Cambridge mathematical library

The late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables, and the second the compilation of a collection of results of value to mathematicians and physicists who encounter Bessel functions in the course of their researches. The completeness of the theoretical account, combined with the wide scope of the collection of practical examples and the extensive numerical tables, have resulted in a book which is indispensable to pure mathematicians, to applied mathematicians, and to physicists alike.

The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir 'Sur la Theorie des Nombres Entiers Algebriques' first appeared in installments in the Bulletin des sciences mathematiques in 1877. This is a translation of that work by John Stillwell, who also adds a detailed introduction that gives the historical background as well as outlining the mathematical obstructions that Dedekind was striving to overcome. The memoir gives a candid account of Dedekind's development of an elegant theory as well as providing blow by blow comments as he wrestles with the many difficulties encountered en-route.