LEADER 04433nam 2200553Ia 450 001 9910812251103321 005 20200520144314.0 010 $a0-88385-957-2 035 $a(CKB)2670000000205164 035 $a(EBL)3330405 035 $a(OCoLC)923220141 035 $a(UkCbUP)CR9780883859575 035 $a(Au-PeEL)EBL3330405 035 $a(CaPaEBR)ebr10729376 035 $a(OCoLC)929120138 035 $a(RPAM)12569065 035 $a(MiAaPQ)EBC3330405 035 $a(EXLCZ)992670000000205164 100 $a20011025d2003 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical miniatures /$fSvetoslav Savchev, Titu Andreescu 205 $a1st ed. 210 $aWashington, D.C. $cMathematical Association of America$dc2003 215 $a1 online resource (xi, 223 pages) $cdigital, PDF file(s) 225 0$aAnneli Lax new mathematical library ;$vv. 43 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 $a0-88385-645-X 327 $g1.$tA telescoping sum --$g2.$tLagrange's identity --$g3.$tPerfect squares --$g4.$tLest common multiples --$g5.$tTrig substitutions --$tCoffee break 1 --$g6.$tPopoviciu's theorem --$g7.$tCatalan's identity --$g8.$tSeveral inequalities --$g9.$tVectors --$g10.$tMathematical induction at work --$tCoffee break 2 --$g11.$tA highly divisible determinant --$g12.$tHermite's identity --$g13.$tComplete sequences --$g14.$tThree polynomials --$g15.$tMore about induction --$tCoffee break 3 --$g16.$tA classical identity --$g17.$tMultiplicative functions --$g18.$tThe "arbitrary" Proizvolov --$g19.$tHo?lder's inequality --$g20.$tSymmetry --$tCoffee break 4 --$g21.$tHe knows I know he knows --$g22.$tA special inequality --$g23.$tTwo inductive constructions --$g24.$tSome old-fashioned geometry --$g25.$tExtremal arguments --$tCoffee break 5 --$g26.$tThe AMS inequality --$g27.$tHelly's theorem for one dimension --$g28.$tTwo approaches --$g29.$tRadical axis --$g30.$tThe pigeonhole principle --$tCoffee break 6 --$g31.$tThe three jug problem --$g32.$tRectifying trajectories --$g33.$tNumerical systems --$g34.$tMore on polynomials --$g35.$tGeometric transformations --$tCoffee break 7 --$g36.$tThe Game of life problem --$g37.$tTetrahedra with a point in common --$g38.$tShould we count --$g39.$tLet's count now --$g40.$tSome elementary number theory --$tCoffee break 8 --$g41.$tEuclid's game --$g42.$tPerfect powers --$g43.$tThe 2n-1 problem --$g44.$tThe 2n+1 problem --$g45.$tThe 3n problem --$tCoffee break --$g46.$tPairwise sums --$g47.$tInteger progressions --$g48.$tIncomparable sets --$g49.$tMorse's sequence --$g50.$tA favorite of Erdo?s. 330 $aMathematical Miniatures is a problem collection of arresting mathematical insight and ingenuity. The authors brought together materials from mathematical competitions, books, research papers, discussions, and their own work. Such mathematical substance went far beyond the purposes of a traditional problem-solving book. The most attractive results refused to fit into the schemes of an instruction manual meant to exemplify typical problem solving techniques. A broader interpretation of these problems had to be identified, and this book is the fruit of that effort. Savchev and Andreescu detach certain statements or groups of related statements into independent sections. Treating these gems separately, in self-contained essays, emphasizes the source of their natural charm---connections with genuine mathematical experience. The essays are of impressive diversity, enlivened by fresh and original ideas. They involve concepts not only useful but also beautiful and nonstandard, with lots of esthetic appeal. The book is thus not so much a mathematical toolchest: it is an anthology of mathematical verse. 410 0$aAnneli Lax New Mathematical Library 606 $aMathematics$vProblems, exercises, etc 606 $aProblem solving 615 0$aMathematics 615 0$aProblem solving. 676 $a510 700 $aSavchev$b Svetoslav$01707387 701 $aAndreescu$b Titu$f1956-$0285837 712 02$aMathematical Association of America, 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812251103321 996 $aMathematical miniatures$94195357 997 $aUNINA