Galois Theory

Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra. Key topics and features of this book include: approaches Galois theory from the linear algebra point of view, following Artin; develops the basic concepts and theorems of Galois theory, including algebraic, normal, separable, and Galois extensions, and the Fundamental Theorem of Galois Theory; presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity; and excellent motivaton and examples throughout.