early th century pictured excavations maiden castle dorset october first stratigraphic excavation reach wide popularity public hissarlik site ancient troy carried heinrich schliemann frank calvert wilhelm rpfeld scholars individuated nine different cities overlapped one another prehistory hellenistic period meanwhile work sir arthur evans knossos crete revealed ancient existence equally advanced minoan civilization next major figure development archaeology sir mortimer


wheeler whose highly disciplined approach excavation systematic coverage brought science swiftly wheeler developed grid system excavation improved student kathleen kenyon archaeology became professional activity first half th century became possible study archaeology subject universities even schools end th century nearly professional archaeologists least developed countries graduates adaptation innovation archaeology continued period maritime archaeology urban archaeology became


prevalent rescue archaeology developed result increasing commercial development ref name renfrew bahn renfrew bahn ref purpose cast skull taung child uncovered south africa child infant ''australopithecus africanus'' species early form hominin purpose archaeology learn past societies development human race development humanity occurred within prehistoric cultures make use writing thereby written records exist study purposes without written sources way understand


prehistoric societies archaeology archaeology study past human activity stretches back nbsp million years ago find first stone tools oldowan industry many important developments human history occurred prehistory evolution humanity paleolithic period hominins developed australopithecines africa eventually modern ''homo sapiens'' archaeology also sheds light many humanity 's technological advances instance ability use fire development stone tools discovery metallurgy beginnings religion creation


agriculture without archaeology would know little nothing use material culture humanity pre dates writing ref name ncl however prehistoric pre literate cultures studied using archaeology historic literate cultures well sub discipline historical archaeology many literate cultures ancient greece mesopotamia surviving records often incomplete biased extent many societies literacy restricted elite classes clergy bureaucracy court temple literacy even aristocrats sometimes restricted


subject biases sampling bias differential preservation ref name archaeological often archaeology provides means learn existence behaviors people past across millennia many thousands cultures societies billions people come gone little written record existing records misrepresentative incomplete writing known today exist human civilization th millennium bc relatively small number technologically advanced civilizations contrast ''homo sapiens'' existed least


descendants people produced monetary value collectors simply strong aesthetic appeal many people identify archaeology recovery aesthetic religious political economic treasures rather reconstruction past societies view often espoused works popular fiction raiders lost ark mummy king solomon 's mines unrealistic subjects treated seriously accusations pseudoscience invariably levelled proponents '' see pseudoarchaeology '' however endeavours real fictional representative modern archaeology theory sign lubbock lake landmark


lubbock texas one approach archaeological theory adhered archaeologists archaeology developed late th century first approach archaeological theory practiced cultural history archaeology held goal explaining cultures changed adapted rather highlighting fact therefore emphasizing historical particularism ref name autogenerated early th century many archaeologists studied past societies direct continuing links existing ones native americans siberians mesoamericans etc followed direct historical approach compared continuity


past contemporary ethnic cultural groups ref name autogenerated archaeological movement largely led american archaeologists like lewis binford kent flannery arose rebelled established cultural history archaeology ref name binford ref name flannery proposed new archaeology would scientific anthropological hypothesis testing scientific method important parts became known processual archaeology ref name autogenerated new postmodern movement arose led british archaeologists michael shanks ref name shanks tilley ref name shanks tilley ref name shanks ref name shanks christopher tilley ref name tilley daniel miller ref name miller tilley ref name miller etal ian hodder ref name hodder ref name hodder ref name hodder ref name hodder ref


name hodder ref name hodder become known post processual archaeology questioned processualism 's appeals scientific positivism impartiality emphasized importance self critical theoretical reflexivity however approach criticized processualists lacking scientific rigor validity processualism post processualism still debate meanwhile another theory known historical processualism emerged seeking incorporate focus process post processual archaeology 's emphasis reflexivity history ref name pauketat archaeological theory borrows wide range influences including neo evolutionary thought ref name hinshaw span class mw reflink text span phenomenology postmodernism agency theory cognitive science structural functionalism


gender based feminist archaeology systems theory methods video showing different works archaeological recovery analysis archaeological investigation usually involves several distinct phases employs variety methods practical work begin however clear objective archaeologists looking achieve must agreed upon done site surveyed find much possible surrounding area second excavation may take place uncover archaeological features buried ground third information collected


excavation studied evaluated attempt achieve original research objectives archaeologists considered good practice information published available archaeologists historians although sometimes neglected ref name renfrew remote sensing actually starting dig location remote sensing used look sites located within large area provide information sites regions two types remote sensing instruments passive active passive instruments detect natural energy reflected emitted


observed scene passive instruments sense radiation emitted object viewed reflected object source instrument active instruments emit energy record reflected satellite imagery example passive remote sensing two active remote sensing instruments '''lidar''' light detection ranging lidar uses laser light amplification stimulated emission radiation transmit light pulse receiver sensitive detectors measure backscattered reflected light distance object determined recording time transmitted backscattered


pulses using speed light calculate distance travelled lidars determine atmospheric profiles aerosols clouds constituents atmosphere '''laser altimeter''' laser altimeter uses lidar see measure height instrument platform surface independently knowing height platform respect mean earth 's surface topography underlying surface determined field survey monte alb n archaeological site archaeological project continues alternatively begins field survey regional survey attempt systematically locate previously unknown sites


region site survey attempt systematically locate features interest houses middens within site two goals may accomplished largely methods survey widely practiced early days archaeology cultural historians prior researchers usually content discovering locations monumental sites local populace excavating plainly visible features gordon willey pioneered technique regional settlement pattern survey viru valley coastal peru ref name willey ref name willey survey levels became


information settlement patterns settlement structure survey data commonly assembled maps may show surface features artifact distribution inverted kite aerial photo excavation roman building nesley near tetbury gloucestershire simplest survey technique surface survey involves combing area usually foot sometimes use mechanized transport search features artifacts visible surface surface survey cannot detect sites features completely buried earth overgrown vegetation surface survey may also include mini excavation techniques


augers corers shovel test pits materials found area surveyed deemed sterile aerial survey conducted using cameras attached airplanes balloons uavs even kites bird 's eye view useful quick mapping large complex sites aerial photographs used document status archaeological dig aerial imaging also detect many things visible surface plants growing buried man made structure stone wall develop slowly types features middens may develop rapidly photographs


ripening grain changes colour rapidly maturation revealed buried structures great precision aerial photographs taken different times day help show outlines structures changes shadows aerial survey also employs ultraviolet infrared ground penetrating radar wavelengths lidar thermography geophysical survey effective way see beneath ground magnetometers detect minute deviations earth 's magnetic field caused iron artifacts kilns types stone structures even ditches middens devices measure electrical resistivity soil also widely used archaeological features whose electrical


resistivity contrasts surrounding soils detected mapped archaeological features composed stone brick higher resistivity typical soils others organic deposits unfired clay tend lower resistivity although archaeologists consider use metal detectors tantamount treasure hunting others deem effective tool archaeological surveying examples formal archaeological use metal detectors include musketball distribution analysis english civil war battlefields metal distribution analysis prior excavation th century ship wreck service cable location


evaluation metal detectorists also contributed archaeology made detailed records results refrained raising artifacts archaeological context uk metal detectorists solicited involvement portable antiquities scheme regional survey underwater archaeology uses geophysical remote sensing devices marine magnetometer side scan sonar sub bottom sonar excavation excavations year old edgewater park site iowa archaeological excavation discovered prehistoric caves vill innsbruck austria pow remains wake island archaeological excavation existed even field still domain amateurs


remains source majority data recovered field projects reveal several types information usually accessible survey stratigraphy three dimensional structure verifiably primary context modern excavation techniques require precise locations objects features known provenance provenience recorded always involves determining horizontal locations sometimes vertical position well also see primary laws archaeology likewise association relationship nearby objects features needs recorded later analysis allows archaeologist deduce artifacts features


likely used together may different phases activity example excavation site reveals stratigraphy site occupied succession distinct cultures artifacts recent cultures lie ancient cultures excavation expensive phase archaeological research relative terms also destructive process carries ethical concerns result sites excavated entirety percentage site excavated depends greatly country method statement issued sampling even important


excavation survey sometimes large mechanical equipment backhoes jcbs used excavation especially remove topsoil overburden though method increasingly used great caution following rather dramatic step exposed area usually hand cleaned trowels hoes ensure features apparent next task form site plan use help decide method excavation features dug natural subsoil normally excavated portions produce visible archaeological section recording feature example pit


ditch consists two parts cut fill cut describes edge feature feature meets natural soil feature 's boundary fill feature filled often appear quite distinct natural soil cut fill given consecutive numbers recording purposes scaled plans sections individual features drawn site black white colour photographs taken recording sheets filled describing context information serves permanent


record destroyed archaeology used describing interpreting site analysis five seven known fossil teeth ''homo luzonensis'' found callao cave philippines artifacts structures excavated collected surface surveys necessary properly study process known post excavation analysis usually time consuming part archaeological investigation uncommon final excavation reports major sites take years published basic level analysis artifacts found cleaned catalogued compared published


