PREFACE T O TH E RUSSIA N EDITIO N x i
The second part ("Th e Secon d Year of Education") consist s of 9 chapters, som e
of whic h jus t continu e th e discussio n i n th e firs t par t (fo r example , th e chapter s
"Graphs-2" an d "Combinatorics-2") . Othe r chapter s ar e comprise d o f materia l
considered t o b e too complicated fo r th e firs t year : "Invariants" , "Induction" , "In -
equalities".
Appendix A tell s abou t five mai n type s o f mathematica l contest s popula r i n
the forme r Sovie t Union . Thes e contest s ca n b e hel d a t session s o f mathematica l
circles or use d t o organiz e contest s betwee n differen t circle s or eve n schools .
Advice to th e teache r i s usually give n unde r th e remar k labelle d "Fo r teach -
ers" . Rar e occasion s o f "Methodologiea l remarks " contai n mostl y reeommen -
dations about th e methodology of problem solving: the y draw attention to the basi c
patterns o f proofs o r method s o f recognizing an d classifyin g problems .
§3. Technicalitie s an d legen d
(1) Th e mos t difflcul t problem s ar e marke d wit h a n asteris k (*) .
(2) Almos t al l o f th e problem s ar e commente d o n i n Appendi x B : eithe r a
full solutio n o r a t leas t a hin t an d answer . I f a proble m i s computational , the n
we usuall y provid e onl y a n answer . W e d o no t giv e th e solution s t o problem s fo r
independent solutio n (this , i n particular , goe s fo r al l th e problem s fro m Chapter s
8 an d 17).
(3) All the references can be found a t the end of the book in the list of references.
The book s we recommend mos t ar e marke d wit h a n asterisk .
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