nbUfnbujljt !txbwmfcb!!WJJ!lmbtTj! - Ganatleba

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- 18 - Tuki am mcnebis namdvili ganxorcieleba gvsurs, unda SeveguoT imas, rom moswavles bevri muSaoba mouwevs. unarCvevis ganviTarebis erTaderTi gza aris bevri damoukidebeli muSaoba da didi gamocdilebis dagroveba.! amas veraviTari meTodika Tu maswavleblis ostatoba ver Secvlis. oRond, cxadia, moswavlis es muSaoba saTanado Sinaarsisa da mimarTulebisa unda iyos. amitomaa Cveneul saxelmZRvaneloebSi Zalian mravlad sxvadasxvagvari amocanebi. Tanac, raime erTi gvaris amocanebi mizandasaxulad meordeba, TandaTanobiTi garTulebiT, Tanac, wlebis ganmavlobaSi. amocanaTa TviTeuli es Uboxzpcb romelime unarCvevas aviTarebs. amas ki, samwuxarod, didi dro da bevri muSaoba sWirdeba. Cveneul saxelmZRvaneloebSi mravladaa grZelpirobiani kompleqsuri amocanebi _ romelTa amosaxsnelad ramdenime sul sxvadasxva moqmedebis Catarebaa saWiro. magali- Tad: daTvaleT, gazomeT da SeavseT cxrili; daxazeT amaTuim saxis mravalkuTxedi, miniSneT misi umoklesi gverdi da masSi CaxazeT raime; daxazeT cxrili da daajgufeT asoebi; aRwereT sityvierad; Tuki aqvs, CawereT + niSani, Tuki ar aqvs _ CawereT _ niSani da ase Semdeg. TviTeuli es davaleba Zalian advilia, Tumca, mTlianobaSi, amocana sakmao Tanmimdevrulobas, yuradRebis mokrebasa da Zalisxmevas moiTxovs. magram saqme isaa, rom es kompleqsuroba Ubonjnefwsvmjb, anu Sedgeba ramdenime nabijisagan, romlebic cal-calke sruldeba. moswavlem jer mxolod pirvel nabijs unda miaqcios yuradReba, Seasrulos igi, Semdeg daiviwyos da momdevnoze gadavides, da ase Semdeg, ese igi, mas ar uwevs fsUespvmbe ramdenime ramis keTeba (rac Zalian Zneli iqneboda). arsebiTad, esaa amocanebi algoriTmis (instruqciis) Sesrulebaze. moswavles maTze sakmao droisa da Zalebis daxarjva mouwevs, Tanac, amiT maTematikis codnasac TiTqos bevri araferi
- 19 - emateba. samagierod, amgvari amocanebi saukeTesod aviTarebs unarCvevebs. amgvari amocanebi Zalian mniSvnelovania, radgan xels uwyobs moswavlis azrovnebis mowesrigebas da saSemsruleblo unarCvevaTa ganviTarebas. miT umetes, rom amgvari amocanebis instruqciaSi (algoriTmis aRweraSi) CarTulia logikuri kavSirebi da kvantorebi: Tuki, an, romelime, erTerTi, erTaderTi, yoveli... mTavaria, moswavlem gaigos, rom araa saWiro yvelaferze erTad fiqri: Seasrule jer erTi, Semdeg es daiviwye da gadadi meoreze, Semdeg esec daiviwye da gadadi mesameze... ... Tanac, rogorc yvela sxva saxis amocanebis jaWvedi, esec iwyeba jer Zalian advili, sul ornabijiani algoriTmebiT. § 4. maTematikis mravalmxrivi da Tan gaerTianebuli (integrirebuli) swavleba Cveneuli kursi bolomde, XII klasis CaTvliT, gaerTianebulia (integrirebulia) _ maTematikis yvela sxvadasxva dargi da maTi gamoyenebani erTiani saxelmZRvaneloebiT iswavleba. amasTan, dawyebiTi klasebidanve safuZvlianad muSavdeba saymawvilo sawyisebi aramarto ariTmetikisa, algebrisa da planimetriisa, aramed agreTve: stereometriisa, mxazvelobiTi geometriisa, kombinatorikisa da simravleTa Teoriisa, miaxloebiT SefasebaTa, maTematikuri statistikisa da modelirebisa, informatikisa, topologiisa da grafTa Teoriisa, logikisa. didi yuradReba eqceva am dargTa Soris kavSirebis warmoCenas da agreTve maTematikis mravalferovan gamoyenebebs: bunebismcodneoba-biologiasa Tu geografiaSi, fizikasa Tu astronomiaSi, qimiasa Tu teqnikaSi, ekonomikasa Tu sociologiaSi, agreTve humanitarul mecnierebebSi: istoriaSi, eTnografiaSi, kulturologiaSi da xelovnebaTmcodneobaSi. yvelaze mniSvnelovania maTematikisa da logikis integracia. logikis erTi nawili Cven Caqsovili gvaqvs maTematikis programaSi, xolo meore, ufro enobrivi nawili (ritorika) _
Page 1 and 2: - 1 - nbUfnbujljt q o r b u d a !tx
Page 3 and 4: - 3 - maTematikis maswavleblis mecx