survey work protect sites squatters builders miners peru small drones helped researchers produce three dimensional models peruvian sites instead usual flat maps days weeks instead months years ref name peru ref drones costing little proven useful drones flown least six peruvian archaeological sites including colonial andean town machu llacta sea level drones continue altitude problems andes leading plans make drone blimp employing open source software ref name peru jeffrey quilter archaeologist


harvard university said go three metres photograph room metres photograph site go metres photograph entire valley ref name peru september drones weighing used mapping ground ruins greek city aphrodisias data analysed austrian archaeological institute vienna academic sub disciplines academic disciplines large number archaeological sub disciplines characterized specific method type material eg lithic analysis music archaeobotany geographical chronological focus


scientific knowledge reveal details line 's construction ethnoarchaeology ethnoarchaeology ethnographic study living people designed aid interpretation archaeological record ref name gould ref name gould b ref name yellen ref name yellen ref name gould yellen ref name yellen approach first gained prominence processual movement continues vibrant component post processual current archaeological approaches ref name hinshaw ref name sillet et al ref name schott sillitoe ref name ogundele ref name kuznar early ethnoarchaeological research focused hunter gatherer foraging societies today ethnoarchaeological research encompasses much wider range human behaviour experimental archaeology experimental archaeology represents application experimental method develop


highly controlled observations processes create impact archaeological record ref name ascher ref name saraydar shimada ref name saraydar shimada ref name gifford gonzalez et al ref name frison context logical positivism processualism goals improving scientific rigor archaeological epistemologies experimental method gained importance experimental techniques remain crucial component improving inferential frameworks interpreting archaeological record archaeometry archaeometry aims systematize archaeological measurement emphasizes application analytical techniques physics chemistry engineering field research frequently focuses definition chemical composition archaeological remains source analysis ref name glasscock et al


archaeometry also investigates different spatial characteristics features employing methods space syntax techniques geodesy well computer based tools geographic information system technology ref name gis critique representation beyond rare earth elements patterns may also used ref name anthropic soil transformation fingerprinted rey patterns relatively nascent subfield archaeological materials designed enhance understanding prehistoric non industrial culture scientific analysis structure properties materials associated human activity ref name mit cultural resources management archaeology subsidiary activity within cultural resources management crm also called cultural


heritage management chm united kingdom ref name university exeter sogaer department archaeology crm archaeologists frequently examine archaeological sites threatened development today crm accounts archaeological research done united states much western europe well us crm archaeology growing concern since passage national historic preservation act nhpa taxpayers scholars politicians believe crm helped preserve much nation 's history prehistory would otherwise lost


construction work archaeologically sensitive areas developer 's expense england ultimate responsibility care historic environment rests department culture media sport ref name department culture media sport historic environment association english heritage ref name english heritage stonehenge history england english heritage scotland wales northern ireland responsibilities lie historic scotland cadw ref name cadw northern ireland environment agency ref name built environment respectively france institut national du patrimoine national institute cultural heritage trains curators specialized archaeology mission


enhance objects discovered curator link scientific knowledge administrative regulations heritage objects public among goals crm identification preservation maintenance cultural sites public private lands removal culturally valuable materials areas would otherwise destroyed human activity proposed construction study involves least cursory examination determine whether significant archaeological sites present area affected proposed construction exist time money must allotted excavation


initial survey test excavations indicate presence extraordinarily valuable site construction may prohibited entirely cultural resources management however criticized crm conducted private companies bid projects submitting proposals outlining work done expected budget unheard agency responsible construction simply choose proposal asks least funding crm archaeologists face considerable time pressure often forced complete work fraction time might allotted purely scholarly endeavour


compounding time pressure vetting process site reports required us submitted crm firms appropriate state historic preservation office shpo shpo 's perspective difference report submitted crm firm operating deadline multi year academic project end result cultural resource management archaeologist successful must able produce academic quality documents corporate world pace annual ratio open academic archaeology positions inclusive post doc temporary non


tenure track appointments annual number archaeology msc phd students disproportionate cultural resource management considered intellectual backwater individuals strong backs weak minds ref name flannery attracted graduates crm offices thus increasingly staffed advance degreed individuals track record producing scholarly articles also extensive crm field experience protection karl von habsburg blue shield international fact finding mission libya protection archaeological finds public catastrophes wars armed conflicts increasingly implemented internationally happens one


hand international agreements hand organizations monitor enforce protection united nations unesco blue shield international deal protection cultural heritage thus also archaeological sites also applies integration united nations peacekeeping blue shield international undertaken various fact finding missions recent years protect archaeological sites wars libya syria egypt lebanon importance archaeological finds identity tourism sustainable economic growth repeatedly emphasized internationally president blue shield international karl von habsburg said cultural property protection


mission lebanon april united nations interim force lebanon cultural assets part identity people live certain place destroy culture also destroy identity many people uprooted often prospects anymore subsequently flee homeland ref name unifilunmissionsorg ref popular views archaeology extensive excavations beit she'an israel permanent exhibition german multi storey car park explaining archaeological discoveries made construction building early archaeology largely attempt uncover spectacular artifacts features explore


vast mysterious abandoned cities mostly done upper class scholarly men general tendency laid foundation modern popular view archaeology archaeologists many public view archaeology something available narrow demographic job archaeologist depicted romantic adventurist occupation ref name mcgeough ref hobby job scientific community cinema audiences form notion archaeologists relationships past constituted ref name mcgeough often


impression archaeology takes place distant foreign land collect monetarily spiritually priceless artifacts modern depiction archaeology incorrectly formed public 's perception archaeology much thorough productive research indeed conducted dramatic locales cop n valley kings bulk activities finds modern archaeology sensational archaeological adventure stories tend ignore painstaking work involved carrying modern surveys excavations data processing archaeologists refer mark portrayals pseudoarchaeology ref name romancing


past archaeology archaeologists also much reliant public support question exactly work often discussed ref name denning current issues controversy public archaeology excavations site gran dolina atapuerca mountains spain motivated desire halt looting curb pseudoarchaeology help preserve archaeological sites education fostering public appreciation importance archaeological heritage archaeologists mounting public outreach campaigns ref name anthropological studies center asc seek stop looting combatting people illegally take artifacts protected sites alerting people


live near archaeological sites threat looting common methods public outreach include press releases encouragement school field trips sites excavation professional archaeologists making reports publications accessible outside academia public appreciation significance archaeology archaeological sites often leads improved protection encroaching development threats one audience archaeologists' work public increasingly realize work benefit non academic non archaeological audiences responsibility educate inform public archaeology local heritage awareness aimed


increasing civic individual pride projects community excavation projects better public presentations archaeological sites knowledge usdept agriculture forest service usfs operates volunteer archaeology historic preservation program called passport time pit volunteers work professional usfs archaeologists historians national forests throughout us volunteers involved aspects professional archaeology expert supervision ref name rapidcityjournal television programs web videos social media also bring understanding underwater archaeology broad audience ''mardi gras'' shipwreck project integrated one hour hd documentary ref name mystery mardi


gras shipwreck ref short videos public viewing video updates expedition part educational outreach webcasting also another tool educational outreach one week live underwater video ''queen anne 's revenge'' shipwreck project webcast internet part ''qar divelive'' educational program reached thousands children around world created co produced nautilus productions marine grafics project enabled students talk scientists learn methods technologies utilized underwater archaeology team uk popular archaeology


programs ''time team'' ''meet ancestors'' resulted huge upsurge public interest possible archaeologists make provisions public involvement outreach larger projects many local archaeological organizations operate within community archaeology framework expand public involvement smaller scale local projects archaeological excavation however best undertaken well trained staff work quickly accurately often requires observing necessary health safety indemnity insurance issues involved working modern building site tight deadlines certain charities local


government bodies sometimes offer places research projects either part academic work defined community project also flourishing industry selling places commercial training excavations archaeological holiday tours archaeologists prize local knowledge often liaise local historical archaeological societies one reason community archaeology projects starting become common often archaeologists assisted public locating archaeological sites professional archaeologists neither funding time archaeological legacy institute ali registered c non profit media


education corporation registered oregon ali founded website http archaeologychannelorg archaeology channel support organization 's mission nurturing bringing attention human cultural heritage using media efficient effective ways possible ref name archaeology channel us archaeological legacy institute pseudoarchaeology pseudoarchaeology umbrella term activities falsely claim archaeological fact violate commonly accepted scientific archaeological practices includes much fictional archaeological work discussed well actual activity many non fiction authors ignored scientific methods processual archaeology


specific critiques contained post processualism example type writing erich von niken book ''chariots gods'' together many subsequent lesser known works expounds theory ancient contacts human civilization earth technologically advanced extraterrestrial civilizations theory known palaeocontact theory ancient astronaut theory exclusively niken 's idea originate works nature usually marked renunciation well established theories basis limited evidence interpretation evidence preconceived theory


mind looting looter 's pit morning following excavation taken rontoy huaura valley peru june several small holes left looters' prospecting probes seen well footprints looting archaeological sites ancient problem instance many tombs egyptian pharaohs looted antiquity ref name civilizations archaeology stimulates interest ancient objects people search artifacts treasure cause damage archaeological sites commercial academic demand artifacts unfortunately contributes directly illicit antiquities trade smuggling antiquities abroad


