Field extensions, roots of polynomials, splitting fields, construction with straightedge and compass, Galois groups, and solvability by radicals.

- Linear Transformations: Canonical forms, triangular form, nilpotent transformations, Jordan form, and Hermitian, unitary, and normal operators.

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