Page 5 and 6: - 5 - gonebrivi unarebi, romlebic u
Page 7 and 8: - 7 - li sakiTxebis gasameoreblad _
Page 9 and 10: - 9 - veswrafviT moswavlis aramarto
Page 11 and 12: - 11 - xuli unda iyos SiSi. SiSze d
Page 13 and 14: - 13 - ganviTarebaSi da gaZlierebaS
Page 15 and 16: - 15 - mxolod `Sav Sromaze~ damyare
Page 17: - 17 - pasuxi moswavleebs aTqmevino
Page 21 and 22: - 21 - (cxadia, ubralo ariTmetikis
Page 23 and 24: - 23 - lia sazogadod klasifikaciuri
Page 25 and 26: - 25 - moswavle, romelsac kiTxva uW
Page 27 and 28: - 27 - jerovani yuradRebis miqceva
Page 29 and 30: - 29 - gadauWreli SesaWiria. xolo d
Page 31 and 32: - 31 - moswavlem daaklo raime sityv
Page 33 and 34: - 33 - moklea. am dros umjobesia, r
Page 35 and 36: - 35 - rialos~ axal an Znel sakiTxT
Page 37 and 38: - 37 - yvela moswavles ar moeTxoveb
Page 39 and 40: - 39 - moswavlemac gaiazros isini,
Page 41 and 42: - 41 - ramdenimewuTian saklaso wera
Page 43 and 44: - 43 - dasaTvleli Tu sxva saklaso s
Page 45 and 46: - 45 - Cveneuli meTodikiT momuSave
Page 47 and 48: - 47 - (ara damatebiTi Zneli) sakiT
Page 49 and 50: - 49 - miviCnevT maswavleblis nakla
Page 51 and 52: - 51 - klasSi mainc amoxsnis. amito
Page 53 and 54: - 53 - im terminebis farglebSi, rom
Page 55 and 56: - 55 - `saymawvilo maTematikis~ kid
Page 57 and 58: - 57 - farTobi {fuZis perimetrisa d
Page 59 and 60: - 59 - tronomiis, logikis, filosofi
Page 61 and 62: - 61 - mTliani simravlis tolZalovan
Page 63 and 64: - 63 - es asea, magram saamisod ram
Page 65 and 66: - 65 - amis ramdenime konkretuli ni
Page 67 and 68: - 67 - magram es yovelive _ gumanis
Page 69 and 70:
- 69 - kiTxi ukve karga xnis ganmav
Page 71 and 72:
- 71 - ar varga. kanonzomierebas ki
Page 73 and 74:
- 73 - mniSvneloba gansakuTrebiT di
Page 75 and 76:
- 75 - klasSi Cven nivTieri TvalsaC
Page 77 and 78:
- 77 - programa gverdiT darCeba. xo
Page 79 and 80:
- 79 - naxevarsfero, cilindri, naxe
Page 81 and 82:
- 81 - 14. CamowereT, romel nivTebs
Page 83 and 84:
- 83 - nfdbejofpcb/! Tuki damatebiT
Page 85 and 86:
- 85 - sxva. sakontrolo weris rveul
Page 87 and 88:
- 87 - `10~-s an `5+ ~-s Cveulebriv
Page 89 and 90:
- 89 - moswavlem mimdinare gakveTil
Page 91 and 92:
5. 4/16 4/30 - 91 - sw # 13 sw # 14
Page 93 and 94:
- 93 - C(1,5), D(1,75), K(3), E(3,5
Page 95 and 96:
- 95 - kg. 2. I. 53 sm; II. 950 g;
Page 97 and 98:
- 97 - 6. ara, radgan 12m-ic da 8n-
Page 99 and 100:
- 99 - II. 8 ⋅100000 + 9 ⋅10000
Page 101 and 102:
- 101 - 3. 2), 3), 2) da 4). saSual
Page 103 and 104:
- 103 - meore SemTxvevaSi: u ≈ 40
Page 105 and 106:
- 105 - S0 ⊂ S . 5. aguredi (marT
Page 107 and 108:
- 107 - denoba ar aRemateba mocemul
Page 109 and 110:
- 109 - 7. uTvalavi yofiTi sityvaa
Page 111 and 112:
- 111 - 7. pasuxi unda SevarCioT mi
Page 113 and 114:
- 113 - (1; 4)II, (2; 4)II }. {(7;
Page 115 and 116:
- 115 - g. 4. 1. I. +7, +3,1, 3,1,
Page 117 and 118:
- 117 - Tavi X. g. 1. 1. I. {1; 3,0
Page 119 and 120:
g. 8. 1. I. -3; II. ( 4 2) - 119 -
Page 121 and 122:
- 121 - zisgan. aqvs simetriis 4 Re
Page 123 and 124:
- 123 - iqneba Semoxazuli wrexazis
Page 125 and 126:
- 125 - 3. I. 25; II. -11. 4. orive
Page 127 and 128:
- 127 - jixuri, 31-e - Zelskami. II
Page 129 and 130:
- 129 - 5. I. katis myol mobinadreT
Page 131 and 132:
- 131 - nawili tolia 21 km-is (1 q)
Page 133 and 134:
- 133 - sakontrolo wera # 7 rigi I
Page 135 and 136:
- 135 - II meoTxedSi (1 q). 5. xali
Page 137 and 138:
- 137 - 2. I. 2a - 5 (2 q); II. y +
Page 139 and 140:
- 139 - 1 x + 1 x nawils, rac 1 mTe
Page 141:
- 141 - математики. М.-1
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nbUfnbujljt !txbwmfcb!!WJJ!lmbtTj! - Ganatleba

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