private collectors caused great cultural economic damage many countries whose governments lack resources deter looters damage destroy archaeological sites denying future generations information ethnic cultural heritage indigenous peoples especially lose access control 'cultural resources' ultimately denying opportunity know past ref name autogenerated w f hodge director southwest museum released statement museum would longer purchase accept collections looted contexts ref name hodge first conviction transport artifacts


illegally removed private property http wwwnpsgov history local law fhpl archrsrcsprotpdf archaeological resources protection act arpa public law statute state indiana ref name munson et al archaeologists trying protect artifacts may placed danger looters locals trying protect artifacts archaeologists viewed looters locals historical archaeology sites subjected looting metal detector hobbyists search artifacts using increasingly advanced technology efforts underway among major archaeological organizations increase education legitimate cooperation amateurs professionals metal


detecting community looting deliberate accidental looting occur amateurs unaware importance archaeological rigor collect artifacts sites place private collections descendant peoples united states examples case kennewick man illustrated tensions native americans archaeologists summarized conflict need remain respectful toward sacred burial sites academic benefit studying years american archaeologists dug indian burial grounds places considered sacred removing artifacts human remains storage


continue studies contradictory situation addressed native american graves protection repatriation act nagpra sought reach compromise limiting right research institutions possess human remains due part spirit postprocessualism archaeologists begun actively enlist assistance indigenous peoples likely descended study archaeologists also obliged examine constitutes archaeological site view native peoples believe constitute sacred space many native peoples natural features lakes mountains even


individual trees cultural significance australian archaeologists especially explored issue attempted survey sites give protection developed work requires close links trust archaeologists people trying help time study cooperation presents new set challenges hurdles fieldwork benefits parties involved tribal elders cooperating archaeologists prevent excavation areas sites consider sacred archaeologists gain elders' aid interpreting finds also


active efforts recruit aboriginal peoples directly archaeological profession repatriation ''see repatriation reburial human remains'' new trend heated controversy first nations groups scientists repatriation native artifacts original descendants example occurred june community members elders number algonquian nations ottawa area convened kitigan zibi reservation near maniwaki quebec inter ancestral human remains burial goods dating back years determined however remains directly


related algonquin people inhabit region remains may iroquoian ancestry since iroquoian people inhabited area algonquin moreover oldest remains might relation algonquin iroquois belong earlier culture previously inhabited area remains artifacts including jewelry tools weapons originally excavated various sites ottawa valley including morrison allumette islands part canadian museum civilization 's research collection decades since late th century elders


various algonquin communities conferred appropriate reburial eventually deciding traditional redcedar birchbark boxes lined redcedar chips muskrat beaver pelts inconspicuous rock mound marks reburial site close boxes various sizes buried reburial scientific study possible although negotiations times tense kitigan zibi community museum able reach agreement ref name canadian geographic online african diaspora archaeology similar experience native americans history african diaspora archaeology one controversies whiteness


archaeology anthropology lack inclusion african descendant community possession human remains collections universities museums nineties anthropologist michael blakey director research new york african burial ground project initiated protocol collaborating african descendant community society black archaeologists created united states co founders ayana omilade flewellen archaeologist university california riverside justin dunnavant archaeologist assistant professor anthropology university california los angeles intend build


restorative justice based structure archaeology suggest define descendants genealogical terms also welcome input african americans whose ancestors shared historical experience enslavement united states senate unanimously passed bill december centers african american cemeteries risk south carolina bill made better protect historic african burial grounds lead creation african american burial grounds network barbados eight days becoming republic november announced plans construction ''newton enslaved burial ground memorial''


archaeological periods list archaeological sites country list archaeologists list archaeology awards list paleoethnobotanists notes although american english usually use ae spellings ''archaeology'' standard spelling across english speaking world including united states ref name hirstspelling ref us government bodies university presses use ''archeology'' accordance gpo style manual ref name society american archaeology another uncommon variant ''arch ology'' using archaic ligature '' '' ref name hirstspelling references ref ref name anthropological studies center asc ref ref name archaeological ref ref name ascher ascher ref ref name autogenerated trigger ref ref name autogenerated ref ref name billmand feinman billman feinman ref ref name binford binford


ref ref name built environment ref ref name cadw ref ref name canadian geographic online ref ref name civilizations time life lost civilizations series ramses ii magnificence nile ref ref name denning ref ref name department culture media sport historic environment ref ref name english heritage stonehenge history england english heritage ref ref name flannery flannery ref ref name flannery flannery ref ref name frison ref ref name gifford gonzalez et al gifford gonzalez ref ref name gis critique representation beyond ref ref name glasscock et al glascock et al ref ref name gould yellen gould yellen ref ref name gould gould ref ref name gould b gould b ref ref name haviland et al ref ref name hinshaw hinshaw ref ref name hodder hodder ref ref name hodder hodder ref ref name hodder hodder ref ref name hodder hodder ref ref name hodder hodder ref


ref name hodder hodder ref ref name hodge hodge ref ref name kuznar kuznar ref ref name miller etal miller et al ref ref name miller tilley miller tilley ref ref name mit ref ref name munson et al ref ref name ncl ref ref name ogundele ogundele ref ref name pauketat pauketat timothy r ref ref name planning policy guidance archaeology planning planning building environment communities local government ref ref name rapidcityjournal ref ref name redman ref ref name renfrew bahn renfrew bahn ref ref name renfrew renfrew bahn ref ref name romancing past archaeology ref ref name saraydar shimada saraydar shimada ref ref name saraydar shimada saraydar shimada ref ref name schott sillitoe schott sillitoe ref ref name shanks tilley shanks tilley ref ref name shanks tilley shanks tilley ref ref name shanks shanks ref ref


name shanks shanks ref ref name sillet et al sillet et al ref ref name society american archaeology ref ref name archaeology channel us archaeological legacy institute ref ref name university exeter sogaer department archaeology ref ref name tilley tilley ref ref name virt ref ref name willey willey ref ref name willey willey ref ref name yellen yellen ref ref name yellen yellen ref ref name yellen yellen ref bibliography reading ''archaeology'' magazine lewis binford ''new perspectives archaeology'' glyn daniel ''a short history archaeology'' kevin greene ''introduction archaeology'' thomas hester harry shafer kenneth l feder ''field methods archaeology'' th edition ian


history archaeological thought nd edition alison wylie ''thinking things essays philosophy archaeology'' university california press berkeley ca external links https wwwpastscapeorguk records archaeological sites architecture england https archivetoday http archaeologorg archaeologorg https archivetoday http wwwarchaeologydailycom archaeology daily news http wwwarchaeologytimescom archaeology times top archaeology news around world http wwwbritarchacuk council british archaeology https webarchiveorg web http geocitiescom emuseoros estudio de museolog rosario http wwwfastionlineorg fasti online online database archaeological sites http wwwgreatarchaeologycom great archaeology http wwwarmadaleorguk kite htm kite aerial photographers archaeology http wwwnpsgov history archeology visit indexhtm nps archeology program visit archeology archeology travel guides http wwwarchaeologygovlk sri lanka archaeology


http wwwarchaeologicalorg archaeological institute america http wwwarchaeologychannelorg archaeology channel http archaeologydataserviceacuk archaeology data service open access online archive uk global archaeology http wwwaaanetorg archaeology division american anthropological association http wwwcivilizationca cmc exhibitions online exhibitions archaeology canadian museum civilization archaeology http wwwsaaorg society american archaeology https webarchiveorg web http wwwworldarchaeologicalcongressorg site aboutphp world archaeological congress http wwwpassportintimecom us forest service volunteer program ''passport time'' http wwwarchaeologyws worldarchnewshtml world archaeology news weekly update bbc radio archaeologist win scutt http usaklihoyukorg en italian archaeological mission u akl h k http sitereportsnabunkengojp en comprehensive database archaeological site reports japan anthropology


physical map earth political map earth '''geography''' greek ''geographia'' literally earth description field science devoted study lands features inhabitants phenomena earth planets first person use word eratosthenes bc geography encompassing discipline seeks understanding earth human natural complexities merely objects also changed come geography often defined terms two branches human geography physical geography human geography concerned


study people communities cultures economies interactions environment studying relations across space place physical geography concerned study processes patterns natural environment like atmosphere hydrosphere biosphere geosphere four historical traditions geographical research spatial analyses natural human phenomena area studies places regions studies human land relationships earth sciences geography called world discipline bridge human physical sciences introduction geography systematic


study universe features traditionally geography associated cartography place names although many geographers trained toponymy cartology main preoccupation geographers study space temporal database distribution phenomena processes features well interaction humans environment space place affect variety topics economics health climate plants animals geography highly interdisciplinary interdisciplinary nature geographical approach depends attentiveness relationship physical human phenomena spatial patterns


