poles equator ref name tropopauseheight variation due weather troposphere bounded tropopause boundary marked places temperature inversion ie layer relatively warm air colder one others zone isothermal height although variations occur temperature usually declines increasing altitude troposphere troposphere mostly heated energy transfer surface thus lowest part troposphere ie earth 's surface typically warmest section troposphere promotes vertical


mixing hence origin name greek word ''tropos'' meaning turn troposphere contains roughly mass earth 's atmosphere troposphere denser overlying layers larger atmospheric weight sits top troposphere causes severely compressed fifty percent total mass atmosphere located lower troposphere nearly atmospheric water vapor moisture found troposphere layer earth 's weather takes place basically

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weather associated cloud genus types generated active wind circulation although tall cumulonimbus thunder clouds penetrate tropopause rise lower part stratosphere conventional aviation activity takes place troposphere layer accessed propeller driven aircraft km orange layer troposphere gives way whitish stratosphere blue mesosphere layers within five principal layers largely determined temperature several secondary layers may distinguished properties ozone layer


contained within stratosphere layer ozone concentrations parts per million much higher lower atmosphere still small compared main components atmosphere mainly located lower portion stratosphere though thickness varies seasonally geographically ozone earth 's atmosphere contained stratosphere ionosphere region atmosphere ionized solar radiation responsible auroras daytime hours stretches includes


mesosphere thermosphere parts exosphere however ionization mesosphere largely ceases night auroras normally seen thermosphere lower exosphere ionosphere forms inner edge magnetosphere practical importance influences example radio propagation earth homosphere heterosphere defined whether atmospheric gases well mixed surface based homosphere includes troposphere stratosphere mesosphere lowest part thermosphere chemical composition atmosphere depend molecular weight gases mixed


bottom heterosphere upper part heterosphere composed almost completely hydrogen lightest element planetary boundary layer part troposphere closest earth 's surface directly affected mainly turbulent diffusion day planetary boundary layer usually well mixed whereas night becomes stably stratified weak intermittent mixing depth planetary boundary layer ranges little clear calm nights afternoon dry regions average temperature


atmosphere earth 's surface depending reference physical properties pressure thickness average atmospheric pressure sea level defined international standard atmosphere sometimes referred unit standard atmospheres atm total atmospheric mass sup sup kg sup sup lb less would inferred average sea level pressure earth 's area megahectares portion displaced earth 's mountainous terrain atmospheric pressure total weight air unit area point pressure


measured thus air pressure varies location weather entire mass atmosphere uniform density equal sea level density nbsp kg per sup sup sea level upwards would terminate abruptly altitude actually decreases exponentially altitude dropping half every factor e every average scale height atmosphere however atmosphere accurately modeled customized equation layer takes gradients temperature molecular composition solar radiation gravity account summary


mass earth 's atmosphere distributed approximately follows k rm n line international convention marks beginning space human travelers considered astronauts comparison summit mt everest commercial airliners typically cruise lower density temperature air improve fuel economy weather balloons reach highest x flight reached even k rm n line significant atmospheric effects auroras still occur meteors begin glow


region though larger ones may burn penetrate deeply various layers earth 's ionosphere important hf radio propagation begin nbsp km extend beyond nbsp km comparison international space station space shuttle typically orbit nbsp km within f layer ionosphere encounter enough atmospheric drag require reboosts every months otherwise orbital decay occur resulting return earth depending solar activity satellites experience noticeable atmospheric drag altitudes high nbsp km temperature temperature trends two thick layers


atmosphere measured january december microwave sounding units advanced microwave sounding units noaa weather satellites instruments record microwaves emitted oxygen molecules atmosphere source division atmosphere layers mostly reference temperature discussed temperature decreases altitude starting sea level variations trend begin nbsp km temperature stabilizes large vertical distance rest troposphere stratosphere starting nbsp km temperature increases height due heating within


ozone layer caused capture significant ultraviolet radiation sun dioxygen ozone gas region still another region increasing temperature altitude occurs high altitudes aptly named thermosphere nbsp km speed sound ideal gas constant composition speed sound depends temperature pressure density speed sound atmosphere altitude takes form complicated temperature profile see illustration right mirror altitudinal changes density


pressure density mass temperature mass density altitude nrlmsise standard atmosphere model eight dotted lines decade eight cubes density air sea level nbsp kg sup sup nbsp g l g cm sup sup density measured directly calculated measurements temperature pressure humidity using equation state air form ideal gas law atmospheric density decreases altitude increases variation approximately modeled using barometric formula sophisticated models used predict


orbital decay satellites average mass atmosphere quadrillion tonnes mass earth according american national center atmospheric research total mean mass atmosphere nbsp kg annual range due water vapor nbsp kg depending whether surface pressure water vapor data used somewhat smaller previous estimate mean mass water vapor estimated nbsp kg dry air mass nbsp kg optical properties solar radiation sunlight energy earth receives


sun earth also emits radiation back space longer wavelengths humans cannot see part incoming emitted radiation absorbed reflected atmosphere may glints light seen twinkling orbiting satellite million miles away found reflected light ice crystals atmosphere ref name nyt ref ref name grl ref scattering light passes earth 's atmosphere photons interact ' 'scattering'' light interact atmosphere called ' 'direct radiation'' see look directly


sun ''indirect radiation'' light scattered atmosphere example overcast day cannot see shadow direct radiation reaching scattered another example due phenomenon called rayleigh scattering shorter blue wavelengths scatter easily longer red wavelengths sky looks blue seeing scattered blue light also sunsets red sun close horizon sun 's rays pass atmosphere normal reaching eye much


blue light scattered leaving red light sunset absorption rough plot earth 's atmospheric transmittance opacity various wavelengths electromagnetic radiation including visible light different molecules absorb different wavelengths radiation example sub sub sub sub absorb almost radiation wavelengths shorter nanometers water h sub sub absorbs many wavelengths nbsp nm molecule absorbs photon increases energy molecule heats atmosphere atmosphere also cools emitting radiation discussed combined absorption spectra gases atmosphere


depending black body emission curves therefore hotter objects tend emit radiation shorter wavelengths colder objects emit less radiation longer wavelengths example sun approximately radiation peaks near nbsp nm visible human eye earth approximately radiation peaks near nbsp nm much long visible humans temperature atmosphere emits infrared radiation example clear nights earth 's surface cools faster cloudy nights clouds h sub sub strong absorbers emitters infrared


one example circumstances observers onboard ships see vessels horizon light refracted direction curvature earth 's surface refractive index air depends temperature ref name edl n ref giving rise refraction effects temperature gradient large example effects mirage circulation idealised view three pairs large circulation cells ''atmospheric circulation'' large scale movement air troposphere means ocean circulation heat distributed around earth large scale structure


atmospheric circulation varies year year basic structure remains fairly constant determined earth 's rotation rate difference solar radiation equator poles evolution earth 's atmosphere earliest atmosphere first atmosphere consisted gases solar nebula primarily hydrogen probably simple hydrides found gas giants jupiter saturn notably water vapor methane ammonia ref name zahnle ref second atmosphere outgassing volcanism supplemented gases produced late heavy bombardment earth huge asteroids produced next atmosphere consisting largely


nitrogen plus carbon dioxide inert gases ref name zahnle major part carbon dioxide emissions dissolved water reacted metals calcium magnesium weathering crustal rocks form carbonates deposited sediments water related sediments found date early billion years ago billion years ago nitrogen formed major part stable second atmosphere influence life taken account rather soon history atmosphere hints early life forms appear early billion


years ago earth time maintained climate warm enough liquid water life early sun put lower solar radiance today puzzle known faint young sun paradox geological record however shows continuous relatively warm surface complete early temperature record earth exception one cold glacial phase billion years ago late archean eon oxygen containing atmosphere began develop apparently produced photosynthesizing cyanobacteria see great oxygenation event found stromatolite fossils


billion years ago early basic carbon isotopy isotope ratio proportions strongly suggests conditions similar current fundamental features carbon cycle became established early billion years ago ancient sediments gabon dating billion years ago provide record earth 's dynamic oxygenation evolution fluctuations oxygenation likely driven lomagundi carbon isotope excursion third atmosphere year ref constant arrangement continents plate tectonics influences long term evolution atmosphere transferring carbon dioxide large continental


carbonate stores free oxygen exist atmosphere billion years ago great oxygenation event appearance indicated end banded iron formations time oxygen produced photosynthesis consumed oxidation reduced materials notably iron free oxygen molecules start accumulate atmosphere rate production oxygen began exceed availability reducing materials removed oxygen point signifies shift reducing atmosphere oxidizing atmosphere sub sub showed major variations reaching


steady state end precambrian following time span million years ago present day phanerozoic eon earliest period cambrian oxygen requiring metazoan life forms began appear amount oxygen atmosphere fluctuated last million years reaching peak around million years ago significantly higher today 's two main processes govern changes atmosphere plants using carbon dioxide atmosphere releasing oxygen plants using oxygen


night process photorespiration remaining oxygen used break organic material breakdown pyrite volcanic eruptions release sulfur atmosphere reacts oxygen hence reduces amount atmosphere however volcanic eruptions also release carbon dioxide plants convert oxygen cause variation amount oxygen atmosphere known periods much oxygen atmosphere associated rapid development animals oxygen high energy molecule needed power complex life forms ref name schmidt rohr schmidt rohr


k oxygen high energy molecule powering complex multicellular life fundamental corrections traditional bioenergetics ''acs omega'' ''' ''' http dxdoiorg acsomega b ref today 's atmosphere contains oxygen great enough rapid development animals air pollution introduction atmosphere chemicals particulate matter biological materials cause harm discomfort organisms stratospheric ozone depletion caused air pollution chiefly chlorofluorocarbons ozone depleting substances since human activity increased concentrations various greenhouse gases importantly carbon dioxide methane nitrous oxide increase caused


observed rise global temperatures global average surface temperatures higher decade animation shows buildup tropospheric northern hemisphere maximum around may maximum vegetation cycle follows late summer following peak vegetation drawdown atmospheric due photosynthesis apparent particularly boreal forests images space october nasa started website containing daily images full sunlit side earth https epicgsfcnasagov images taken deep space climate


observatory dscovr show earth rotates day see also aerial perspective air classical element air glow airshed atmospheric dispersion modeling atmospheric electricity atmospheric radiation measurement climate research facility arm us atmospheric stratification biosphere climate system earth 's energy budget cospar international reference atmosphere cira environmental impact aviation global dimming historical temperature record hydrosphere hypermobility travel kyoto protocol leaching agriculture lithosphere reference atmospheric model references external links https earthnullschoolnet interactive global map current atmospheric ocean surface conditions atmospheric thermodynamics air environments articles containing video clips


