Includes bibliographical references (p. [189]) and index.
"This textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of [pi] and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will learn about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths."--BOOK JACKET.
Field extensions -- Roots -- Galois theory -- A bit of group theory -- Applications -- Algebraic theory of differential equations.