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Abstract Algebra Theory and Applications [Judson ] - mklabgr - 02-01-2025
Thomas W. Judson’s Abstract Algebra: Theory and Applications is a rigorous but accessible undergraduate introduction to abstract algebra, designed primarily for mathematics majors at the junior/senior level. The book begins with mathematical preliminaries, integers, and proof techniques before developing group theory in depth: groups, cyclic and permutation groups, cosets, Lagrange’s theorem, isomorphisms, normal subgroups, factor groups, homomorphisms, group actions, and the Sylow theorems. A notable feature is its emphasis on applications, with dedicated chapters on cryptography, algebraic coding theory, matrix groups, and symmetry.
The second major part moves from groups to rings, polynomials, integral domains, Boolean algebras, vector spaces, finite fields, and Galois theory, giving the reader a broad foundation in the central structures of modern algebra. Judson combines theoretical and computational exercises, with roughly 400 exercises in the current open-textbook version, and integrates Sage for computational exploration. Overall, it is particularly valuable as a first serious course in abstract algebra because it balances proofs and theory with concrete examples and applications, while remaining an openly available textbook that can be used for either a one- or two-semester course.
https://drive.google.com/file/d/1yXfpmIFkuO6zw5Tu2pdy1-o3nisHTYa1/view?usp=sharing