'''air''' name given atmosphere earth '''air''' '''air''' may also refer arts entertainment media art ''air'' maillol sculpture aristide maillol ''air'' painting painting jan van kessel elder films ''air'' film anime adaptation visual novel ''air'' film american post apocalyptic film air love destructive first half ''the end evangelion'' anime film music groups air band french electronic music duo air free jazz trio founded air jazz rock band jazz rock group featuring tom


googie coppola air singer japanese singer albums ''air'' cecil taylor album ''air'' agua de annique album ''air'' astronoid album ''air'' air jazz rock band ''air'' pete namlook ''air'' kym ''air'' andreas vollenweider ''air ep '' afgan isyana sarasvati rendy pandugo songs air tyson ritter song air song ekseption self titled album ''ekseption'' air adaptation js bach music air song brian eno talking heads album ''fear music'' air song


ben folds five album ''godzilla album'' air song shawn mendes astrid shawn mendes album ''handwritten'' air song anthrax album ''spreading disease'' music related uses air music song like vocal instrumental composition ''air g string'' august wilhelmj 's adaptation air johann sebastian bach air de cour secular vocal music france late renaissance early baroque period air guitar form dance movement performer pretends play imaginary guitar associated independent recording


air independent recording company recording studio based london uk australian independent record labels association organisation representing australian owned record labels independent artists radio india radio radio broadcast service india art international radio arts oriented radio station television ''air america 's investigative reports'' pbs documentary series retitled expos america 's investigative reports second season air ''stargate universe'' series premiere television series ''stargate universe'' video games ''air'' video game air combat based mainframe computer game ''air'' video game japanese visual novel arts entertainment media related uses abs cbn


international report defunct international newscast abs cbn broadcasting corporation air gallery female artists cooperative gallery united states air common colloquialism broadcast air ''air'' comics comic book series published vertigo imprint dc comics air nightclub capacity superclub located digbeth birmingham uk ''air'' novel novel author geoff ryman air roller coaster former name flying roller coaster alton towers theme park united kingdom themed ''galactica'' ''annals improbable research'' bi monthly magazine devoted


scientific humour art resistance organization game ''year zero'' brands organisations air worldwide formerly named applied insurance research risk modeling data analytics company headquartered boston massachusetts aar corporation new york stock exchange ticker symbol air air jordan popular brand basketball shoes promoted retired chicago bulls superstar michael jordan computing technology air program program suite medical image registration adobe integrated runtime adobe air cross platform run time environment developed adobe systems building rich internet applications ipad air apple tablet macbook air apple ultraportable laptop places


r mountains massif northern niger sultanate agadez also known sultanate r arab islamic republic failed union attempt tunisia libya people donna air born british actress glen air born australian rugby league player michael jordan american basketball player nicknamed royal airness steve mcnair american football player nicknamed air science healthcare aminoimidazole ribotide anterior interval release type arthroscopic knee surgery oxygen gas atmosphere planet sky sports adelaide international raceway car racing circuit adelaide south australia air range boardsport tricks consisting


jumps without rotation airs ground term used dressage technology active infrared combines infrared illumination spectral range nbsp nm visible spectrum human eye ccd cameras sensitive light air conditioning form cooling heating ventilation disinfection modifies condition air air injection reactor early automobile emissions control system air air rocket air interception rocket unguided projectile fired aircraft engage flying targets transportation air national rail code airbles railway station motherwell scotland air x ussr aircraft series yakovlev stands


alexei ivanovich rykov one communist leaders air mtr station code airport station hong kong uses air classical element element ancient greek philosophy western alchemy airoran language indonesian language iso code air ''applied innovative research'' scientific journal compressed air air kept pressure greater atmospheric pressure another word ''ambience'' character mood etc see also air university disambiguation aire disambiguation airs disambiguation ayr disambiguation ayre one six sheadings isle man ire


bose einstein condensate representative image '''thermal physics''' '''thermal physics''' combined study thermodynamics statistical mechanics kinetic theory gases umbrella subject typically designed physics students functions provide general introduction three core heat related subjects authors however define thermal physics loosely summation thermodynamics statistical mechanics thermal physics seen study system larger number atom unites thermodynamics statistical mechanics overview thermal physics generally speaking study statistical nature physical


systems energetic perspective starting basics heat temperature thermal physics analyzes first law thermodynamics second law thermodynamics statistical perspective terms number microstates corresponding given macrostate addition concept entropy studied via quantum theory central topic thermal physics canonical probability distribution electromagnetic nature photons phonons studied show oscillations electromagnetic fields crystal lattices much common waves form basis provided


one incorporates quantum theory topics studied thermal physics include chemical potential quantum nature ideal gas ie terms fermions bosons bose einstein condensation gibbs free energy helmholtz free energy chemical equilibrium phase equilibrium equipartition theorem entropy absolute zero transport processes mean free path viscosity conduction see also heat transfer physics information theory philosophy thermal statistical physics thermodynamic instruments references reading external links http physicsweberedu thermal linkshtml thermal physics links web physics education thermodynamics


gives methods writing formulas solving equations much clearer easier older method writing everything words word ''algebra'' also used certain specialized ways special kind algebraic structure called algebra word used example phrases linear algebra algebraic topology mathematician research algebra called algebraist etymology word ''algebra'' comes title book muhammad ibn musa al khwarizmi word ''algebra'' comes ref bonesetting ref name crc press ref translit al jabr

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title early th century book '' sup c sup ilm al jabr wa l muq bala'' science restoring balancing persian mathematician astronomer al khwarizmi work term ''al jabr'' referred operation moving term one side equation ''al muq bala'' balancing referred adding equal terms sides shortened ''algeber'' ''algebra'' latin word eventually entered english language th century either spanish italian medieval latin originally referred surgical procedure setting broken dislocated bones mathematical meaning


first recorded english th century different meanings algebra word algebra several related meanings mathematics single word qualifiers single word without article algebra names broad part mathematics single word article plural algebra algebras denotes specific mathematical structure whose precise definition depends context usually structure addition multiplication scalar multiplication see algebra field authors use term algebra make subset


following additional assumptions associative commutative unital finite dimensional universal algebra word algebra refers generalization concept allows n ary operations qualifier distinction without article means part algebra linear algebra elementary algebra symbol manipulation rules taught elementary courses mathematics part primary secondary education abstract algebra study algebraic structures article means instance abstract structure like lie algebra associative algebra vertex operator algebra


sometimes meanings exist qualifier sentence ''commutative algebra study commutative rings commutative algebras integers'' algebra branch mathematics algebra began computations similar arithmetic letters standing numbers ref name citeboyer allowed proofs properties true matter numbers involved example quadratic equation math ax bx c math math b c math numbers whatsoever except math math cannot math math quadratic formula used quickly easily find values


unknown quantity math x math satisfy equation say find solutions equation historically current teaching study algebra starts solving equations quadratic equation general questions equation solution many solutions equation said nature solutions considered questions led extending algebra non numerical objects permutations vectors matrices polynomials structural properties non numerical objects abstracted algebraic


structures groups rings fields th century mathematics divided two subfields arithmetic geometry even though methods developed much earlier may considered nowadays algebra emergence algebra soon thereafter infinitesimal calculus subfields mathematics dates th th century second half th century many new fields mathematics appeared made use arithmetic geometry almost used algebra today algebra grown considerably includes many branches


mathematics seen mathematics subject classification none first level areas two digit entries called ''algebra'' today algebra includes section general algebraic systems field theory polynomials commutative algebra linear multilinear algebra matrix theory associative rings algebras nonassociative rings algebras category theory homological algebra k theory group theory algebra also used extensively number theory algebraic geometry history early history algebra al khw rizm 's ''al kit b al mu ta ar f b al abr wa l muq bala'' roots algebra traced ancient babylonians developed


lettered diagrams coefficients equations used ''algebra'' specific numbers whether represented numerals written words idea generality implied al khwarizmi 's exposition scheme expressing algebraically general propositions readily available geometry ref diophantus rd century ad alexandrian greek mathematician author series books called ''arithmetica'' texts deal solving algebraic equations led number theory modern notion diophantine equation earlier traditions discussed direct influence


