(1) Leçons sur la théorie des espaces à connexion projective (2) Differential Systems (3) Introduction mathématique aux théories quantiques (4) Éléments de géométrie infinitésimale (5) Über einige neuere Fortschritte der additiven Zahlentheorie

Abstract

(1) PROF. CARTAN'S work on the theory of spaces with projective connexions is executed in accordance with a plan originally set forth in another work of his on generalized spaces. The present volume is divided into two parts, the first of which serves as an introduction to the second, and presents a survey of the different methods employed in projective differential geometry with emphasis upon those which may be generalized in the theory of spaces with projective connexions proper. Prof. Cartan chooses the simplest of problems here ; indeed certain of them are chosen only for their instrumentality in illustrating the different methods employed. Thus, as he says, the first part cannot lay claim to being in any sense an exhaustive treatise on projective differential geometry.

(1) Leçons sur la théorie des espaces à connexion projective

By Prof. E. Cartan. Rédigées par Dr. P. Vincensini. (Cahiers scientifiques, Fascicule 17.) Pp. vi + 308. (Paris: Gauthier-Villars, 1937.) 85 francs.

(2) Differential Systems

By Prof. Joseph Miller Thomas. (American Mathematical Society, Colloquium Publications, Vol. 21.) Pp. ix + 118. (New York: American Mathematical Society, 1937.) 2 dollars.

(3) Introduction mathématique aux théories quantiques

Par Prof. Gaston Julia. (Cahiers scientifiques. Fascicule 16.) Première partie. Pp. vi + 220. (Paris: Gauthier-Villars, 1936.) 60 francs.

(4) Éléments de géométrie infinitésimale

Par Prof. Gaston Julia. (Cours de la Faculté des Sciences.) Deuxième édition. Pp. vii + 262. (Paris: Gauthier-Villars, 1936.) 60 francs.

(5) Über einige neuere Fortschritte der additiven Zahlentheorie.

Von Edmund Landau. (Cambridge Tracts in Mathematics and Mathematical Physics, No. 35.) Pp. vii + 94. (Cambridge: At the University Press, 1937.) 6s. net.