Galois Theory

This book on basic Galois theory is refreshingly different from the many books on the same subject already on the market. It covers the standard basic material-symmetric polynomials, field extensions, normal and Galois extensions, the Galois correspondence, cyclotomic extensions, solvable groups, finite fields, and separable and inseparable extensions. However, it also contains the following original features: a sketch of the early history of the subject, containing a large number of excerpts from original works and a discussion of the problems of notation, discovery, mathematical habits, and disputes of former times; a complete chapter on explicit constructions with ruler and compass; a chapter on the life of Evariste Galois; and a chapter on recent developments that attempts to give an idea of what researchers in Galois theory are working on today.

The book requires only standard algebra (groups, rings, fields) as background and is eminently suitable for an undergraduate course on Galois theory. It contains a large number of useful exercises, most with their solutions. Because of its exciting and very human approach, it should attract even students who are not mathematics majors to the beautiful subject of Galois theory.

Jean-Pierre Escofier is Maitre de conferences at the University of Rennes 1, France. He has also worked for over 20 years with high-school teachers in the French IREM, Research Institute for the Teaching of Mathematics.