本书讲述了：Iishhatlgebraouldeheinderellafurtory.nheath-ematicsrogramnchools,eometryasfteneenheavoriteaugh-ter.hemountfeometricnowledgetudiednchoolsspprox-imatelyqualoheevelchievednncientreecendummarizedyuclidnislementsthirdentury.C.).orongime,eom-tryasaughtccordingouclid;implifiedariantsaveecentlyppeared.npitefllhehangesntroducedneometryours-es,eometryetainshenfluencefuclidndhenclinationfherandiosecientificevolutionhatccurrednreece.orehannceaveetersonhoaid,Iidn\'thooseathsyrofession,but\'lleverorgetheeautyfhelegantdificeuiltneometryithtstricteductionforendoreomplicatedropositions,lleginningromheeryimplest,ostbvioustatements!\"Unfortunately,aveevereardimilarssessmentoncerningl-gebra.lgebraoursesnchoolsomprisetrangeixturefsefulules,ogicaludgments,ndxercisesnsingidsuchsablesfog-arithmsndocketalculators.uchourseslosernpiritoherandfathematicsevelopednncientgyptndabylonhanoheinefevelopmenthatppearednncientreecendhenon-tinuedromheenaissancenesternurope.evertheless,lgebrasustsundamental,ustseep,ndustseautifulseometry.Moreover,romhetandpointfheodernivisionfathemat-icsntoranches,helgebraoursesnchoolsncludelementsromeveralranches:lgebra,umberheory,ombinatorics,nditfrobabilityheory.

Preface.ntegersTopic:umbers).Isotational.Therrationalityftherquareoots.Decompositionntorimeactors.implestropertiesfolynomialsopic:olynomials).Rootsndheivisibilityfolynomials.Multipleootsndheerivative.Birmmialormulaupplement:olynomialsndernoulliumbers.initeetsTopic:ets).Setsndubsets.Combinatorics.Setlgebra0.heanguagefrobabilityupplement:hehebyshevnequality.rimeumbersTopic:umbers)1.heumberfrimeumberssnfinite2.uler\'sroofhatheumberfrimeumberssnfinite3.istributionfrimeumbersupplement:hehebyshevnequalityorr(n).ealumbersndolynomialsTopic:umbersndolynomials)4.xiomsfheealumbers5.imitsndnfiniteums6.epresentationfealumberssecimalractions7.ealootsfolynomialsupplement:turm\'sheorem.nfiniteetsTopic:ets)8.quipotence9.ontinuum0.hinetsupplement:ormalumbers.owereriesTopic:olynomials)1.olynomialsseneratingunctions2.owereries3.artitioumerorumupplement:heulerentagonheorem.upplement:eneratingunctionorernoulliumbersatesfivesfathematiciansentionednheextndex.