persian mathematician mu ammad ibn al khw rizm c later wrote ''the compendious book calculation completion balancing'' established algebra mathematical discipline independent geometry arithmetic hellenistic mathematicians hero alexandria diophantus well indian mathematicians brahmagupta continued traditions egypt babylon though diophantus' ''arithmetica'' brahmagupta 's ''br hmasphu asiddh nta'' higher level example first complete arithmetic solution written words instead symbols including zero negative solutions quadratic equations described brahmagupta book ''brahmasphutasiddhanta'' published


ad ref name bradley bradley michael ''the birth mathematics ancient times '' p infobase publishing ref later persian arab mathematicians developed algebraic methods much higher degree sophistication although diophantus babylonians used mostly special ''ad hoc'' methods solve equations al khwarizmi 's contribution fundamental solved linear quadratic equations without algebraic symbolism negative numbers zero thus distinguish several types equations ref name meri ref context algebra identified theory equations greek mathematician diophantus traditionally known father algebra


context identified rules manipulating solving equations persian mathematician al khwarizmi regarded father algebra ref name gandz see page sense al khwarizmi entitled called father algebra diophantus al khwarizmi first teach algebra elementary form sake diophantus primarily concerned theory numbers ref open debate whether diophantus al khwarizmi entitled known general sense father algebra support diophantus point fact


algebra found ''al jabr'' slightly elementary algebra found ''arithmetica'' ''arithmetica'' syncopated ''al jabr'' fully rhetorical support al khwarizmi point fact introduced methods reduction balancing transposition subtracted terms side equation cancellation like terms opposite sides equation term ''al jabr'' originally referred ref name boyer see ''the arabic hegemony'' p certain terms ''al jabr'' ''muqabalah'' mean usual interpretation similar


implied translation word ''al jabr'' presumably meant something like restoration completion seems refer transposition subtracted terms side equation word ''muqabalah'' said refer reduction balancing cancellation like terms opposite sides equation ref gave exhaustive explanation solving quadratic equations supported geometric proofs treating algebra independent discipline right ref name gandz algebra also longer concerned series problems


resolved exposition starts primitive terms combinations must give possible prototypes equations henceforward explicitly constitute true object study also studied equation sake generic manner insofar simply emerge course solving problem specifically called define infinite class problems ref name rashed armstrong ref another persian mathematician omar khayyam credited identifying foundations algebraic geometry found general geometric solution cubic equation book ''treatise demonstrations


problems algebra'' laid principles algebra part body persian mathematics eventually transmitted europe yet another persian mathematician sharaf al n al found algebraic numerical solutions various cases cubic equations also developed concept function indian mathematicians mahavira bhaskara ii persian mathematician al karaji ref name boyer al karkhi ax n see ''the arabic hegemony'' p abu'l wefa capable algebraist well trigonometer nbsp successor al karkhi evidently used translation become arabic disciple diophantus without diophantine


analysis nbsp particular al karkhi attributed first numerical solution equations form ax sup n sup bx sup n sup c equations positive roots considered ref chinese mathematician zhu shijie solved various cases cubic quartic quintic higher order polynomial equations using numerical methods th century solution cubic equation fibonacci representative beginning revival european algebra ab al asan ibn al al qala took first steps toward introduction algebraic symbolism also computed ''n'' sup sup ''n'' sup sup used method successive approximation


determine square roots modern history algebra italian mathematician girolamo cardano published solutions cubic quartic equations book ''ars magna'' fran ois vi te 's work new algebra close th century important step towards modern algebra ren descartes published ''la g om trie'' inventing analytic geometry introducing modern algebraic notation another key event development algebra general algebraic solution cubic quartic equations developed mid th century idea determinant developed japanese mathematician seki k wa


th century followed independently gottfried leibniz ten years later purpose solving systems simultaneous linear equations using matrices gabriel cramer also work matrices determinants th century permutations studied joseph louis lagrange paper ''r flexions sur la r solution alg brique des quations'' devoted solutions algebraic equations introduced lagrange resolvents paolo ruffini first person develop theory permutation groups like predecessors also context solving algebraic equations abstract algebra developed th century


deriving interest solving equations initially focusing called galois theory constructibility issues george peacock founder axiomatic thinking arithmetic algebra augustus de morgan discovered relation algebra ''syllabus proposed system logic'' josiah willard gibbs developed algebra vectors three dimensional space arthur cayley developed algebra matrices noncommutative algebra areas mathematics word algebra name linear algebra lecture aalto university subareas algebra word algebra


name linear algebra one example others group theory ring theory field theory examples section list areas mathematics word algebra name elementary algebra part algebra usually taught elementary courses mathematics abstract algebra algebraic structures groups rings fields axiomatically defined investigated linear algebra specific properties linear equations vector spaces matrices studied boolean algebra branch algebra abstracting computation truth values ''false'' ''true'' commutative algebra


study commutative rings computer algebra implementation algebraic methods algorithms computer programs homological algebra study algebraic structures fundamental study topological spaces universal algebra properties common algebraic structures studied algebraic number theory properties numbers studied algebraic point view algebraic geometry branch geometry primitive form specifying curves surfaces solutions polynomial equations algebraic combinatorics algebraic methods used study combinatorial questions relational algebra set finitary relations


nbsp coefficient br nbsp term br nbsp operator br nbsp constant term br nbsp ''x'' ''y'' ''c'' variables constants elementary algebra basic form algebra taught students presumed knowledge mathematics beyond basic principles arithmetic arithmetic numbers arithmetical operations occur algebra numbers often represented symbols called variables ''a'' ''n'' ''x'' ''y'' ''z'' useful allows general formulation arithmetical laws ''a''


''b'' ''b'' ''a'' ''a'' ''b'' thus first step systematic exploration properties real number system allows reference unknown numbers formulation equations study solve instance find number ''x'' ''x'' going bit find number ''x'' ''ax'' ''b'' ''c'' step leads conclusion nature specific numbers allow us solve


operations involved allows formulation functional relationships instance sell ''x'' tickets profit ''x'' dollars ''f'' ''x'' ''x'' ''f'' function ''x'' number function applied polynomials graph polynomial function degree thumb upright polynomial expression sum finite number non zero terms term consisting product constant finite number variables raised whole number powers example ''x'' sup sup


''x'' polynomial single variable ''x'' polynomial expression expression may rewritten polynomial using commutativity associativity distributivity addition multiplication example ''x'' ''x'' polynomial expression properly speaking polynomial polynomial function function defined polynomial equivalently polynomial expression two preceding examples define polynomial function two important related problems algebra factorization polynomials expressing given polynomial


product polynomials cannot factored computation polynomial greatest common divisors example polynomial factored ''x'' ''x'' related class problems finding algebraic expressions roots polynomial single variable education suggested elementary algebra taught students young eleven years old though recent years common public lessons begin eighth grade level nbsp nbsp yo nbsp united states however us schools algebra


started ninth grade abstract algebra abstract algebra extends familiar concepts found elementary algebra arithmetic numbers general concepts listed fundamental concepts abstract algebra sets rather considering different types numbers abstract algebra deals general concept ' 'sets'' collection objects called elements selected property specific set collections familiar types numbers sets examples sets include set two two matrices set second degree polynomials ''ax'' sup sup ''bx''


addition subtraction multiplication division binary operations defined different sets addition multiplication matrices vectors polynomials identity elements numbers zero one abstracted give notion ''identity element'' operation zero identity element addition one identity element multiplication general binary operator identity element ''e'' must satisfy ''a'' ''e'' ''a'' ''e'' ''a'' ''a'' necessarily unique exists holds addition ''a''


''e'' identity element associativity addition integers property called associativity grouping numbers added affect sum example general becomes ''a'' ''b'' ''c'' ''a'' ''b'' ''c'' property shared binary operations subtraction division octonion multiplication commutativity addition multiplication real numbers commutative order numbers affect result example general becomes ''a''


every member ''a'' ''s'' exists member ''a'' sup sup ''a'' ''a'' sup sup ''a'' sup sup ''a'' identical identity element operation associative ''a'' ''b'' ''c'' members ''s'' ''a'' ''b'' ''c'' identical ''a'' ''b'' ''c'' group also commutative two members ''a'' ''b'' ''s'' ''a'' ''b'' identical ''b'' ''a'' group said abelian example set integers operation addition


group group identity element inverse element ''a'' negation ''a'' associativity requirement met integers ''a'' ''b'' ''c'' ''a'' ''b'' ''c'' ''a'' ''b'' ''c'' non zero rational numbers form group multiplication identity element since ''a'' ''a'' ''a'' rational number ''a'' inverse ''a'' since ''a'' integers multiplication operation however form group


general multiplicative inverse integer integer example integer multiplicative inverse integer theory groups studied group theory major result theory classification finite simple groups mostly published separates finite simple groups roughly basic types semi groups quasi groups monoids algebraic structures similar groups less constraints operation comprise set closed binary operation


necessarily satisfy conditions semi group ''associative'' binary operation might identity element monoid semi group identity might inverse every element quasi group satisfies requirement element turned either unique left multiplication right multiplication however binary operation might associative groups monoids monoids semi groups class wikitable examples set colspan natural numbers '''n''' colspan integers '''z''' colspan rational numbers '''q''' br real numbers '''r''' br complex numbers '''c''' colspan integers modulo


br '''z''' '''z''' operation closed yes yes yes yes yes yes yes yes yes identity n n inverse n n ''a'' n ''a'' n ''a'' br ''a'' n respectively n


respectively associative yes yes yes yes yes yes yes yes commutative yes yes yes yes yes yes yes yes structure monoid monoid abelian group monoid abelian group quasi group monoid quasi group abelian group monoid rings fields groups one binary operation fully explain behaviour different types numbers structures


