color delivered onto drawing surface drawing media either dry eg graphite charcoal pastels cont silverpoint use fluid solvent carrier marker pen ink watercolor pencils used dry like ordinary pencils moistened wet brush get various painterly effects rarely artists drawn usually decoded invisible ink metalpoint drawing usually employs either two metals silver lead rarely used gold platinum copper brass bronze tinpoint paper comes variety different sizes qualities ranging newspaper grade high quality


relatively expensive paper sold individual sheets papers vary texture hue acidity strength wet smooth paper good rendering fine detail toothy paper holds drawing material better thus coarser material useful producing deeper contrast newsprint typing paper may useful practice rough sketches tracing paper used experiment half finished drawing transfer design one sheet another cartridge paper basic type drawing paper sold pads bristol board even heavier acid free boards frequently smooth

Humanities
Visual arts
Fine arts
Drawing


finishes used drawing fine detail distort wet media ink washes applied vellum extremely smooth suitable fine detail coldpressed watercolor paper may favored ink drawing due texture acid free archival quality paper keeps color texture far longer wood pulp based paper newsprint turns yellow becomes brittle much sooner basic tools drawing board table pencil sharpener eraser ink drawing blotting paper tools used circle compass ruler set square fixative used


prevent pencil crayon marks smudging drafting tape used secure paper drawing surface also mask area keep free accidental marks sprayed spattered materials washes easel slanted table used keep drawing surface suitable position generally horizontal position used painting technique raphael study became ''alba madonna'' sketches antoine watteau ''trois crayons'' technique almost draftsmen use hands fingers apply media exception


handicapped individuals draw mouth feet prior working image artist typically explores various media work may try different drawing implements practice sheets determine value texture apply implement produce various effects artist 's choice drawing strokes affects appearance image pen ink drawings often use hatching groups parallel lines cross hatching uses hatching two different directions create darker tone broken hatching lines intermittent breaks form lighter tones controlling


subject creating depth looking like shadows cast light artist 's position sometimes artist leaves section image untouched filling remainder shape area preserve painted masking fluid cut frisket applied drawing surface protecting surface stray marks mask removed another method preserve section image apply spray ''fixative'' surface holds loose material firmly sheet prevents smearing


however fixative spray typically uses chemicals harm respiratory system employed well ventilated area outdoors another technique subtractive drawing drawing surface covered graphite charcoal erased make image tone pencil portrait henry macbeth raeburn hatching shading shading technique varying tonal values paper represent shade material well placement shadows careful attention reflected light shadows highlights result


realistic rendition image blending uses implement soften spread original drawing strokes blending easily done medium immediately fix graphite chalk charcoal although freshly applied ink smudged wet dry effects shading blending artist use blending stump tissue kneaded eraser fingertip combination piece chamois useful creating smooth textures removing material lighten tone continuous tone achieved graphite smooth


surface without blending technique laborious involving small circular oval strokes somewhat blunt point shading techniques also introduce texture drawing include hatching stippling number methods produce texture addition choice paper drawing material technique affect texture texture made appear realistic drawn next contrasting texture coarse texture obvious placed next smoothly blended area similar effect achieved drawing different tones close together light edge next


dark background stands eye almost appears float surface form proportion proportions human body measuring dimensions subject blocking drawing important step producing realistic rendition subject tools compass used measure angles different sides angles reproduced drawing surface rechecked make sure accurate another form measurement compare relative sizes different parts subject


refined accurate polished form lines primitive volumes removed replaced final likeness drawing underlying construction fundamental skill representational art taught many books schools correct application resolves uncertainties smaller details makes final image look consistent ref name drawinghale ref refined art figure drawing relies upon artist possessing deep understanding anatomy human proportions trained artist familiar skeleton structure joint location muscle placement tendon movement different parts work


together movement allows artist render natural poses appear artificially stiff artist also familiar proportions vary depending age subject particularly drawing portrait two point perspective drawing perspective drawing figure worm 's eye perspective linear perspective method portraying objects flat surface dimensions shrink distance set parallel straight edges object whether building table follows lines eventually converge vanishing point typically convergence point somewhere along


horizon buildings built level flat surface multiple structures aligned buildings along street horizontal tops bottoms structures typically converge vanishing point fronts sides building drawn parallel lines forming side converge second point along horizon may drawing paper two point perspective converging vertical lines third point horizon produces three point perspective depth also portrayed


several techniques addition perspective approach objects similar '' 'size''' appear ever smaller viewer thus back wheel cart appears slightly smaller front wheel depth portrayed use '''texture''' texture object gets away becomes compressed busy taking entirely different character close depth also portrayed reducing contrast distant objects making colors less saturated reproduces effect '''atmospheric'''