ref sign william hughes ref sign united states national research council geography discipline split broadly two main subsidiary fields human geography physical geography former largely focuses built environment humans create view manage influence space latter examines natural environment organisms climate soil water landforms produce interact difference approaches led third field environmental geography combines physical human geography concerns interactions environment humans branches physical physical geography physiography focuses


geography earth science aims understand physical problems issues lithosphere hydrosphere atmosphere pedosphere global flora fauna patterns biosphere physical geography study earth 's seasons climate atmosphere soil streams landforms oceans gallery caption physical geography divided many broad categories including file l nea de wallacejpg biogeography file cyclone catarina iss march jpg climatology meteorology file mile beachjpg coastal geography file gavin plantjpg environmental management file meridian convergence spehrical excesspng geodesy file delicate arch lasallejpg geomorphology file receding glacier ensvg glaciology file meandersvg hydrology hydrography file khajuraho landscapejpg landscape ecology file world jpg oceanography file pangea interpretacionpng alt view supercontinent pangea breaking palaeogeography


file soil profilejpg pedology file milankovitch variations svpng quaternary science gallery human human geography anthropogeography branch geography focuses study patterns processes shape human society encompasses human political cultural social economic aspects gallery caption human geography divided many broad categories file qichwa conchucos jpg cultural geography file pepsi indiajpg development geography file christaller model jpg economic geography file star lifesvg health geography file british empire jpg historical time geog file un general assemblyjpg political geog geopolitics file pyramide comorespng pop geog demography file religionsymbolsvg religion geography file us hoosier familyjpg social geography file gare du nord usfrt paris metro png transportation geography file tourists jpg tourism


geography file new york jan jpg urban geography gallery various approaches study human geography also arisen time include behavioral geography culture theory feminist geography geosophy integrated integrated geography concerned description spatial interactions humans natural world requires understanding traditional aspects physical human geography like ways human societies conceptualize environment integrated geography emerged bridge human physical geography result increasing specialisation two sub fields since changing human relationship


environment result globalization technological change new approach needed understand changing dynamic relationship examples areas research environmental geography include emergency management environmental management sustainability political ecology geomatics digital elevation model dem geomatics concerned application computers traditional spatial techniques used cartography topography geomatics emerged quantitative revolution geography mid today geomatics methods include spatial analysis geographic information systems gis remote sensing global positioning systems gps geomatics led revitalization geography


departments especially northern america subject declining status regional branch concerned description unique characteristics earth 's surface resulting area combination complete natural elements physical human environment main aim understand define uniqueness character particular region consists natural well human elements attention paid also regionalization covers proper techniques space delimitation regions related fields interplanetary sciences


base geographical questions contrast descriptive tendencies traditional geography programs regional science comprises body knowledge spatial dimension plays fundamental role regional economics resource management location theory urban regional planning transport communication human geography population distribution landscape ecology environmental quality urban planning regional planning spatial planning use science geography assist determining develop develop land meet particular criteria safety beauty economic opportunities preservation built natural heritage


explored globally cartography james cook 's chart new zealand cartography studies representation earth 's surface abstract symbols map making although subdisciplines geography rely maps presenting analyses actual making maps abstract enough regarded separately cartography grown collection drafting techniques actual science cartographers must learn cognitive psychology ergonomics understand symbols convey information earth effectively behavioural psychology induce readers maps act information must learn


geodesy fairly advanced mathematics understand shape earth affects distortion map symbols projected onto flat surface viewing said without much controversy cartography seed larger field geography grew geographers cite childhood fascination maps early sign would end field geographic information systems geographic information systems gis deal storage information earth automatic retrieval computer accurate manner appropriate information 's purpose


addition subdisciplines geography gis specialists must understand computer science database systems gis revolutionized field cartography nearly mapmaking done assistance form gis software gis also refers science using gis software gis techniques represent analyse predict spatial relationships context gis stands ''geographic information science'' remote sensing remote sensing science obtaining information earth features measurements made distance remotely sensed data comes many forms


satellite imagery aerial photography data obtained hand held sensors geographers increasingly use remotely sensed data obtain information earth 's land surface ocean atmosphere supplies objective information variety spatial scales local global b provides synoptic view area interest c allows access distant inaccessible sites provides spectral information outside visible portion electromagnetic spectrum e facilitates studies features areas change time remotely sensed data may analysed either independently conjunction digital data layers eg


methods geographic qualitative methods ethnographical research techniques used human geographers cultural geography tradition employing qualitative research techniques also used anthropology sociology participant observation depth interviews provide human geographers qualitative data history oldest known world maps date back ancient babylon th century bc best known babylonian world map however ''imago mundi'' bc map reconstructed eckhard unger shows babylon euphrates surrounded circular landmass showing assyria urartu several cities turn


us fragments quoted successors anaximander credited invention gnomon simple yet efficient greek instrument allowed early measurement latitude thales also credited prediction eclipses foundations geography traced ancient cultures ancient medieval early modern chinese greeks first explore geography art science achieved cartography philosophy literature mathematics debate first person assert earth spherical


shape credit going either parmenides pythagoras anaxagoras able demonstrate profile earth circular explaining eclipses however still believed earth flat disk many contemporaries one first estimates radius earth made eratosthenes first rigorous system latitude longitude lines credited hipparchus employed sexagesimal system derived babylonian mathematics meridians sub divided degree subdivided minutes measure


longitude different locations earth suggested using eclipses determine relative difference time extensive mapping romans explored new lands would later provide high level information ptolemy construct detailed atlases extended work hipparchus using grid system maps adopting length miles degree rd century onwards chinese methods geographical study writing geographical literature became much comprehensive found europe time th century chinese geographers


liu pei xiu jia dan shen kuo fan chengda zhou daguan xu xiake wrote important treatises yet th century advanced ideas methods western style geography adopted china ptolemy world map reconstituted ptolemy 's ''geographia'' written middle ages fall roman empire led shift evolution geography europe islamic world muslim geographers muhammad al idrisi produced detailed world maps tabula rogeriana geographers yaqut al hamawi abu rayhan biruni ibn battuta ibn khaldun provided detailed


accounts journeys geography regions visited turkish geographer mahmud al kashgari drew world map linguistic basis later piri reis piri reis map islamic scholars translated interpreted earlier works romans greeks established house wisdom baghdad purpose ab zayd al balkh originally balkh founded balkh school terrestrial mapping baghdad suhr b late tenth century muslim geographer accompanied book geographical coordinates instructions making rectangular world map equirectangular projection cylindrical


equidistant projection abu rayhan biruni first described polar equi azimuthal equidistant projection celestial sphere regarded skilled came mapping cities measuring distances many cities middle east indian subcontinent often combined astronomical readings mathematical equations order develop methods pin pointing locations recording degrees latitude longitude also developed similar techniques came measuring heights mountains depths valleys expanse horizon also discussed human


geography planetary habitability earth also calculated latitude kath khwarezm using maximum altitude sun solved complex geodesic equation order accurately compute earth 's circumference close modern values earth 's circumference estimate nbsp km earth radius nbsp km less modern value nbsp km contrast predecessors measured earth 's circumference sighting sun simultaneously two different locations al biruni developed new method using trigonometric calculations based angle plain


mountain top yielded accurate measurements earth 's circumference made possible measured single person single location self portrait alexander von humboldt one early pioneers geography academic subject modern sense european age discovery th th centuries many new lands discovered accounts european explorers christopher columbus marco polo james cook revived desire accurate geographic detail solid theoretical foundations europe problem facing


explorers geographers finding latitude longitude geographic location problem latitude solved long ago longitude remained agreeing zero meridian part problem left john harrison solve inventing chronometer h later international meridian conference adopt convention greenwich meridian zero meridian th th centuries times geography became recognized discrete academic discipline became part typical university curriculum


europe especially paris berlin development many geographic societies also occurred th century foundations soci de g ographie royal geographical society russian geographical society american geographical society national geographic society influence immanuel kant alexander von humboldt carl ritter paul vidal de la blache seen major turning point geography philosophy academic subject past two centuries advancements technology computers led development


geomatics new practices participant observation geostatistics incorporated geography 's portfolio tools west th century discipline geography went four major phases environmental determinism regional geography quantitative revolution critical geography strong interdisciplinary links geography sciences geology botany well economics sociology demographics also grown greatly especially result earth system science seeks understand world holistic view notable geographers gerardus mercator alexander von humboldt nbsp published ''cosmos'' founder


sub field biogeography arnold henry guyot nbsp noted structure glaciers advanced understanding glacier motion especially fast ice flow carl sauer nbsp cultural geographer carl ritter nbsp occupied first chair geography berlin university david harvey born nbsp marxist geographer author theories spatial urban geography winner vautrin lud prize doreen massey nbsp scholar space places globalization pluralities winner vautrin lud prize edward soja nbsp worked regional development planning governance coined terms synekism postmetropolis winner


thrift born nbsp originator non representational theory paul vidal de la blache nbsp founder french school geopolitics wrote principles human geography ptolemy c c nbsp compiled greek roman knowledge book geographia radhanath sikdar nbsp calculated height mount everest sir halford mackinder nbsp co founder lse geographical association strabo bc nbsp c ad nbsp wrote geographica one first books outlining study geography walter christaller nbsp human geographer inventor central place theory william morris davis nbsp father american geography developer cycle


erosion yi fu tuan born nbsp chinese american scholar credited starting humanistic geography discipline institutions societies american association geographers aag american geographical society us anton melik geographical institute slovenia institute geographical information systems pakistan karachi geographical society pakistan national geographic society us royal canadian geographical society canada royal danish geographical society denmark royal geographical society uk russian geographical society russia publications ''african geographical review'' ''annals american association geographers'' ''antipode'' ''geographical review'' ''the geographical journal'' ''the professional geographer'' see also geographical space notes references


external links https wwwdictionarycom browse geography definition geography dictionarycom https wwwlexicocom en definition geography definition geography lexico https wwwetymonlinecom word geography origin meaning geography online etymology dictionary https wwwoxfordlearnersdictionariescom topic geography topic dictionaries oxford learner 's dictionaries earth sciences social sciences main topic articles