' 'distributive'' integers example ring integers additional properties make integral domain field ''ring'' additional property elements excluding form ''abelian group'' multiplicative identity written multiplicative inverse ''a'' written ''a'' sup sup rational numbers real numbers complex numbers examples fields see also outline algebra outline linear algebra algebra tile references citations works cited


children mix chemicals test tubes part hands chemistry education program samara russia '''chemistry education''' '''chemical education''' study teaching learning chemistry one subset stem education discipline based education research dber ref name ref topics chemistry education include understanding students learn chemistry determining efficient methods teach chemistry constant need improve chemistry curricula learning outcomes based findings chemistry education research cer chemistry education improved changing teaching methods providing appropriate training chemistry instructors within

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many modes including classroom lectures demonstrations laboratory activities importance chemistry education important field chemistry fundamental world universe subject laws chemistry human beings depend orderly progress chemical reactions within bodies described central science chemistry connects physical sciences life sciences applied sciences chemistry applications food medicine industry environment areas learning chemistry allows students learn scientific method gain skills critical thinking deductive reasoning problem solving communication teaching chemistry


students young age increase student interest stem careers chemistry also provides students many transferable skills applied career teaching strategies common method teaching chemistry lecture laboratory component laboratory courses became central part chemistry curriculum towards end th century german scientist justus von liebig plays major role shifting model lecture demonstrations one includes laboratory component liebig one first chemists conduct laboratory


widespread adoption laboratory methods today american chemical society professional training requires students gain hours laboratory experience outside introductory chemistry get bachelor 's degree similarly royal society chemistry requires students gain hours laboratory experience get bachelor 's degree ref name ref however since twenty first century role laboratory courses chemistry curriculum questioned major journals ref name main argument laboratory courses little evidence impact student learning researchers asking questions


laboratory work curriculum distinctive laboratory work cannot met elsewhere curriculum ref name researchers asking evidence investment space time resources chemistry laboratories provides value student learning theories education several different philosophical perspectives describe work chemistry education carried practitioner 's perspective first one might call ''practitioner perspective'' wherein individuals responsible teaching chemistry teachers instructors professors ones ultimately define chemistry


education actions perspective chemical educators second perspective defined self identified group ''chemical educators'' faculty members instructors opposed declaring primary interest typical area laboratory research organic inorganic biochemistry etc take interest contributing suggestions essays observations descriptive reports practice public domain journal publications books presentations dr robert l lichter executive director camille henry dreyfus foundation speaking plenary session th biennial conference chemical education recent bcce meetings https webarchiveorg web http wwwchemiastateedu bcce http wwwchempurdueedu bcce


posed question terms like chemical educator' even exist higher education perfectly respectable term activity namely chemistry professor one criticism view professors bring formal preparation background education jobs lack professional perspective teaching learning enterprise particularly discoveries made effective teaching students learndemonstration chemistry class chemistry education research cer third perspective ''chemistry education research'' cer cer type discipline based education research dber focusing


teaching learning chemistry overarching goal chemistry education researchers help students develop expert like coherent useful knowledge chemistry ref name ref thus field cer involves investigating students construct understanding chemical phenomena develop practical skills relevant discipline cer findings inform curriculum design eg suggesting certain learning objectives instructional approaches developing instruments measure ref name ref name following example physics education research per cer tends take theories methods developed pre college science education research


generally takes place schools education applies understanding comparable problems post secondary settings addition pre college settings like science education researchers cer practitioners tend study teaching practices others opposed focusing classroom practices chemistry education research typically carried ''in situ'' using human subjects secondary post secondary schools chemistry education research utilizes quantitative qualitative data collection methods ref name ref quantitative methods typically involve collecting data analyzed using various statistical methods qualitative methods include interviews observations document analysis journaling methods


common social science research ref name scholarship teaching learning sotl also emergent perspective called ''the scholarship teaching learning'' sotl although debate best define sotl one primary practices mainstream faculty members organic inorganic biochemistry etc develop informed view practices carry research reflection teaching constitutes deep understanding student learning systems thinking approach systems thinking chemistry education stice project proposed


systems thinking approach post secondary education general chemistry education chemistry education largely relied reductionist approach involves studying complex topic sum parts reductionist approach beneficial increasing knowledge natural world however insufficient tackling global issues sustainability climate change pollution poverty etc due limitations reductionist approach researchers suggesting complementary systems thinking approach chemistry education ref name ref systems thinking approach involves learning concepts holistic perspective allowing chemistry students think critically chemistry relates


chemistry rsc publishes theoretical perspectives literature reviews empirical papers including systematic evaluations innovative practice '''''education chemistry'' eic ''' published royal society chemistry covers areas chemical education eic rsc 's educational magazine whereas cerp peer reviewed research journal '''''foundations chemistry'' foch ''' published springer covers philosophical historical aspects chemical education '''''journal chemical education'' ''' published chemical education division american chemical society covers school university education '''''the chemical educator'' ''' published springer verlag covers areas chemical education ''list


scientific journals chemistry'' research chemistry education also published journals wider science education field degrees offered chemistry us offers chemistry education degrees undergraduate graduate levels following degrees offered bachelor science chemistry education master science chemistry education phd chemistry education additionally colleges universities offer chemistry degrees specialization chemistry education examples bachelor science chemistry specialization chemical education university virginia masters art chemistry emphasis chemical education


university california santa barbara compendium graduate programs chemistry award ms phd degrees research teaching learning chemistry found https sitesgooglecom miamiohedu bretzsl cer resources cer graduate programs undergraduate students interested chemistry major following areas chemistry chemical engineering biochemistry environmental chemistry analytical chemistry forensic chemistry see also advancing chemistry enhancing learning laboratory constructivism science education references external links http chemconnectionsorg welcome chemconnections


proposed script greek alphabet linglist grc koi isoexception dialect glotto none '''koine greek''' ref name collins ref ref name mw ref modern also known '''alexandrian dialect''' '''common attic''' '''hellenistic''' '''biblical greek''' common supra regional form greek spoken written hellenistic period roman empire early byzantine empire evolved spread

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greek following conquests alexander great fourth century bc served lingua franca much mediterranean region middle east following centuries based mainly attic related ionic speech forms various admixtures brought dialect levelling varieties ref name bubenik ref koine greek included styles ranging conservative literary forms spoken vernaculars time dominant language byzantine empire developed medieval greek turned modern greek literary koine medium


much post classical greek literary scholarly writing works plutarch polybius ref name bubenik koine also language christian new testament septuagint rd century bc greek translation hebrew bible early christian theological writing church fathers context koine greek also known biblical new testament ecclesiastical patristic greek roman emperor marcus aurelius also wrote private thoughts koine greek work known ''the meditations'' koine greek continues used liturgical language


several different senses scholars apollonius dyscolus second century ad aelius herodianus second century ad maintained term ''koine'' refer proto greek language others used refer vernacular form greek speech differed somewhat literary language ref name andriotes andriotis nikolaos p ''history greek language'' ref koine greek became language literature first century bc people distinguished two forms written literary post classical form confused atticism vernacular day day vernacular ref name andriotes others chose refer koine


dialect alexandria alexandrian dialect even universal dialect time modern classicists often used former sense origins history greek speaking areas hellenistic period bc koine greek arose common dialect within armies alexander great ref name andriotes leadership macedon newly formed common variety spoken ptolemaic kingdom egypt seleucid empire mesopotamia ref name andriotes replaced existing ancient greek dialects everyday form people anywhere could understand ref name ref though elements koine greek


took shape classical greece post classical period greek defined beginning death alexander great bc cultures greek sway turn began influence language passage next period known medieval greek dates foundation constantinople constantine great ad post classical period greek thus refers creation evolution koine greek throughout entire hellenistic roman eras history start middle ages ref name andriotes linguistic roots common greek dialect


unclear since ancient times hellenistic period scholars thought koine result mixture four main ancient greek dialects composition four view supported early twentieth century paul kretschmer book ''die entstehung der koine'' ulrich von wilamowitz moellendorff antoine meillet based intense ionic elements koine instead instead considered koine simplified form ionic ref name andriotes view accepted scholars


today given greek linguist georgios hatzidakis showed despite composition four stable nucleus koine greek attic words koine greek regarded attic admixture elements especially ionic also dialects degree importance non attic linguistic elements koine vary depending region hellenistic world ref name andriotes respect varieties koine spoken ionian colonies anatolia eg pontus cf pontic greek would intense ionic characteristics others


laconia cyprus would preserve doric arcadocypriot characteristics respectively literary koine hellenistic age resembles attic degree often mentioned ''common attic'' ref name andriotes sources first scholars studied koine alexandrian early modern times classicists whose prototype literary attic greek classical period frowned upon variety ancient greek koine greek therefore considered decayed form greek worthy attention ref name andriotes reconsideration historical linguistic importance koine


greek began early th century renowned scholars conducted series studies evolution koine throughout entire hellenistic period roman empire sources used studies koine numerous unequal reliability significant ones inscriptions post classical periods papyri two kinds texts authentic content studied directly ref name andriotes significant sources septuagint greek translation hebrew bible greek new testament teaching texts aimed


