Aufgaben und Lehrsätze aus der Analysis.

MOST French and German mathematical text-books differ from the English books in one important particular: they contain no examples for solution. The working of problems and examples has long been one of the features of English mathematical teaching. All able mathematical students of a generation ago were expected to gain practice in manipulation by solving hard problems. Wolstenholme's problem book reflects the tendency of the period in which it was compiled, a large proportion of its examples being somewhat artificial in character despite the elegant solutions they admit. Now the tendency is to avoid problems involving hard manipulation, it being considered that familiarity with mathematical subjects can be gained by working easy examples constructed to test a student's knowledge of fundamental principles. The new Wolstenholme still remains to be written.Aufgaben und Lehrsätze aus der Analysis.Von Prof. G. Pólya G. Szegö. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 19 and 20.) Erster Band: Reihen, Integralrechnung, Funktionentheorie. Pp. xvi + 338. 15 gold marks. Zweiter Band: Funktionentheorie, Nullstellen, Polynome, Determinanten, Zahlentheorie. Pp. x + 407. 18 gold marks. (Berlin: Julius Springer, 1925.)