'''mathematical economics''' application mathematical methods represent theories analyze problems economics convention applied methods beyond simple geometry differential integral calculus difference differential equations matrix algebra mathematical programming computational methods ref name chiang http wwwmhprofessionalcom productphpisbn toc ref proponents approach claim allows formulation theoretical relationships rigor generality simplicity mathematics allows economists form meaningful testable propositions wide ranging complex subjects could less easily expressed informally language mathematics allows economists make specific

Social science
Economics
Mathematical economics


change one factors dynamic analysis tracing changes economic system time example economic growth ref name chiang ref name samuelson ref formal economic modeling began th century use differential calculus represent explain economic behavior utility maximization early economic application mathematical optimization economics became mathematical discipline throughout first half th century introduction new generalized techniques period around second world war game theory would greatly broaden use mathematical formulations economics ref


name debreuneumann debreu g rard mathematical economics ''the new palgrave dictionary economics'' nd edition http wwwdictionaryofeconomicscom articleid pde edition current q mathematical economics topicid result number abstract republished revisions theoretic models mathematical form economic content ''econometrica'' pp https wwwjstororg pss von neumann john oskar morgenstern ''theory games economic behavior'' princeton university press ref ref name samuelson rapid systematizing economics alarmed critics discipline well noted economists john maynard keynes robert heilbroner friedrich hayek others criticized broad use mathematical models human behavior arguing human choices irreducible mathematics history use


mathematics service social economic analysis dates back th century mainly german universities style instruction emerged dealt specifically detailed presentation data related public administration gottfried achenwall lectured fashion coining term statistics time small group professors england established method reasoning figures upon things relating government referred practice ''political arithmetick'' sir william petty wrote length issues would later concern economists


taxation velocity money national income analysis numerical rejected abstract mathematical methodology petty 's use detailed numerical data along john graunt would influence statisticians economists time even though petty 's works largely ignored english scholars mathematization economics began earnest th century economic analysis time would later called classical economics subjects discussed dispensed algebraic means calculus used importantly johann heinrich von th nen 's ''the isolated


state'' economists develop explicit abstract models behavior order apply tools mathematics th nen 's model farmland use represents first example marginal analysis th nen 's work largely theoretical also mined empirical data order attempt support generalizations comparison contemporaries th nen built economic models tools rather applying previous tools new problems meanwhile new cohort scholars trained mathematical methods physical sciences gravitated economics advocating applying methods


subject described today moving geometry mechanics included ws jevons presented paper general mathematical theory political economy providing outline use theory marginal utility political economy published ''the principles political economy'' declaring subject science must mathematical simply deals quantities jevons expected collection statistics price quantities would permit subject presented become exact science others preceded followed expanding mathematical representations economic


problems marginalists roots neoclassical economics equilibrium quantities solution two reaction functions cournot duopoly reaction function expressed linear equation dependent upon quantity demanded augustin cournot l walras built tools discipline axiomatically around utility arguing individuals sought maximize utility across choices way could described mathematically ref name dow ref time thought utility quantifiable units known utils cournot walras francis ysidro edgeworth considered precursors modern mathematical economics ref name cwe ref augustin


cournot cournot professor mathematics developed mathematical treatment duopoly market condition defined competition two sellers ref name cwe treatment competition first published ''researches mathematical principles wealth'' referred cournot duopoly assumed sellers equal access market could produce goods without cost assumed goods homogeneous seller would vary output based output market price would determined total quantity supplied


profit firm would determined multiplying output per unit market price differentiating profit function respect quantity supplied firm left system linear equations simultaneous solution gave equilibrium quantity price profits ref name stability ref cournot 's contributions mathematization economics would neglected decades eventually influenced many marginalists ref name stability cournot 's models duopoly oligopoly also represent one first formulations non cooperative games today solution given nash equilibrium cournot 's work


expressed system arbitrarily many equations walras 's attempts produced two famous results economics first walras' law second principle tonnement walras' method considered highly mathematical time edgeworth commented length fact review '' l ments d' conomie politique pure'' elements pure economics walras' law introduced theoretical answer problem determining solutions general equilibrium notation different modern notation constructed using modern summation notation walras assumed


equilibrium money would spent goods every good would sold market price good every buyer would expend last dollar basket goods starting assumption walras could show n markets n markets cleared reached equilibrium conditions nth market would clear well easiest visualize two markets considered texts market goods market money one two markets reached equilibrium state


additional goods conversely money enter exit second market must state equilibrium well walras used statement move toward proof existence solutions general equilibrium commonly used today illustrate market clearing money markets undergraduate level tonnement roughly french ''groping toward'' meant serve practical expression walrasian general equilibrium walras abstracted marketplace auction goods auctioneer would call prices market participants would wait could


satisfy personal reservation prices quantity desired remembering auction ''all'' goods everyone reservation price desired basket goods buyers satisfied given market price would transactions occur market would clear price surplus shortage would exist word ''t tonnement'' used describe directions market takes ''groping toward'' equilibrium settling high low prices different goods price agreed upon goods process appears dynamic walras


presented static model transactions would occur markets equilibrium practice markets operate manner francis ysidro edgeworth edgeworth introduced mathematical elements economics explicitly ''mathematical psychics essay application mathematics moral sciences'' published adopted jeremy bentham 's felicific calculus economic behavior allowing outcome decision converted change utility using assumption edgeworth built model exchange three assumptions individuals self interested individuals act maximize utility individuals


monopoly producing good jointness supply jointness demand first class economy airplane plane flies sets seats fly might actually lower price seen consumer one two commodities tax applied common sense traditional numerical analysis seemed indicate preposterous seligman insisted results edgeworth achieved quirk mathematical formulation suggested assumption continuous demand function infinitesimal change


first fundamental theorem welfare economics models lacked inequalities next generation mathematical economics landmark treatise ''foundations economic analysis'' paul samuelson identified common paradigm mathematical structure across multiple fields subject building previous work alfred marshall ''foundations'' took mathematical concepts physics applied economic problems broad view example comparing le chatelier 's principle tonnement drives fundamental premise mathematical economics systems economic actors may modeled behavior described much like system extension followed


model general equilibrium ''review economic studies'' pp ref unlike earlier versions models von neumann inequality constraints model expanding economy von neumann proved existence uniqueness equilibrium using generalization brouwer 's fixed point theorem von neumann 's model expanding economy considered matrix pencil nbsp '' '''a''' '''b''' '' nonnegative matrices nbsp '''a''' '''b''' von neumann sought probability vectors nbsp ''p'' nbsp ''q'' positive number nbsp '' '' would solve complementarity equation '' p sup sup '' nbsp '''''a''''' '' nbsp '''b''''' nbsp ''q'' along two inequality systems expressing


economic efficiency model transposed probability vector ''p'' represents prices goods probability vector q represents intensity production process would run unique solution '' '' represents rate growth economy equals interest rate proving existence positive growth rate proving growth rate equals interest rate remarkable achievements even von neumann von neumann 's results viewed special case linear programming von neumann 's model uses nonnegative matrices study von neumann 's


model expanding economy continues interest mathematical economists interests computational economics input output economics russian born economist wassily leontief built model input output analysis 'material balance' tables constructed soviet economists followed earlier work physiocrats model described system production demand processes leontief described changes demand one economic sector would influence production another practice leontief estimated coefficients simple models address economically interesting questions production economics leontief technologies produce outputs using


constant proportions inputs regardless price inputs reducing value leontief models understanding economies allowing parameters estimated relatively easily contrast von neumann model expanding economy allows choice techniques coefficients must estimated technology mathematical optimization maximum paraboloid function x inputs mathematics mathematical optimization optimization mathematical programming refers selection best element set available alternatives simplest case optimization problem involves maximizing minimizing real function


selecting input values function computing corresponding values function solution process includes satisfying general necessary sufficient conditions optimality optimization problems specialized notation may used function input generally optimization includes finding best available element function given defined domain may use variety different computational optimization techniques ref name schmedders schmedders karl numerical optimization methods economics ''the new palgrave dictionary economics'' nd edition v pp nbsp http wwwdictionaryofeconomicscom articleid pde n edition current q optimization topicid result number abstract ref economics closely enough linked optimization agents


