Book Review: Mordell, Diophantine equations
Serge Lang · Bulletin of the American Mathematical Society · 1970
Singer.The Hoffman-Singer theory of maximal algebras and the Helson-Lowdenslager work on invariant subspaces and cocylces is made available for the first time in book form.Also included are extensions of the works of these authors due to deLeeuw and Glicksberg and Gamelin.This review would be incomplete without a few words on the merits of these books as textbooks.Browder's book seems ideal for a onesemester course for students who already know some function theory and basic Ban ach space theory.Because of the more detailed treatment, the student may find it easier to read Browder.The first two chapters of Gamelin can be also used as material for an introductory course.The later chapters offer a magnificent selection of topics that can be offered in specialized courses.Browder's book does not offer any exercises.It also lacks a terminological index.Gamelin's book contains exercises of varying degrees of complexity.Some of the problems are actually theorems from recent papers.In such cases the author purposely omits the references.The reviewer feels that it would have been nicer to give references to some of the more difficult exercises.