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 .