economy influential definition relatedly describes economics ''qua'' science study human behavior relationship ends scarce means alternative uses optimization problems run modern economics many explicit economic technical constraints microeconomics utility maximization problem dual problem expenditure minimization problem given level utility economic optimization problems theory posits consumers maximize utility subject budget constraints firms maximize profits subject production functions input costs market demand ref name dixit dixit k


kantorovich koopmans acknowledged george b dantzig deserved share nobel prize linear programming economists conducted research nonlinear programming also nobel prize notably ragnar frisch addition kantorovich hurwicz koopmans arrow samuelson linear optimization linear programming developed aid allocation resources firms industries russia united states berlin airlift linear programming used plan shipment supplies prevent berlin starving soviet blockade nonlinear programming


extensions nonlinear optimization inequality constraints achieved albert w tucker harold kuhn considered nonlinear optimization problem minimize math f x math subject math g x leq math math h j x math math f cdot math function minimized math g cdot math functions math math ''inequality constraints'' math dots math math h j cdot math functions math l math equality constraints math j dots l math allowing inequality constraints kuhn tucker approach generalized classic method lagrange multipliers allowed equality constraints kuhn tucker approach


inspired research lagrangian duality including treatment inequality constraints ref name lemar chal ref duality theory nonlinear programming particularly satisfactory applied convex minimization problems enjoy convex analytic duality theory fenchel rockafellar convex duality particularly strong polyhedral convex functions arising linear programming lagrangian duality convex analysis used daily operations research scheduling power plants planning production schedules factories routing airlines routes flights planes crews ref name lemar chal variational calculus optimal control ''economic dynamics''


allows changes economic variables time including dynamic systems problem finding optimal functions changes studied variational calculus optimal control theory second world war frank ramsey harold hotelling used calculus variations end following richard bellman 's work dynamic programming english translation l pontryagin ''et al'' 's earlier work optimal control theory used extensively economics addressing dynamic problems especially economic growth equilibrium stability economic systems textbook example


optimal consumption saving crucial distinction deterministic stochastic control models applications optimal control theory include finance inventories production example functional analysis course proving existence optimal equilibrium model economic growth john von neumann introduced functional analytic methods include topology economic theory particular fixed point theory generalization brouwer 's fixed point theorem ref name debreuneumann ref name neumann following von neumann 's program kenneth arrow g rard debreu formulated abstract models economic equilibria using convex sets


fixed point theory introducing arrow debreu model proved existence uniqueness equilibrium also proved every walras equilibrium pareto efficient general equilibria need unique models primal vector space represented ''quantities'' dual vector space represented ''prices'' ref name lk kantorovich leonid victor polterovich functional analysis durlauf l blume ed ''the new palgrave dictionary economics'' nd edition http wwwdictionaryofeconomicscom articleid pde f abstract ed palgrave macmillan ref russia mathematician leonid kantorovich developed economic models partially ordered vector spaces


emphasized duality quantities prices kantorovich renamed ''prices'' objectively determined valuations abbreviated russian nbsp nbsp alluding difficulty discussing prices soviet union ref name lk even finite dimensions concepts functional analysis illuminated economic theory particularly clarifying role prices normal vectors hyperplane supporting convex set representing production consumption possibilities however problems describing optimization time uncertainty require use infinite dimensional function spaces agents choosing among functions stochastic processes ref name lk differential decline


rise john von neumann 's work functional analysis topology broke new ground mathematics economic theory ref name neumann ref name neumannmorgenstern neumann john von oskar morgenstern ''theory games economic behavior'' princeton ref also left advanced mathematical economics fewer applications differential calculus particular general equilibrium theorists used general topology convex geometry optimization theory differential calculus approach differential calculus failed establish existence equilibrium however decline differential calculus exaggerated differential calculus always used graduate training applications


moreover differential calculus returned highest levels mathematical economics general equilibrium theory get practiced get set humorous designation due jacques h dr ze however g rard debreu stephen smale led revival use differential calculus mathematical economics particular able prove existence general equilibrium earlier writers failed novel mathematics baire category general topology sard 's lemma differential topology economists associated use differential analysis include egbert dierker andreu mas colell


megiddo bezalel peleg influenced economic research politics economics example research fair prices cooperative games fair values voting games led changed rules voting legislatures accounting costs public works projects example cooperative game theory used designing water distribution system southern sweden setting rates dedicated telephone lines usa earlier neoclassical theory bounded ''range'' bargaining outcomes special cases example bilateral monopoly along contract curve edgeworth box


von neumann morgenstern 's results similarly weak following von neumann 's program however john nash used fixed point theory prove conditions bargaining problem noncooperative games generate unique equilibrium solution noncooperative game theory adopted fundamental aspect experimental economics behavioral economics information economics industrial organization political economy also given rise subject mechanism design sometimes called reverse game theory private public policy applications ways improving economic efficiency incentives information sharing ref name abstract ''the new palgrave dictionary economics''


nd edition br nbsp nbsp nbsp nbsp myerson roger b mechanism design http wwwdictionaryofeconomicscom articleid pde edition current q mechanism design topicid result number abstract br nbsp nbsp nbsp nbsp revelation principle http wwwdictionaryofeconomicscom articleid pde r edition current q moral topicid result number abstract br nbsp nbsp nbsp nbsp sandholm tuomas computing mechanism design http wwwdictionaryofeconomicscom articleid pde c edition field keyword q algorithmic mechanism design topicid result number abstract nisan noam amir ronen algorithmic mechanism design ''games economic behavior'' pp https wwwcscmuedu sandholm cs f algorithmic mechanism designpdf nisan noam ''et al'' ed ''algorithmic game theory'' cambridge university press http wwwcupcamacuk asia catalogue catalogueaspisbn description ref nash john harsanyi reinhard selten received nobel memorial prize economic sciences work non cooperative games harsanyi selten awarded work repeated games later work extended results computational methods


modeling ref name comp gt halpern joseph computer science game theory ''the new palgrave dictionary economics'' nd edition http wwwdictionaryofeconomicscom articleid pde c edition current q topicid result number abstract br nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp shoham yoav computer science game theory ''communications acm'' pp http wwwroboticsstanfordedu shoham www papers csgt cacm shohampdf br nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp rothalvin e economist engineer game theory experimentation computation tools design economics ''econometrica'' pp https webarchiveorg web http kuznetsfasharvardedu aroth papers engineerpdf ref agent based computational economics agent based computational economics ace named field relatively recent dating published work studies economic processes including whole economies dynamic systems interacting agents


time falls paradigm complex adaptive systems corresponding agent based models agents real people computational objects modeled interacting according rules whose micro level interactions create emergent patterns space time rules formulated predict behavior social interactions based incentives information theoretical assumption mathematical ''optimization'' agents markets replaced less restrictive postulate agents ''bounded'' rationality ''adapting'' market forces ace models apply numerical methods analysis computer based simulations complex dynamic problems


agent based method modeling social interactions ref name comp gt dimensions approach include standard economic subjects competition collaboration market structure industrial organization transaction costs welfare economics mechanism design ref name abstract information uncertainty macroeconomics method said benefit continuing improvements modeling techniques computer science increased computer capabilities issues include common experimental economics general comparison development common framework empirical validation resolving open questions agent based modeling ultimate scientific objective method described


test ing theoretical findings real world data ways permit empirically supported theories cumulate time researcher 's work building appropriately work gone mathematicization economics surface volatility smile surface whereby current market implied volatility z axis options underlier plotted strike price time maturity x axes ref name black scholes ref course th century articles core journals economics almost exclusively written economists academia result much material


transmitted journals relates economic theory economic theory continuously abstract mathematical subjective assessment mathematical techniques employed core journals showed decrease articles use neither geometric representations mathematical notation survey ten top economic journals finds nbsp articles published lacked statistical analysis data lacked displayed mathematical expressions indexed numbers margin page econometrics world


moore made several errors work choice models limitations use mathematics accuracy moore 's models also limited poor data national accounts united states time first models production static published dynamic moving equilibrium model designed explain business cycles periodic variation correction supply demand curves known cobweb model formal derivation model made later nicholas kaldor


largely credited exposition application lm model keynesian macroeconomic model designed make predictions intersection real economic activity eg spending income savings rates decisions made financial markets money supply liquidity preference model longer widely taught graduate level common undergraduate macroeconomics courses much classical economics presented simple geometric terms elementary mathematical notation mathematical economics however conventionally makes use calculus matrix algebra economic analysis order make powerful claims would


difficult without mathematical tools tools prerequisites formal study mathematical economics contemporary economic theory general economic problems often involve many variables mathematics practical way attacking solving alfred marshall argued every economic problem quantified analytically expressed solved treated means mathematical work economics become increasingly dependent upon mathematical methods mathematical tools employs become sophisticated result mathematics become considerably important professionals economics


rigorous mathematical broadly speaking formal economic models may classified stochastic deterministic discrete continuous practical level quantitative modeling applied many areas economics several methodologies evolved less independently stochastic models formulated using stochastic processes model economically observable values time econometrics based statistics formulate test hypotheses processes estimate parameters world wars herman wold developed representation stationary stochastic processes terms autoregressive models