haze cause eye focus primarily objects drawn foreground chiaroscuro study drawing william adolphe bouguereau artistry composition image important element producing interesting work artistic merit artist plans element placement art communicate ideas feelings viewer composition determine focus art result harmonious whole aesthetically appealing stimulating illumination subject also key element creating artistic piece interplay light shadow valuable


method artist 's toolbox placement light sources make considerable difference type message presented multiple light sources wash wrinkles person 's face instance give youthful appearance contrast single light source harsh daylight serve highlight texture interesting features drawing object figure skilled artist pays attention area within silhouette lies outside exterior termed negative space important


representation figure objects placed background figure appear properly placed wherever viewed study draft drawing made preparation planned final image studies used determine appearances specific parts completed image experimenting best approach accomplishing end goal however well crafted study piece art right many hours careful work go completing study process person drawing barberini faun munichindividuals display


differences ability produce visually accurate drawings visually accurate drawing described recognized particular object particular time particular space rendered little addition visual detail seen object represented little deletion visual detail ref name cohen ref investigative studies aimed explain reasons individuals draw better others one study posited four key abilities drawing process motor skills required mark making drawer 's perception drawing perception objects drawn


ability make good representational decisions ref name cohen following hypothesis several studies sought conclude processes significant affecting accuracy drawings drawing process ''academic study male torso'' jean auguste dominique ingres national museum warsaw motor control motor control important physical component 'production phase' drawing process suggested motor control plays role drawing ability though effects significant ref name cohen perception suggested individual 's ability perceive


object drawing important stage drawing process ref name cohen suggestion supported discovery robust relationship perception drawing ability evidence acted basis betty edwards' draw book ''drawing right side brain'' edwards aimed teach readers draw based development reader 's perceptual abilities furthermore influential artist art critic john ruskin emphasised importance perception drawing process book ''the elements drawing'' stated


nearly convinced see keenly enough little difficult drawing see visual memory also shown influence one 's ability create visually accurate drawings short term memory plays important part drawing one 's gaze shifts object drawing drawing decision making studies comparing artists non artists found artists spend time thinking strategically drawing particular artists spend time 'metacognitive' activities considering different hypothetical plans might progress drawing


see also academy figure architectural drawing composition contour drawing diagram digital illustration engineering drawing figure drawing graphic design illustration landscape painting painting plumbago drawing sketch drawing subtractive drawing technical drawing visual arts image references '''notes''' '''further reading''' edwards betty ''the new drawing right side brain'' harpercollins publishers ltd rev ed edition brommer gerald f ''exploring drawing'' worcester massachusetts davis publications bodley gallery new york ''modern master drawings'' hillberry jd ''drawing realistic textures pencil'' north light books landa robin take line walk creativity journal


boston wadsworth lohan frank ''pen ink techniques'' contemporary books ruskin j elements drawing mineola ny dover publications inc spears heather ''the creative eye'' london arcturus world book inc ''the world book encyclopedia volume '' ''drawing thinking confronting electronic age'' edited marc treib external links https webarchiveorg web http wwwlearningdesigncom portfolio drawdev kiddrawinghtml timeline drawing development children https webarchiveorg web http nasonartcom writing ondrawing html drawing essay craft drawing artist norman nason archived http nasonartcom writing ondrawing html original april http libmmacontentdmoclcorg cdm compoundobject collection p coll id rec ''leonardo da vinci anatomical drawings royal library windsor castle'' exhibition


catalog fully online pdf metropolitan museum art great drawing resource http libmmacontentdmoclcorg cdm compoundobject collection p coll id rec ''leonardo da vinci master draftsman'' exhibition catalog fully online pdf metropolitan museum art great drawing resource http wwwmetmuseumorg toah hd draw hd drawhtm '' drawing middle ages'' summary drawing used part artistic process middle ages


mathematics '' 'differential topology''' field dealing topological properties smooth properties smooth manifolds sense differential topology distinct closely related field differential geometry concerns ''geometric'' properties smooth manifolds including notions size distance rigid shape comparison differential topology concerned coarser properties number holes manifold homotopy type topology diffeomorphism group many coarser properties may captured algebraically differential topology strong links algebraic topology morse theory

