Scientific Serials

Abstract

Bulletin of the American Mathematical Society, November. —The first “Cambridge Colloquium” was held at Buffalo in 1896. In consequence of the British Association holding its meeting in 1897 at Toronto there was no Colloquium held in that year. The second Colloquium was held in the present year (August 22–27), at Harvard University. Two courses of six lectures each were delivered, the lecturers being Profs. Osgood and Webster. The latter gentleman took as his text “The partial differential equations connected with wave propagation”—an abstract of this course is to be given in a future number. Prof. Osgood lectured “On some methods and problems of the general theory of functions.” Lecture i. was devoted to Picard's theorem, and the application of Riemann's geometric methods in the general theory of functions. Lectures ii. and iii. discussed the representation of multiple-valued functions by means of single-valued functions of a parameter, treated geometrically by Riemann's methods and also Poincare's theorem. Lectures iv. and v. dwelt on some recent study of the relation between the properties of a function defined by a power series and the coefficients of that series. The last lecture was on certain Cantor's sets, and their application in a question concerning Cauchy's definition of an analytic function. The lectures are very fully reported, and illustrated with diagrams and bibliographical notes. The “Colloquium” is a very interesting and useful addition to the ordinary meetings of the Society. The above meeting was held at the same time as the American Association for the Advancement of Science held its semicentennial meeting, at which about 900 members were present. The section of mathematics and astronomy was well attended. The committee of the section accepted twelve papers in pure mathematics, thirteen in applied mathematics, and sixteen in astronomy. The titles of these are given, and short abstracts of their contents follow. Interesting notes and a list of recent mathematical publications close the number. The Bulletin well maintains the high position it has attained.