determinist trend wold jan tinbergen applied time series analysis economic data contemporary research time series statistics consider additional formulations stationary processes autoregressive moving average models general models include autoregressive conditional heteroskedasticity arch models generalized arch garch models non stochastic mathematical models may purely qualitative example models involved aspect social choice theory quantitative involving rationalization financial variables example hyperbolic coordinates specific forms functional relationships variables cases economic predictions model merely assert direction movement


rate math display inline r math much tax cut increase wages''''' blockquote answer question follow john h cochrane hoover institution suppose open economy production function math display block f kl f k l quad k k l math variables equation math display inline math total output math display inline f kl math production function math display inline k math total capital stock math display inline l math total labor stock standard choice production function cobb douglas production function math display block ak alpha l alpha k alpha l quad alpha math math display inline math factor productivity


moment let 's focus '' 'static''' effect capital tax cut math display inline dx tau f' k k math substitute equation equation wage changes respect tax rate find math display block dw tau frac f' k k tau tau frac dx tau math therefore '' 'static''' effect capital tax cut wages math display block dw dx tau math based model seems possible may achieve rise wage worker greater amount tax cut considers static effect know dynamic effect must


accounted dynamic model may rewrite equation changes taxes per worker respect tax rate math display block begin aligned dx tau f' k k tau left f' k f'' k k right dk tau f' k k tau tau f' k f' k f'' k k f'' k tau tau f' k f'' k tau f' k k f' k tau left tau f' k f'' k k right end aligned math recalling math display inline dw tau f' k k tau math math display block frac dw dx frac f' k k tau frac f' k tau left tau frac f' k f'' k k right frac tau frac f' k kf'' k math using cobb douglas production function math display block f' k kf'' k alpha math therefore '' 'dynamic''' effect capital


tax cut wages math display block dw dx alpha tau alpha math take math display inline alpha tau math dynamic effect lowering capital taxes wages even larger static effect moreover positive externalities capital accumulation effect tax cut wages would larger model derived important note result combination standard result small open economy labor bears small capital income tax fact starting positive


tax rate burden tax increase exceeds revenue collection due first order deadweight loss result showing certain assumptions corporate tax cut boost wages workers lost revenue imply magnitude correct rather suggests basis policy analysis grounded handwaving assumptions reasonable model acceptable approximation reality better models developed ces production function let 's assume instead


cobb douglas production function general constant elasticity substitution ces production function math display block f k left alpha k rho alpha right rho math math display inline rho sigma math math display inline sigma math elasticity substitution capital labor relevant quantity want calculate math display inline f' kf'' math '''' may derived math display block f' kf'' rho alpha rho alpha alpha k rho math therefore may use find math display block begin aligned tau f' kf'' tau alpha alpha k rho rho alpha alpha k rho alpha rho pt rho tau alpha alpha k rho alpha rho rho alpha alpha k rho alpha rho end aligned math therefore general ces model dynamic effect capital tax cut wages math display block dw dx rho alpha alpha k rho alpha rho rho tau alpha alpha k rho alpha rho math


recover cobb douglas solution math display inline rho math math display inline rho math case perfect substitutes exist find math display inline dw dx math effect changes capital taxes wages math display inline rho infty math case perfect complements exist find math display inline dw dx math cut capital taxes increases wages exactly one dollar criticisms defences adequacy mathematics qualitative complicated economics friedrich hayek contended use formal techniques projects scientific exactness


appropriately account informational limitations faced real economic agents interview economic historian robert heilbroner stated heilbroner stated much economics naturally quantitative therefore lend mathematical exposition testing predictions mathematical economics philosopher karl popper discussed scientific standing economics argued mathematical economics suffered tautological words insofar economics became mathematical theory mathematical economics ceased rely empirical refutation rather relied mathematical proofs disproof ref name boland ref


according popper falsifiable assumptions tested experiment observation unfalsifiable assumptions explored mathematically consequences consistency assumptions sharing popper 's concerns assumptions economics generally mathematical economics milton friedman declared assumptions unrealistic friedman proposed judging economic models predictive performance rather match assumptions reality mathematical economics form pure mathematics considering mathematical economics jm keynes wrote ''the general theory'' defense mathematical economics response criticisms paul samuelson


argued mathematics language repeating thesis josiah willard gibbs economics language mathematics sometimes necessary representing substantive problems moreover mathematical economics led conceptual advances economics particular samuelson gave example microeconomics writing people ingenious enough grasp complex parts ''without'' resorting language mathematics ordinary individuals fairly easily ''with'' aid mathematics economists state mathematical economics deserves support like forms mathematics particularly neighbors mathematical optimization


mathematical statistics increasingly theoretical computer science mathematical economics mathematical sciences history theoretical advances regularly contributed reform applied branches economics particular following program john von neumann game theory provides foundations describing much applied economics statistical decision theory games nature econometrics general equilibrium theory industrial organization last decade rise internet mathematical economists optimization experts computer scientists worked problems pricing line services


contributions using mathematics cooperative game theory nondifferentiable optimization combinatorial games robert solow concluded mathematical economics core infrastructure contemporary economics blockquote economics longer fit conversation piece ladies gentlemen become technical subject like technical subject attracts people interested technique subject bad may inevitable case kid technical core economics indispensable infrastructure political economy consult


reference contemporary economics looking enlightenment world today led technical economics history nothing blockquote mathematical economists prominent mathematical economists include following th century enrico barone antoine augustin cournot francis ysidro edgeworth irving fisher william stanley jevons vilfredo pareto l walras th century charalambos aliprantis r g allen maurice allais kenneth j arrow robert j aumann yves balasko david blackwell lawrence e blume graciela chichilnisky george b dantzig g rard debreu mario draghi jacques h dr ze david gale nicholas georgescu roegen roger guesnerie frank hahn john c harsanyi


reading alpha c chiang kevin wainwright ''fundamental methods mathematical economics'' mcgraw hill irwin http wwwmhprofessionalcom productphpisbn contents e roy weintraub ''mathematics economists'' cambridge https archiveorg details mathematicsforec wein contents stephen glaister ''mathematical methods economists'' rd ed blackwell https booksgooglecom booksid ct nrjshxsqc printsec find pg pr onepage q f false v onepage q f false contents akira takayama ''mathematical economics'' nd ed cambridge https booksgooglecom booksid ipealaecc printsec find pg pr onepage q f false v onepage q f false contents nancy l stokey robert e lucas edward prescott ''recursive methods economic dynamics'' harvard university press http wwwhupharvardedu catalogphpisbn desecription chapter preview https booksgooglecom bookshl en lr id twyo qolylac oi fnd pg pr dq v onepage q f dfalse f false links k dixit ''optimization economic theory'' nd ed oxford https booksgooglecom booksid dhrshz vocuc pg find pg pa false v onepage q f false description contents https booksgooglecom booksid dhrshz vocuc pg pr lpg pr dq false lr v onepage q false f false preview kenneth l judd


''numerical methods economics'' mit press https webarchiveorg web http mitpressmitedu catalog item defaultaspttype tid description chapter preview https booksgooglecom booksid wxk z hskac pg pr source gbs toc r cad v onepage q f false links michael carter ''foundations mathematical economics'' mit press https booksgooglecom booksid kysvrggfzq c printsec find pg pr onepage q f false contents ferenc szidarovszky ndor moln r ''introduction matrix theory applications business economics'' world scientific publishing http wwwworldscientificcom worldscibooks description http wwwworldscientificcom doi suppl suppl file chap pdf preview wade hands ''introductory mathematical economics'' nd ed oxford http wwwoupcom us catalog subject economics othercourses mathematicaleconomics view usa sf toc ci contents giancarlo gandolfo ''economic dynamics'' th ed springer https wwwspringercom economics economic theory book description https booksgooglecom booksid zmwxi nhhqc printsec find pg pr v onepage q f false preview john stachurski ''economic dynamics theory computation'' mit press https webarchiveorg web http johnstachurskinet book bookhtml description https booksgooglecom booksid izw rszlluic printsec find pg pr v onepage q f false preview external links ''journal mathematical economics'' http wwwelseviercom wps find journaldescriptioncws home description description aims


scope http erasmusmundus qemuniv paris fr erasmus mundus master qem models methods quantitative economics models methods quantitative economics qem mathematical quantitative methods economics


illustration desargues' theorem result euclidean projective geometry '''geometry''' ''geo '' earth '' metron'' measurement arithmetic one oldest branches mathematics concerned properties space related distance shape size relative position figures ref name risi ref mathematician works field geometry called geometer th century geometry almost exclusively devoted euclidean geometry includes notions point line plane distance angle surface curve fundamental concepts ref name tabak xiv ref th century several

