Eléments de Mathématiques, Livre III, by N. Bourbaki. Topologie générale Part I, Chapters 1-4. Troisième edition Hermann, Paris, 1961. Actualités scientifiques et industrielles 1142 et 1143. 263 + 236 pages. 72 N. F

M. Shimrat
1962 Canadian mathematical bulletin  
In this elementary book real and complex numbers are introduced as vectors on a line and in a plane respectively. Accordingly addition and multiplication are defined geometrically. The second chapter "Conformai Mapping 1 ' analyzes primitive mappings like z' = z + a , z 1 = cz . There is also a discussion of the general idea of a conformai mapping. Chapter III gives an entirely untechnical discussion of cartographical mappings, applications of conformai mapping in aerodynamics (profiles), a
more » ... s (profiles), a nice picture of Zhukovsky "whom Lenin called, in all fairness, the l Father of Russian Aviation' M . On pp. 35»57 we find a detailed study of the mappings z l = (z -a)(z -b)" 1, z 1 = z 2 , and the "Zhukovsky function" z ! = ^.{z+z" 1 ) . The book closes with 10 simple exercises with hints.
doi:10.1017/s0008439500026205 fatcat:skogpco3yzfnzbb6g2k2l2rb3u