sick author title source finally important source information ancient koine modern greek language dialects ''koine'' form preserved ancient language 's oral linguistic details written tradition lost example pontic cappadocian greek preserved ancient pronunciation standard modern greek etc archaism apart improbability sound change occur important region roman empire horrocks notes written certain contexts


letter digraph representing dialects eg never pronounced ancient greek cf standard therefore attributes feature east greek vowel weakening paralleling omission unstressed vowels horrocks name group tsakonian language preserved long instead etc local characteristics doric greek ref name andriotes dialects southern part greek speaking regions dodecanese cyprus etc preserve pronunciation double similar consonants others pronounce


many words preserve ancient double forms etc linguistic phenomena like imply characteristics survived within koine turn countless variations greek speaking world ref name andriotes types papyrus one oldest extant new testament manuscripts greek written papyrus 'most probable date' biblical koine ''biblical koine'' refers varieties koine greek used bible translations greek related texts main sources septuagint rd century bc greek translation hebrew bible


old testament texts included hebrew bible greek new testament compiled originally greek septuagint greek debate degree biblical greek represents mainstream contemporary spoken koine extent contains specifically semitic substratum features could induced either practice translating closely biblical hebrew aramaic originals influence regional non standard greek spoken originally aramaic speaking hellenized jews features discussed context septuagint 's normative absence particles


use denote came pass features biblical greek thought originally non standard elements eventually found way main greek language j thackeray ''a grammar old testament greek according septuagint'' wrote five books pentateuch parts book joshua book isaiah may considered good koine one issue debated scholars whether much translation pentateuch influenced rest septuagint


including translation isaiah another point scholars debated use translation hebrew old testament scholar james barr critical etymological arguments refers community called god constitute people kyriakoula papademetriou explains merely used designating notion meeting gathering men without particular character therefore etymologizing word could needless even misleading could guide false meanings example name used people god israel


new testament greek authors new testament follow septuagint translations half quotations old testament historical present tense term used present tense verbs used narrative sections new testament describe events past respect speaker seen works attributed mark john luke used times ''gospel mark'' passages reader might expect past tense verb scholars presented various explanations


xenophon evidence heavy use verb tense feature vernacular koine scholars argued historical present literary form denote semantic shifts prominent material patristic greek term ''patristic greek'' sometimes used greek written greek church fathers early christian theologians late antiquity christian writers earliest time tended use simple register koin relatively close spoken language time following model bible th century


christianity became state church roman empire learned registers koin also came used differences attic koine greek study sources six centuries symbolically covered koine reveals linguistic changes ancient greek elements spoken language including grammar word formation vocabulary phonology sound system new forms start rare gradually become frequent established changes modern ancient greek introduced via koine koine largely familiar


least partly intelligible writers speakers modern greek differences grammar phonology period generally designated koine greek great deal phonological change occurred start period pronunciation virtually identical ancient greek phonology whereas end much common modern greek phonology three significant changes loss vowel length distinction replacement pitch accent system stress accent system monophthongization several diphthongs ancient distinction long short


vowels gradually lost second century bc vowels isochronic equal length ref name andriotes second century bc ancient greek pitch accent replaced stress accent ref name andriotes psilosis loss rough breathing rough breathing already lost ionic greek varieties anatolia aeolic greek lesbos ref name andriotes diphthongs respectively simplified long vowels ref name andriotes diphthongs became monophthongs already pronounced boeotians since


th century bc written eg became koine first long vowel loss distinctive vowel length openness distinction merging diphthong already merged th century bc argos th century bc corinth eg acquired pronunciation also koine diphthong fronted merging diphthong came pronounced eventually lost final element also merged diphthong already


raised th century bc remains modern greek ref name andriotes diphthongs came pronounced via partly assimilated voiceless consonants ref name andriotes simple vowels mostly preserved ancient pronunciations classically pronounced raised merged th century ad unrounded merge changes known iotacism ref name andriotes consonants also preserved ancient pronunciations great extent except originally pronounced became fricatives


via still today except preceded nasal consonant case retain ancient pronunciations eg latter three initially pronounced aspirates respectively developed fricatives via finally still metrically categorised double consonant may initially pronounced later acquired modern day value ref name andriotes new testament greek phonology


nasals initial aspiration also likely become optional sound many speakers popular variety even commonly used contemporary orthography parentheses denote loss sound name group monophthongization including initial stage fortition second element diphthongs loss vowel timing distinctions carried still distinction four front vowels rather two mid vowels apparently still distinguished quality far less confused


perhaps represented near close vowel fully merged cf horrocks name group still rounded class wikitable letter greek transliteration ipa alpha beta gamma delta epsilon zeta eta


theta iota kappa lambda mu nu xi omicron pi rho sigma tau upsilon


sample koine texts following texts show differences attic greek aspects grammar morphology vocabulary inferred show differences phonology following comments illustrate phonological development within period koine phonetic transcriptions tentative intended illustrate two different stages reconstructed development early conservative variety still relatively close classical attic somewhat later


progressive variety approaching modern greek respects sample roman decree following excerpt decree roman senate town thisbae boeotia bc rendered reconstructed pronunciation representing hypothetical conservative variety mainland greek koin early roman period transcription shows raising partial pre consonantal word final raising retention pitch accent retention word initial rough breathing br br concerning matters citizens thisbae made representations concerning


affairs following decision taken concerning proposal remained true friendship given facilities conduct affairs praetor governor quintus maenius delegate five members senate seemed appropriate light public actions individual good faith sample greek new testament following excerpt beginning gospel john rendered reconstructed pronunciation representing progressive popular variety koin early christian era modernizing features include loss vowel length


distinction monophthongization transition stress accent raising also seen bilabial fricative pronunciation diphthongs loss initial fricative values partial post nasal voicing voiceless stops br br beginning word word god word god beginning god things made without anything made made life life light men light


shines darkness darkness comprehended references notes citations bibliography abel f ''grammaire du grec biblique'' allen w sidney ''vox graeca guide pronunciation classical greek rd ed'' cambridge university press andriotis nikolaos p ''history greek language'' buth randall '' https wwwbiblicallanguagecentercom wp content uploads greek pronunciation pdf koine greek early roman period '' bruce frederick f ''the books parchments chapters transmission bible'' rd ed westwood nj revell chapters conybeare fc stock st george ''grammar


septuagint greek selected readings vocabularies updated indexes'' horrocks geoffrey c ''greek history language speakers'' nd ed oxford blackwell reading bakker egbert j ed ''a companion ancient greek language'' oxford wiley blackwell blass friedrich albert debrunner ''greek grammar new testament early christian literature'' translated revised r w funk chicago university chicago press christidis anastasios phoivos ed ''a history ancient greek beginnings late antiquity'' cambridge uk cambridge university press colvin stephen c ''a historical greek reader


mycenaean koin '' oxford oxford university press easterling p e carol handley ''greek scripts illustrated introduction'' london society promotion hellenic studies evans v dirk obbink eds ''the language papyri'' oxford oxford univ press gignac francis ''a grammar greek papyri roman byzantine periods'' vols milan cisalpino la goliardica horrocks geoffrey ''greek history language speakers'' nd ed oxford wiley blackwell palmer leonard r ''the greek language'' london faber faber stevens gerald l ''new testament greek


intermediate morphology translation'' cambridge uk lutterworth press ''new testament greek primer'' cambridge uk lutterworth press external links https wwwkoinegreekcom koinegreekcom koine greek audio video resources produced living koine greek pronunciation along resources pronunciation https lrclautexasedu eieol ntgol new testament greek online winfred p lehmann jonathan slocum free online lessons https liberalartsutexasedu lrc linguistics research center university texas austin http wwwwestarinstituteorg resources koine greek keyboard free koine greek keyboard unicode keyboard originally developed char matejovsky use westar institute scholars http wwwibiblioorg bgreek forum biblical greek forum online community biblical greek http greek languagecom


greek languagecom dictionaries manuscripts greek new testament tools applying linguistics study hellenistic greek http wwwbiblegreeknet diglot daily di glot tri glot vulgate reading languages attested rd century bc hellenistic civilization hellenism christianity christian liturgical languages greek languages ancient macedonia languages syria languages egypt languages sicily varieties ancient greek


'''bengali literature''' denotes body writings bengali language bengali developed course roughly years earliest extant work bengali literature ''charyapada'' collection buddhist mystic songs old bengali dating back th th centuries timeline bengali literature divided three periods ancient medieval modern medieval bengali literature consists various poetic genres including hindu religious scriptures eg mangalkavya islamic epics eg works syed sultan abdul hakim vaishnava texts eg biographies chaitanya mahaprabhu translations