Formal science
Mathematics
Pure mathematics
Geometry


need surveying construction astronomy various crafts earliest known texts geometry egyptian ''rhind papyrus'' bc ''moscow papyrus'' c bc babylonian clay tablets plimpton bc example moscow papyrus gives formula calculating volume truncated pyramid frustum ref name boyer loc egypt p ref later clay tablets bc demonstrate babylonian astronomers implemented trapezoid procedures computing jupiter 's position motion within time velocity space geometric procedures anticipated oxford calculators including mean speed theorem centuries south egypt


ancient nubians established system geometry including early versions sun clocks th century bc greek mathematician thales miletus used geometry solve problems calculating height pyramids distance ships shore credited first use deductive reasoning applied geometry deriving four corollaries thales' theorem ref name boyer loc ionia pythagoreans p ref pythagoras established pythagorean school credited first proof pythagorean theorem though statement theorem long


known euclid arranged single coherent logical framework ref name boyer loc euclid alexandria p ref ''elements'' known educated people west middle th century contents still taught geometry classes today archimedes c nbsp bc syracuse used method exhaustion calculate area arc parabola summation infinite series gave remarkably accurate approximations pi also studied spiral bearing name obtained formulas volumes surfaces revolution ''woman teaching geometry''


illustration beginning medieval translation euclid 's elements c nbsp indian mathematicians also made many important contributions geometry ''satapatha brahmana'' rd century bc contains rules ritual geometric constructions similar ''sulba sutras'' ref name staal ref according '' ulba tras'' contain earliest extant verbal expression pythagorean theorem world although already known old babylonians contain lists pythagorean triples particular cases diophantine equations ref name cooke arithmetic content '' ulva tras'' consists rules finding pythagorean triples


certain practical use arithmetic rules best conjecture part religious ritual hindu home required three fires burning three different altars three altars different shapes three area conditions led certain diophantine problems particular case generation pythagorean triples make one square integer equal sum two


others ref bakhshali manuscript handful geometric problems including problems volumes irregular solids bakhshali manuscript also employs decimal place value system dot zero ref name hayashi ref aryabhata 's ''aryabhatiya'' includes computation areas volumes brahmagupta wrote astronomical work ''br hma sphu siddh nta '' chapter containing sanskrit verses divided two sections basic operations including cube roots fractions ratio proportion barter practical mathematics including mixture mathematical series plane figures stacking bricks sawing timber piling grain ref name hayashi p ref latter section


stated famous theorem diagonals cyclic quadrilateral chapter also included formula area cyclic quadrilateral generalization heron 's formula well complete description rational triangles ''ie'' triangles rational sides rational areas ref name hayashi p middle ages mathematics medieval islam contributed development geometry especially algebraic geometry al mahani b conceived idea reducing geometrical problems duplicating cube problems algebra th bit ibn qurra known thebit latin dealt arithmetic operations applied ratios


geometrical quantities contributed development analytic geometry ref name referencea ref omar khayy found geometric solutions cubic equations theorems ibn al haytham alhazen omar khayyam nasir al din al tusi quadrilaterals including lambert quadrilateral saccheri quadrilateral early results hyperbolic geometry along alternative postulates playfair 's axiom works considerable influence development non euclidean geometry among later european geometers including witelo c nbsp c nbsp gersonides alfonso john wallis giovanni girolamo saccheri early th century two important developments geometry


first creation analytic geometry geometry coordinates equations ren descartes pierre de fermat ref name boyer ref necessary precursor development calculus precise quantitative science physics ref name edwards ref second geometric development period systematic study projective geometry girard desargues ref name fieldgray ref projective geometry studies properties shapes unchanged projections sections especially relate artistic perspective ref name wylie ref two developments geometry th century changed way studied previously ref name gray ref


discovery non euclidean geometries nikolai ivanovich lobachevsky j nos bolyai carl friedrich gauss formulation symmetry central consideration erlangen programme felix klein generalized euclidean non euclidean geometries two master geometers time bernhard riemann working primarily tools mathematical analysis introducing riemann surface henri poincar founder algebraic topology geometric theory dynamical systems consequence major changes conception geometry concept space became something rich varied


natural background theories different complex analysis classical mechanics ref name bayro corrochano ref important concepts geometry following important concepts geometry ref name tabak xiv ref name schmidt w ref name kline ref axioms illustration euclid 's parallel postulate euclid took abstract approach geometry elements ref name katz ref one influential books ever written ref name berlinski ref euclid introduced certain axioms postulates expressing primary self evident properties points lines planes ref name hartshorne ref proceeded rigorously deduce properties mathematical reasoning characteristic feature euclid 's approach geometry


rigor come known ''axiomatic'' ' 'synthetic'' geometry ref name herbstfujita ref start th century discovery non euclidean geometries nikolai ivanovich lobachevsky j nos bolyai carl friedrich gauss others ref name yaglom ref led revival interest discipline th century david hilbert employed axiomatic reasoning attempt provide modern foundation geometry ref name holme ref points points generally considered fundamental objects building geometry may defined properties thay must euclid 's definition


part ref name euclidall ''euclid 's elements thirteen books one volume'' based heath 's translation green lion press ref synthetic geometry modern mathematics generally defined elements set called space axiomatically defined modern definitions every geometric shape defined set points case synthetic geometry lines another fundamental object viewed set points passes however modern geometries points primitive objects even


without points one oldest geometries whitehead 's point free geometry formulated alfred north whitehead lines euclid described line breadthless length lies equally respect points ref name euclidall modern mathematics given multitude geometries concept line closely tied way geometry described instance analytic geometry line plane often defined set points whose coordinates satisfy given linear equation abstract setting incidence geometry line may


independent object distinct set points lie differential geometry geodesic generalization notion line curved spaces planes plane flat two dimensional surface extends infinitely far ref name euclidall planes used many areas geometry instance planes studied topological surface without reference distances angles ref name munkres munkres james r topology vol upper saddle river prentice hall ref studied affine space collinearity ratios studied distances


studied complex plane using techniques complex analysis angles euclid defines plane angle inclination plane two lines meet lie straight respect ref name euclidall modern terms angle figure formed two rays called ' 'sides'' angle sharing common endpoint called ' 'vertex'' angle acute obtuse b straight c angles acute obtuse angles also known oblique angles euclidean


geometry angles used study polygons triangles well forming object study right ref name euclidall study angles triangle angles unit circle forms basis trigonometry differential geometry calculus angles plane curves space curves surfaces calculated using derivative ref name stewart stewart james ''calculus early transcendentals'' th ed brooks cole cengage learning ref curves curve dimensional object may straight like line curves dimensional space called


plane curves dimensional space called space curves topology curve defined function interval real numbers another space ref name munkres differential geometry definition used defining function required differentiable ref name carmo algebraic geometry studies algebraic curves defined algebraic varieties dimension one ref name mumford surfaces ''x'' sup sup ''y'' sup sup ''z'' sup sup ''r'' sup sup surface two dimensional object sphere paraboloid differential geometry ref name carmo


carmo manfredo perdigao manfredo perdigao carmo differential geometry curves surfaces vol englewood cliffs prentice hall ref topology ref name munkres surfaces described two dimensional 'patches' neighborhoods assembled diffeomorphisms homeomorphisms respectively algebraic geometry surfaces described polynomial equations ref name mumford ref manifolds manifold generalization concepts curve surface topology manifold topological space every point neighborhood homeomorphic euclidean space ref name munkres differential geometry differentiable manifold space neighborhood


diffeomorphic euclidean space ref name carmo manifolds used extensively physics including general relativity string theory length area volume length area volume describe size extent object one dimension two dimension three dimensions respectively ref name treese ref euclidean geometry analytic geometry length line segment often calculated pythagorean theorem ref name cannon ref area volume defined fundamental quantities separate length described calculated terms lengths plane dimensional space ref name treese mathematicians found many explicit


formulas area formulas volume various geometric objects calculus area volume defined terms integrals riemann integral ref name strang ref lebesgue integral ref name bear ref metrics measures visual checking pythagorean theorem triangle zhoubi suanjing nbsp bc pythagorean theorem consequence euclidean metric concept length distance generalized leading idea metrics instance euclidean metric measures distance points euclidean plane hyperbolic metric measures


distance hyperbolic plane important examples metrics include lorentz metric special relativity semi riemannian metrics general relativity different direction concepts length area volume extended measure theory studies methods assigning size ''measure'' sets measures follow rules similar classical area volume ref name tao ref congruence similarity congruence similarity concepts describe two shapes similar characteristics ref name libeskind ref euclidean geometry similarity used describe objects shape congruence used


describe objects size shape ref name freitag ref hilbert work creating rigorous foundation geometry treated congruence undefined term whose properties defined axioms congruence similarity generalized transformation geometry studies properties geometric objects preserved different kinds transformations ref name martin ref compass straightedge constructions classical geometers paid special attention constructing geometric objects described way classically instruments allowed geometric constructions compass straightedge also every construction


complete finite number steps however problems turned difficult impossible solve means alone ingenious constructions using parabolas curves well mechanical devices found dimension koch snowflake fractal dimension log log topological dimension traditional geometry allowed dimensions line plane ambient world conceived three dimensional space mathematicians physicists used higher dimensions nearly two centuries ref name blacklock ref one example mathematical use higher dimensions configuration space physical system