Preface t o th e Russia n Editio n
§1. Introductio n
This boo k wa s originall y writte n t o hel p peopl e i n th e forme r Sovie t Unio n
who dealt wit h extracurricular mathematica l education : schoo l teachers, universit y
professors participatin g i n mathematica l educatio n programs , variou s enthusiast s
running mathematica l circles , o r peopl e wh o just wante d t o rea d somethin g bot h
mathematical an d recreational . And , certainly , student s ca n als o us e thi s boo k
independently.
Another reaso n fo r writin g thi s boo k wa s tha t w e considere d i t necessar y t o
record th e rol e playe d b y th e tradition s o f mathematica l educatio n i n Leningra d
(now St. Petersburg) ove r the last 6 0 years. Thoug h our city was, indeed, the cradl e
of th e olympia d movemen t i n th e USS R (havin g see n th e ver y firs t mathematica l
seminars fo r student s i n 1931-32 , an d th e first cit y olympia d i n 1934), an d stil l
remains on e o f th e leader s i n thi s particula r area , it s hug e educationa l experienc e
has no t bee n adequatel y recorde d fo r th e intereste d readers .
* * *
In spit e o f th e stylisti c variet y o f thi s book' s material , i t i s methodologicall y
homogeneous. Her e we have, we believe, all the basic topics for sessions of a mathe-
matical circle for the first tw o years of extracurricular educatio n (approximately , fo r
students of age 12-14). Ou r main objective was to make the preparation o f sessions
and th e gatherin g o f problem s easie r fo r th e teache r (o r an y enthusias t willin g t o
spend tim e wit h children , teachin g the m non-standar d mathematics) . W e wante d
to talk abou t mathematica l idea s which are important fo r students, an d abou t ho w
to dra w th e students ' atten t ion to thes e ideas .
We mus t emphasiz e tha t th e wor k o f preparin g an d leadin g a sessio n i s itsel f
a creativ e process . Therefore , i t woul d b e unwis e t o follo w ou r recommendation s
blindly. However , w e hop e tha t you r wor k wit h thi s boo k wil l provid e yo u wit h
material fo r mos t o f you r sessions . Th e followin g us e o f thi s boo k seem s t o b e
natural: whil e working on a specific topi c the teacher read s an d analyze s a chapte r
from th e book, an d after tha t begin s to construct a sketch of the session. Certainly ,
some adjustment s will hav e t o b e mad e becaus e o f th e leve l o f a give n grou p o f
students. A s supplementar y source s o f problem s w e recommend [13, 16, 24 , 31,
33], an d [40] .
* * *
We would lik e to mentio n tw o significan t point s o f the Leningra d traditio n o f
extracurricular mathematica l educationa l activity :
ix
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