Humanities
Languages and literature
Bengali Literature


mystic hymns composed various buddhist monks namely luipada kanhapada kukkuripada chatilpada bhusukupada kamlipada dhendhanpada shantipada shabarapada amongst others manuscript discovered palm leaf nepal royal court library bengali linguist haraprasad shastri due language manuscripts partially understood classified shastri name ''sandhya bhasha'' meaning ' 'dusk language''the ''charyapada' 's also considered part assamese maithili odia ref name mukherjee mukherjee prabhat ''the history medieval vaishnavism orissa'' chapter ''the sidhacharyas orissa'' page ref literature medieval


early medieval transitional period considered time many common proverbs rhymes first emerged bengali alphabet became lot like currently ramai pandit halayudh misra notable writers period ref name bpedia ref many works literature period also included parts assamese literature indicating shared legacy era ref name saikia ref pre chaitanya tomb ghiyasuddin azam shah whose patronage writers shah muhammad sagir krittibas ojha muslim writers exploring different themes narratives epics


religion culture cosmology love history often taking inspiration translating arabic persian literary works thousand one nights shahnameh literary romantic tradition saw poems shah muhammad sagir yusuf zulaikha well works zainuddin sabirid khan ''dobhashi'' culture introduced arabic persian vocabulary bengali texts illustrate muslim stories epic poetry included ''nabibangsha'' syed sultan ''janganama'' abdul hakim ''rasul bijoy'' shah barid chandidas celebrated hindu lyrical poet period famed translating jayadeva 's work


sanskrit bengali producing thousands poems dedicated love radha krishna shreekrishna kirtana majority hindu writers period drew inspiration popular maithili language vaishnavite poet known vidyapati maladhar basu 's ''sri krishna vijaya'' chiefly translation th th cantos ''bhagavata purana'' earliest bengali narrative poem assigned definite date ref name sukumarseneng ref composed ce also oldest bengali narrative poem krishna legend ref name bp ref ref name sukumarseneng


''ramayana'' title ''sri rama panchali'' translated krittibas ojha ref name sen sukumar reprint ''bangala sahityer itihas'' voli kolkata ananda publishers pp ref chaitanya era lalon inspired influenced many poets social religious thinkers including rabindranath tagore ref name choudhury p ref kazi nazrul islam allen ginsberg bengali literature flourished arakan following reconquest home prominent writers patronised arakan royal court alaol wrote padmavati well daulat qazi dawlat wazir bahram khan quraishi magan thakur wrote chandravati maradan wrote nasirnama


qazi first poet court patronage started writing satimayna lorchandrani considered first bengali romance teamwork common court alaol finished qazi 's romance latter died managing complete modern present michael madhusudan datta 's first epic ''tilottama sambhab kabya'' published first bengali poem written blank verse bankim chandra chatterjee considered one leading bengali novelists essayists th century also wrote ''vande mataram'' national song india appears novel ''anandamath'' ref


name sukumarsenengbankim chatterjee critically analysed hindu scriptures ''bhagavad gita'' well problems krishnaism historical perspective ''dharmatattva'' ''krishna charitra'' ref name sukumarsenengbankim romesh chunder dutt mir mosharraf hossain notable works fiction girish chandra ghosh dwijendralal ray prominent playwrights time whereas akshay kumar boral ramendra sundar tribedi famous influential essays rassundari devi authored first full fledged autobiography modern bengali literature pre tagore era also saw undercurrent popular literature


focused daily life contemporary bengal prose style well humour works often crass blunt accessible masterpiece regard hutom pechar naksha sketch owl written kaliprasanna singha satirically depicts babu culture th century kolkata notable works regard alaler ghorer dulal spoilt brat peary chand mitra ramtanu lahiri tatkalin banga shamaj ramtanu lahiri contemporary bengali society shibnath shastri naba babu bilas naba bibi bilas bhabanicharan bandopadhyay books arguably portrayed


contemporary bengali dialect popular society effectively also incorporated extinct music genres khisti kheur kabiyal gaan stalwarts like rupchand pakhi bhola moyra books like become rarer since emergence tagore culture burgeoning preference literary elegance refinement bengali society gallery widths heights perrow file bankim chattapadhyayjpg bankim chandra chatterjee 's first novel ''durgeshnandini'' considered benchmark history bengali literature ref name sukumarsenengbankim ref file shaheed minarjpg shaheed minar dhaka displayed annual anniversary bengali language movement file bhasha smritistambha arnab dutta jpg bhasha smritistambha kolkata file kaykobad jpg kaykobad


popular narrative poet file hason rajajpg hason raja 's poetry continues prominent rural bengal gallery bankim tagore sarat nazrul rabindranath tagore asia 's first nobel laureate kazi nazrul islam seated bengali muslim litt rateurs sylhet nazrul 's contributions included profuse enrichment bengali g z l bankim chandra chatterjee 's vande mataram played vital role indian independence movement widely respected india though less respected bangladesh novels popular lesser extent bangladesh bankim memorial award highest literary award given government west bengal


india rabindranath tagore kazi nazrul islam well known prolific writers bengal th century tagore celebrated writer india 's national anthem jana gana mana bangladesh 's amar shonar bangla well source inspiration sri lanka matha similarly nazrul celebrated national poet bangladesh ref name university hawaii press ref ref name times india ref ref name ibn live ref sarat chandra chatterjee wrote novels novellas stories also wrote essays anthologized ''narir mulya '' ''svadesh sahitya '' ''shrikanta charitrahin devdas grihadaha dena paona''


''pather dabi'' among popular works short story writers bengali literature also famous short stories famous short story writers rabindranath tagore manik bandopadhyay tarashankar bandopadhyay bibhutibhushan bandopadhyay rajshekhar basu parasuram syed mujtaba ali premendra mitra rajshekhar basu best known writer satiric short story bengali literature ref name parashuram ref mocked charlatanism vileness various classes bengali society stories written pseudonym parashuram ref name parashuram major works include ''gaddalika'' ''kajjwali'' ''hanumaner swapna'' ''gamanush jatir katha'' ''dhusturimaya ityadi galpa''


''krishnakali ittadi galpa'' ''niltara ittadi galpa'' ''anandibai ittadi galpa'' ''chamatkumari ittadi galpa'' received rabindra puraskar highest literary award paschimbanga ''krishnakali ityadi galpa'' rajsheskhar also noted lexicographer translator essayist ''chalantika'' one popular concise bengali dictionaries bengali language translations ''meghaduta'' ''ramayana'' ''mahabharata'' ''bhagavat gita'' also acclaimed ref name parashuram major essays included ''laghuguru'' ''bichinta'' ref name parashuram prakalpana movement prakalpana movement branded steve leblanc


noted us critic 'a tiny literary revolution' 'nurtured' kolkata fostering new genres prakalpana fiction sarbangin poetry chetanavyasism four decades spearheaded vattacharja chandan beginning probably bilingual bengali english literary movement india mothered bengali literature spread wings worldwide participation well known international avant garde writers mail artists richard kostelanetz john bennett sheila murphy webb notable bengali poets writers artists like vattacharja chandan see also hungry generation new age bengali literature bengali


novels list notable writers list bengali language authors chronological list bengali language authors alphabetical ghosts bengali culture references external links https wwwlocgov acq ovop delhi salrp bengalihtml library congress bengali section http wwwbangla literatureueuocom english magazine bengali literature sayeed abubakar bengali bengali culture


'''ethnohistory''' study cultures indigenous peoples customs examining historical records well sources information lives history also study history various ethnic groups may may still exist term commonly used writing history americas ethnohistory uses historical ethnographic data foundation historical methods materials go beyond standard use documents manuscripts practitioners recognize use source material maps music paintings photography folklore oral tradition


site exploration archaeological materials museum collections enduring customs language placenames ref name axtell ref historical development itneg potters northern philippines person right biologically male wearing women 's clothes common practice pre colonial philippines scholars studying history mexico 's indigenous long tradition dating back colonial era used alphabetic texts sources write history mexico 's indigenous peoples ''handbook middle american indians'' edited archeologist robert wauchope involved creating multiple volumes mesoamerican ethnohistory published ''guide ethnohistorical sources'' appearing


time volumes published term 'ethnohistory' concepts sense used entered literature rather recently fully agreed upon volumes intended inventory sources later hands could utilize produce professionally acceptable ethnohistory mid late th century number ethnohistorians mexico began systematically publish many colonial alphabetic texts indigenous mexican languages branch ethnohistory currently known new philology built earlier tradition practitioners writing


history mexico fully integrated history indigenous peoples united states field arose study american indian communities required indian claims commission gained pragmatic rather theoretical orientation practitioners testifying indian claims emerging methodology used documentary historical sources ethnographic methods among scholars working cases latin americanist howard f cline commissioned work florida indians jicarilla apache field also reached melanesia recent european contact allowed researchers


observe early postcontact period directly address important theoretical questions michael harkin argues ethnohistory part general rapprochement history anthropology late th century ethnohistory grew organically thanks external nonscholarly pressures without overarching figure conscious plan even came engage central issues cultural historical analysis ethnohistorians take pride using special knowledge specific groups linguistic insights interpretation cultural phenomena claim achieve depth analysis average historian capable based solely written


documents produced one group try understand culture terms according cultural code ethnohistory differs historically related methodologies embraces emic perspectives tools analysis field techniques well suited writing histories native american peoples holistic inclusive framework especially important ability bridge differing frameworks access informed context interpretations past definition field become refined years early ethnohistory differed


history proper added new dimension specifically critical use ethnological concepts materials examination use historical source material described william n fenton later james axtell described ethnohistory use historical ethnological methods gain knowledge nature causes change culture defined ethnological concepts categories ref name axtell ref others focused basic concept previously ignored historical actors ed schieffelin asserted example ethnohistory must fundamentally take account people 's sense events constituted


ways culturally constructing past finally simmons formulated understanding ethnohistory form cultural biography draws upon many kinds testimony possible long time period sources allow described ethnohistory endeavor based holistic diachronic approach rewarding joined memories voices living people reflecting upon history ethnohistory research field us harkin situated within broader context convergences divergences fields history anthropology


survey ethnohistoric sources ''kroeber anthr soc papers'' lockhart james charles gibson ethnohistory postconquesst central mexico ''nahuas spaniards postconquest central mexican history philology'' stanford university press ucla latin american studies vol sturtevant wc anthropology history ethnohistory ''ethnohistory'' vogelin ew ethnohistorian 's viewpoint ''the bulletin ohio valley historic indian conference'' external links http ethnohistoryorg american society ethnohistory fields history anthropology historiography theories history


mathematics '''convex geometry''' branch geometry studying convex sets mainly euclidean space convex sets occur naturally many areas computational geometry convex analysis discrete geometry functional analysis geometry numbers integral geometry linear programming probability theory game theory etc classification according mathematics subject classification msc mathematical discipline ''convex discrete geometry'' includes three major branches general convexity polytopes polyhedra discrete geometry though portions latter two included convex geometry general convexity subdivided follows axiomatic generalized convexity convex sets without dimension restrictions convex sets

