Vol. VIII, 1957 Buehbespreehungen - Book Reviews - Notices bibliographiques 255

V a r i a - Misce l laneous - D ive r s

International Congress of Mathematicians, Edinburgh, August 14th- 21st, 1958

A t t h e i n v i t a t i o n of t h e C i ty a n d U n i v e r s i t y of E d i n b u r g h a n d t h e R o y a l Soc i e ty of L o n d o n , t h e I n t e r n a t i o n a l Congress of M a t h e m a t i c i a n s will m e e t in E d i n b u r g h f r o m A u g u s t 14 th to A u g u s t 21st, 1958. His R o y a l H i g h n e s s t h e D u k e of E d i n b u r g h ha s g rac ious ly c o n s e n t e d to e x t e n d his p a t r o n a g e to t h e Congress .

T h e E x e c u t i v e C o m m i t t e e is i n v i t i n g a n u m b e r of m a t h e m a t i c i a n s to de l ive r o n e - h o u r a n d h a l f - h o u r addresses . T h e r e will also be da i ly sessions d e v o t e d to f i f t e e n - m i n u t e c o m m u n i c a t i o n s . Those w ho wish to p r e s e n t such c o m m u n i c a t i o n s will h a v e a n o p p o r t u n i t y of o f fe r ing to do so w h e n t h e y rece ive t h e Second C o m m u n i c a t i o n .

T h e r e will be e igh t sec t ions , n a m e l y : 1. Logic and Foundations. 2. Algebra and Theory o/ Numbers. 3. Analysis. 4. Topology. 5. Geometry. 6. Probability and Statistics. 7. Applied Mathematics, Mathematical Physics and Numerical Analysis. 8. History and Education.

Those who wish to rece ive f u r t h e r i n f o r m a t i o n a b o u t t h e Congress are r e q u e s t e d to c o m m u n i c a t e t h e i r n a m e a n d full add r e s s as soon as poss ib le to t h e s e c r e t a r y : D r F r a n k Smi th i e s , M a t h e m a t i c a l I n s t i t u t e , 16 C h a m b e r s S t ree t , E d i n b u r g h , 1, Sco t l and . T o w a r d s t h e e n d of 1957 t h e y will rece ive a Second C o m m u n i c a t i o n g iv ing more de t a i l ed i n f o r m a t i o n a n d spec i fy ing t h e fees to be p a i d b y m e m b e r s ; a f o r m of a p p l i c a t i o n for m e m b e r s h i p of t h e Congress will be inc luded .

F. Smithies

B u c h b e s p r e c h u n g e n - B o o k R e v i e w s - No t i ce s b i b l i o g r a p h i q u e s

Elementare Differentialgeometrie. V o n W. HAACX (Birkh~Luser Ver lag, Base l u n d S t u t t g a r t 1955). 239 S., 25 Abb . ; g e b u n d e n Fr. 22.-, b r o s c h i e r t Fr . 18.70.

Dieses W e r k i s t aus d e m Bi ich le in Di//erenSialgeometrie I desse lben Ver fassers h e r v o r g e g a n g e n , das 1947 in de r W o t f e n b t i t t e l e r V e r l a g s a n s t a l t e r s ch i enen ist . Sein I n h a l t u m f a s s t e e ine D a r s t e l l u n g de r k l a s s i s chen K u r v e n - u n d F l g c h e n - t h e o r i e au f vek to r i e l l e r Grund lage . I n der n u n v o r l i e g e n d e n Elementaren DiMe- rentialgeometrie b r i n g t HAACK d a r i i b e r h i n a u s eine E i n f i i h r u n g in die C a r t a n s c h e n M e t h o d e n des <~rep~re mobile~> (bewegl iches Dre ibe in) u n d de r sch ie fen Dif feren- t i a l f o r m e n sowie eine e i n g e h e n d e B e h a n d l u n g e in iger E x i s t e n z p r o b l e m e de r Fl~ichentheor ie .

Die D a r s t e l l u n g i s t l e i ch tvers t~ ind l ich geha l t en . HAACKS B u c h e r l e i ch t e r t au f diese Weise d e m Anf~inger d e n Z u g a n g zu d e n w i c h t i g s t e n E r g e b n i s s e n u n d Ar- b e i t s m e t h o d e n de r D i f f e r en t i a lgeome t r i e . I n s b e s o n d e r e sei au f die A u s e i n a n d e r - s e t z u n g de r I d e e n y o n CARTAN h ingewiesen , die j e t z t n a c h u n d n a c h in de r d e u t s c h s p r a c h i g e n L i t e r a t u r zu r I n f i n i t e s i m a l g e o m e t r i e E i n g a n g f inden . De r Ver- Iasser e n t w i c k e l t zue r s t die G r u n d p r o b l e m e m i t e l e m e n t a r e n H i l f s m i t t e l n u n d d a n n h e r n a c h n o c h m a l s v o n n e u e m im S i n n e v o n CARTAN. I n den Sch lusskap i - t e l n v e r w e n d e t HAACK d a n n n u r n o c h den sch ie fen Di f fe ren t ia lka lkf i l . So w i rd