Formal science
Mathematics
Pure mathematics
Geometry
Convex geometry


topological vector spaces convex sets dimensions including convex curves convex sets dimensions including convex surfaces convex sets ''n'' dimensions including convex hypersurfaces finite dimensional banach spaces random convex sets integral geometry asymptotic theory convex bodies approximation convex sets variants convex sets star shaped ''m n'' convex etc helly type theorems geometric transversal theory problems combinatorial convexity length area volume mixed volumes related topics valuations convex bodies inequalities extremum problems convex functions convex programs spherical hyperbolic convexity term ''convex geometry'' also used combinatorics


alternate name antimatroid one abstract models convex sets historical note convex geometry relatively young mathematical discipline although first known contributions convex geometry date back antiquity traced works euclid archimedes became independent branch mathematics turn th century mainly due works hermann brunn hermann minkowski dimensions two three big part results soon generalized spaces higher dimensions bonnesen w


fenchel gave comprehensive survey convex geometry euclidean space '''r''' sup n sup development convex geometry th century relations numerous mathematical disciplines summarized ''handbook convex geometry'' edited p gruber j wills see also list convexity topics notes references '''expository articles convex geometry''' k ball ''an elementary introduction modern convex geometry'' flavors geometry pp nbsp math sci res inst publ vol cambridge univ press cambridge available http wwwmsriorg publications books book files ballpdf online berger ''convexity'' amer math monthly vol doi https dxdoiorg


p gruber ''aspects convexity applications'' exposition math vol v klee ''what convex set'' amer math monthly vol doi https dxdoiorg '''books convex geometry''' bonnesen w fenchel ''theorie der konvexen k rper'' julius springer berlin english translation ''theory convex bodies'' bcs associates moscow id r j gardner ''geometric tomography'' cambridge university press new york second edition p gruber ''convex discrete geometry'' springer verlag new york p gruber j wills editors ''handbook convex geometry vol b'' north holland amsterdam


g pisier ''the volume convex bodies banach space geometry'' cambridge university press cambridge r schneider ''convex bodies brunn minkowski theory'' cambridge university press cambridge second edition c thompson ''minkowski geometry'' cambridge university press cambridge koldobsky v yaskin ''the interface convex geometry harmonic analysis'' american mathematical society providence rhode island '''articles history convex geometry''' w fenchel ''convexity ages'' danish danish mathematical society pp nbsp dansk mat forening copenhagen english translation ''convexity ages'' p gruber j wills editors convexity


applications pp nbsp birkhauser verlag basel p gruber ''zur geschichte der konvexgeometrie und der geometrie der zahlen'' g fischer et al editors ein jahrhundert mathematik pp nbsp dokumente gesch math vol f wieweg sohn braunschweig deutsche mathematiker vereinigung freiburg p gruber ''history convexity'' p gruber j wills editors handbook convex geometry vol pp nbsp north holland amsterdam external links


'''port management''' involves management ports larger ports according syllabus united nations university large ports need deal number disparate activities movement ships containers cargo loading unloading ships containers customs activities well human resources anchorages channels lighters tugs berths warehouse storage spaces allocated released efficient management port involves managing activities resources managing flows money involved agents providing using resources providing management

Applied science
Transportation
Marine transportation
Port management


information smaller ports see also american association port authorities port authority port security references ports harbours ship management


uses transformation writing systems writing technologies among many subareas research american universities offer doctoral study rhetoric composition programs study usually include composition pedagogical theory linguistics professional technical communication qualitative quantitative research methods history rhetoric well influence different writing conventions genres writers' composing processes generally composition scholars also publish fields teaching english second foreign language tesol second language writing writing centers new literacies basic writing many historians composition studies

Humanities
Languages and literature
Linguistics
Composition studies


argue matter exactly defined basic writer counts basic writing complex definition basic disputed framed around issues writing proficiency standard english increasingly racially ethnically diverse college demographics resulted post secondary desegregation mandates example term basic writing attributed seek program started mina p shaughnessy city university new york designed help incoming college students open admissions historically able attend college consistent current educational


theories many courses focused time believed core concepts formal english like spelling usage organization though field advanced courses increasingly aligned curricula found mainstream first year composition basic writing coursework diversified considerably since beginnings non credit bearing 'pre' college courses including stretch studio accelerated offerings although remain typically understood precursors supplements mainstream first year composition first year composition us universities required first year composition course also referred fyc although typically housed


departments english courses literature courses focus literary analysis interpretation colleges universities incorporate literature humanities composition courses much often case composition coursework offers intensive instruction writing non fiction expository texts using academic discourse conventions writing curricula vary considerably institution institution may emphasize many stages different writing processes invention brainstorming drafting revision editing proofreading different forms writing narration exposition description argumentation comparison contrast different portions written product introductions conclusions


thesis statements presentation documentation forms evidence inclusion quotations etc along different modalities composing expand concept 'writing' pedagogies approaches teaching writing grounded range different traditions philosophies advanced composition universities require instruction writing offer courses expand upon skills developed first year composition second level advanced composition may emphasize forms argumentation persuasion digital media research source documentation formats genres writing across range disciplines genres see example skills required


writing esl students receive much attention even esl classes teachers focus speaking listening reading writing paul kei matsuda article situating esl writing cross disciplinary context stresses importance teaching writing specifically understanding needs esl students help improve writing teaching writing progressed several approaches history education united states esl teachers might need explore common methods cognitive social expressive theories create approach meets needs esl writers


help overcome difficulties first one approaches cognitive view says writing progressing one stage another series single steps means good writing planned process includes planning translating reviewing understanding composing sondra perl explains detail approach suggests composition writing occurs recursive process took idea observation different writers thinks writers return backward parts process order move forward overall composition


esl teachers may find approach helpful first teaching beginning esl students level students large amounts vocabulary grammar knowledge style essays basis writing english al buainain haifa article student writing errors efl points researcher asked esl students using survey would like learned learned better writing classes found largest percentages expressed specific needs vocabulary grammar many kinds grammar make esl students confused


especially many exceptions writing styles different different languages esl students need time master therefore esl teachers find effective way teach esl students vocabulary grammar style writing english requires cognitive approach meet needs emphasizes steps organization process writing another approach social view shows importance teaching writing making students learn different languages discourse communities david bartholomae emphasizes article inventing university uses inventing


university phrase describes writing process student experience writing teachers ask write topic relates discourse community new discourse community thought members academic discipline select audience esl students become good grammar style face large problem enter chosen academic field bartholomae article illustrates academic community particular language vocabulary problem academic field language


even jargon differs one another problem faced esl students american students struggle begin first year academic life social approach used esl teachers second step make sure students master basics english writing grammar style moreover expressive view represented donald murray 's article teach writing process product allows wittier creating freer movement suggests three elements good writing


integrity originality spontaneity however difficult evaluate paper therefore standards cannot relied upon judge writing addition elements important elements help assess good writing esl teachers might use approach used highly advanced esl students difficult ask esl students write freely possess limited vocabulary grammar need examples help find cognitive approach esl teachers may use common ways teaching writing


need first understand student 's difficulties learning writing one essential difficulties esl students find studying english especially since writing important academic community esl students may need jump student speak english ever student uses academic language short time may put large burden shoulders hence teaching writing esl students different teaching native speakers esl teachers need choose effective way meet needs esl students would helpful


engage cultural critique aaron schutz anne ruggles gere 's article ''college english'' service learning english studies described schutz 's course mainly focused service learning local activism engaged students collaborative research writing surrounding campus wide issues instance racial discrimination occurred local student union allowed students engage cultural awareness well cultural critique furthermore ''empowering education'' ira shor delineates pedagogy teacher facilitates discussion generative themes produced students using example


basic writing course working class students low budget college new york city several decades ago ref name ref freirean approach teaching literacy writing shor reviews ''empowering education'' demonstrates generative words manifested researching local issues language students' communities many linguistic sociological items educators selected key concerns generative themes expressed generative words ref name framework teachers students research items collaboratively students presented research problems community may begin decide


might analyze upend power structures rhetorical situations contribute exacerbate issues shor 's classroom generative themes emerg ed student culture often related sex abortion drugs family education careers work economic crisis ref name shor believes important allow students build basis problem posing upon prior knowledge experiences make multicultural ref name shor also reviews paolo freire 's literacy project brazil described freire 's ''pedagogy oppressed'' enforces idea people creators culture


visuals oral discussion creation word lists basis people begin use language express dominant culture operates home culture operates systemic actions impact world way freire shor believe problem posing education situated multicultural practices well critical literacy practices shor insists subject matter best introduced problems related student experience language familiar ref name critical reception overall previous scholars' discussion multiculturalism classroom seems


privilege cross cultural interactions valuing students' home languages well cultural ideologies however donald lazere 's ''political literacy composition rhetoric'' lazere criticizes hairston daniell schutz gere scholars approaches singular focus localism lieu global critical approaches study culture composition classroom ref name ref addition lazere critical scholars' tendency diminish power edited american english eae misrepresent power students' regional code ref name lazere supports shor 's approach multicultural critical


pedagogy admits level discomfort applying classroom especially respect much responsibility stock shor places students ref name current approaches lazere 's critique previous scholarship related multiculturalism pedagogies ''political literacy composition rhetoric'' elsewhere prompted current composition theorists second language writing field composition general consider multicultural pedagogies embrace globalism much localism example lisa eck 's thinking globally teaching locally describes eck teaches world literature courses students read


cultural narratives problematize article references use tsitsi dangarembga 's ''nervous conditions'' composition classroom ref name ref teaching attempting answer question multicultural pedagogical practices could still based research critical literacy problem posing education approach engages students kind literary criticism necessary analyzing evaluating critical discourse work make hybrid postcolonial identities familiar even analogous times understand process identity formation average postmodern college student also use otherness


cultures reproduced foreign texts estrange american familiar ref name kinds inquiry students using analyze text show text ''both'' processes identity formation kinds processes necessary critically evaluate public discourse ref name furthermore jennifer wilson 's approach critical pedagogy second language writing describes article engaging second language writers freshman composition critical approach utilizes perspective provides opportunities types writing necessary


cultures well investigating relationships language power ref name even important insists c ritical pedagogy concerned minimizing power differential student teacher composition classrooms one way students maximize voices publish work authentic ways ref name writing across curriculum academic discourse monolithic words curricula address concept academic discourse applied specific parts writing curriculum many compositionists created writing across curriculum wac movement


situates writing intensive instruction specific academic discourse communities reading apprenticeship connections according writing theorists reading pleasure provides effective way mastering art writing formal study writing language grammar vocabulary blockquote studies sought improve writing providing reading experiences place grammar study additional writing practice found experiences beneficial beneficial grammar study extra writing practice blockquote apprenticeship approach provides one variant reading connection arguing composition classroom resemble pottery piano


workshops minimizing dependence excessive self reflection preoccupation audience explicit rules watching master according michael polanyi apprentice unconsciously picks rules art including explicitly known master writing instructors according approach serve models coaches providing explicit feedback response learner 's compositions students focus attention task hand inaccessible confusing multitude explicit rules strategies writing disciplines many university writing programs include writing disciplines wid courses focus


genres writing procedures occur within specific fields research writing center many colleges universities writing center offers supplementary tutorial support writing specifically english classes across curriculum many universities north america offer writing instruction via writing centers european association teaching academic writing eataw example specifically concerns study advancement writing centers europe writing centers serve purpose writing social process demands engaging tutors writers since multimodality resonated composition


studies many writing centers developed associated centers support students' multimodal multimedia composing models work include digital studio multiliteracy center see also cognitive rhetoric comics studies communication studies composition language conference college composition communication contrastive rhetoric digital rhetoric english studies media theory composition national writing project professional communication technical communication technical writing theories rhetoric composition pedagogy writing assessment writing center writing center assessment references reading bartholomae david ''the tidy house basic writing american curriculum'' ''writing margins'' palgrave macmillan new york berlin


siegel white farnham jamie ''writing program architecture thirty cases reference research'' u utah p horner winifred bryan lynee lewis gaillet eds ''the present state scholarship history rhetoric twenty first century guide'' u missouri miller susan ''textual carnivals politics composition'' carbondale southern illinois miller susan ''the norton book composition studies'' new york ny ww norton company north stephen ''the making knowledge composition studies'' upper montclair nj boynton cook perryman clark staci african american languages rhetoric students' writing new directions


srtol students' right language ''college composition communication'' phelps louise wetherbee ''composition human science'' new york oxford royster jacqueline jones ''traces stream literacy social change among african american women'' university pittsburgh press tate gary ''teaching composition bibliographical essays'' fort worth tcu p external links http inventious ccc college composition communication ''ccc'' online archive https webarchiveorg web http wwwcompositionstudiesuwinnipegca composition studies https webarchiveorg web http wwwbgsuedu cconline homehtm computers composition http wwwncteorg cccc conference college composition communication http wwweataweu european association teaching academic writing eataw http ewhieeeorg soc pcs q node ieee transactions professional communication http rhetoricsocietyorg


rhetoric society america rhetoric composition language systems education


'''jewish american literature''' holds essential place literary history united states encompasses traditions writing english primarily well languages important yiddish critics authors generally acknowledge notion distinctive corpus practice writing jewishness america many writers resist pigeonholed jewish voices also many nominally jewish writers cannot considered representative jewish american literature one example isaac asimov beginnings beginning memoirs petitions composed sephardic immigrants arrived america

Humanities
Languages and literature
Jewish American Literature


mid th century jewish american writing grew subsequent centuries flourish genres well including fiction poetry drama first notable voice jewish american literature emma lazarus whose poem new colossus statue liberty became great hymnal american immigration gertrude stein became one influential prose stylists early th century early twentieth century saw appearance two pioneering american jewish novels abraham cahan 's rise david levinsky henry roth 's call sleep reached mature


expression th century jewish american novels saul bellow j salinger norman mailer bernard malamud chaim potok philip roth work explored conflicting pulls secular society jewish tradition acutely felt immigrants passed ellis island children grandchildren present day recent authors like paul auster michael chabonayelet waldman joshua cohen helen epstein jonathan safran foer alan kaufman nicole krauss lev raphael art spiegelman continued examine dilemmas identity work turning attention especially holocaust


trends ongoing assimilation cultural rediscovery exhibited younger generations american jews arguably influential american jewish novels leon uris' ''exodus'' story struggle create modern state israel translated russian became inspiration hundreds thousands russian immigrants israel modern jewish american novels often contain many jewish characters address issues themes importance jewish american society assimilation zionism israel antisemitism along recent phenomenon known new antisemitism four jewish american writers nobel


literature also strongly celebrated american life primarily american jewish literature perhaps preeminent example great breakthrough novel saul bellow ''the adventures augie march'' according sanford v sternlicht first generation jewish american authors presented realistic portrayals warts jewish immigrants contrast second third generation jewish american authors deliberately reinforced negative stereotypes satire selective realism see also american literature literature chicago culture new york city early english jewish literature hebrew literature israeli literature ladino literature list


jewish american authors list jewish american playwrights list jewish american poets secular jewish culture yiddish literature references reading chametzky jules et al ''jewish american literature norton anthology'' w w norton company inc fried lewis ed ''handbook american jewish literature analytical guide topics themes sources'' greenwood press furman andrew ''israel jewish american imagination survey jewish american literature israel '' suny press kramer michael p hana wirth nesher ''the cambridge companion jewish american literature'' cambridge university press kugelmass jack ed ''key texts american jewish


culture'' rutgers university press nadel b ''jewish writers north america guide information sources'' gale group rubin derek ed ''who jewish american writer'' schocken weber donald ''haunted new world'' indiana university press book 's subtitle ''jewish american culture cahan goldbergs'' reflects broad critical focus wirth nesher hana ''call english languages jewish american literature'' princeton university press external links links currently unavailable https webarchiveorg web http wwwmyjewishlearningcom culture literature finaledittojewishamericanlithtm comprehensive historical overview jewish american literature https webarchiveorg web http wwwjewishliteraryreviewcom news reviews


focusing jewish american literature yiddish language literature jewish american history jewish theatre american literature ethnic background jewish american culture


'''music psychology''' '''psychology music''' may regarded branch psychology musicology aims explain understand musical behaviour experience including processes music perceived created responded incorporated everyday life ref name tan ref ref name thompson ref modern music psychology primarily empirical knowledge tends advance basis interpretations data collected systematic observation interaction human participants music psychology field research practical relevance many areas including music performance composition education criticism therapy

Social science
Psychology
Music psychology


th century focused primarily mathematical modelling pitch tone ref name deutsch et al psychology music earliest recorded experiments date th century bce notably work pythagoras establishment simple string length ratios formed consonances octave view sound music could understood purely physical standpoint echoed theorists anaxagoras boethius important early dissenter aristoxenus foreshadowed modern music psychology view music could understood


human perception relation human memory despite views majority musical education middle ages renaissance remained rooted pythagorean tradition particularly quadrivium astronomy geometry arithmetic music ref name deutsch et al psychology music research vincenzo galilei father galileo demonstrated string length held constant varying tension thickness composition could alter perceived pitch argued simple ratios enough account musical phenomenon perceptual approach necessary also claimed differences various


tuning systems perceivable thus disputes unnecessary study topics including vibration consonance harmonic series resonance furthered scientific revolution including work galileo kepler mersenne descartes included speculation concerning nature sense organs higher order processes particularly savart helmholtz koenig ref name deutsch et al psychology music rise empirical study brass spherical helmholtz resonator based original design circa latter th century saw development modern music psychology alongside emergence general empirical psychology one