Formal science
Mathematics
Pure mathematics
Geometry
Differential topology


height function torus describe homotopy type central goal field differential topology classification smooth manifolds diffeomorphism since dimension invariant smooth manifolds diffeomorphism type classification often studied classifying connected manifolds dimension separately dimension smooth manifolds diffeomorphism circle real number line allowing boundary half closed interval math math fully closed interval math math ref name milnor milnor j weaver dw topology differentiable viewpoint princeton university press ref


dimension every closed surface classified diffeomorphism genus number holes equivalently euler characteristic whether orientable famous classification closed surfaces ref name leetopological lee j introduction topological manifolds vol springer science business media ref ref name hirsch ref already dimension two classification non compact surfaces becomes difficult due existence exotic spaces jacob 's ladder dimension william thurston 's geometrization conjecture proven grigori perelman gives partial classification compact three manifolds included theorem


poincar conjecture states closed simply connected three manifold homeomorphic fact diffeomorphic sphere cobordism ''w'' ''m'' ''n'' generalises notion diffeomorphism beginning dimension classification becomes much difficult two reasons firstly every finitely presented group appears fundamental group manifold since fundamental group diffeomorphism invariant makes classification manifolds least difficult classification finitely presented groups word problem groups equivalent halting problem impossible


classify groups full topological classification impossible secondly beginning dimension four possible smooth manifolds homeomorphic distinct non diffeomorphic smooth structures true even euclidean space math mathbb r math admits many exotic math mathbb r math structures means study differential topology dimensions higher must use tools genuinely outside realm regular continuous topology topological manifolds one central open problems differential topology four dimensional smooth poincar conjecture asks every smooth manifold homeomorphic


manifolds considering critical points differentiable functions manifold demonstrating smooth structure manifold enters set tools available often times geometric analytical techniques may used equipping smooth manifold riemannian metric studying differential equation care must taken ensure resulting information insensitive choice extra structure genuinely reflects topological properties underlying smooth manifold example hodge theorem provides geometric analytical interpretation de rham


cohomology gauge theory used simon donaldson prove facts intersection form simply connected manifolds cases techniques contemporary physics may appear topological quantum field theory used compute topological invariants smooth spaces famous theorems differential topology include whitney embedding theorem hairy ball theorem hopf theorem poincar hopf theorem donaldson 's theorem poincar conjecture description differential topology considers properties structures require smooth structure manifold defined smooth manifolds 'softer'


manifolds extra geometric structures act obstructions certain types equivalences deformations exist differential topology instance volume riemannian curvature invariants distinguish different geometric structures smooth manifold mdash one smoothly flatten certain manifolds might require distorting space affecting curvature volume hand smooth manifolds rigid topological manifolds john milnor discovered spheres one smooth structure see exotic sphere donaldson 's theorem michel kervaire exhibited topological manifolds


differential topology distinguishes differential geometry studying primarily problems ''inherently global'' consider example coffee cup donut point view differential topology donut coffee cup ''the same'' sense inherently global view though way differential topologist tell whether two objects sense looking tiny ''local'' piece either must access entire ''global'' object point


view differential geometry coffee cup donut ' 'different'' impossible rotate coffee cup way configuration matches donut also global way thinking problem important distinction geometer need entire object decide looking instance tiny piece handle decide coffee cup different donut handle thinner curved piece


donut put succinctly differential topology studies structures manifolds sense interesting local structure differential geometry studies structures manifolds interesting local sometimes even infinitesimal structure mathematically example problem constructing diffeomorphism two manifolds dimension inherently global since ''locally'' two manifolds always diffeomorphic likewise problem computing quantity manifold invariant differentiable mappings inherently global since local invariant ''trivial'' sense


questions specifically pertaining local diffeomorphism invariants tangent space point differential topology also deals questions like specifically pertain properties differentiable mappings math r n math example tangent bundle jet bundles whitney extension theorem forth distinction concise abstract terms differential topology study infinitesimal local global properties structures manifolds ''only trivial'' local moduli differential geometry study structures manifolds one ''non trivial'' local moduli see also


list differential geometry topics glossary differential geometry topology important publications differential geometry important publications differential topology basic introduction mathematics curved spacetime notes references external links


curves surfaces three dimensional euclidean space study shapes formed basis development modern differential geometry th century th century since late th century differential geometry grown field concerned generally geometric structures differentiable manifolds geometric structure one defines notion size distance shape volume rigidifying structure example riemannian geometry distances angles specified symplectic geometry volumes may computed conformal geometry angles specified gauge theory certain fields

Formal science
Mathematics
Differential Geometry


physicists development quantum field theory standard model particle physics outside physics differential geometry finds applications chemistry economics engineering control theory computer graphics computer vision recently machine learning history development history development differential geometry subject begins least far back classical antiquity intimately linked development geometry generally notion space shape topology details history concept manifold see article


history manifolds varieties section focus primarily history application infinitesimal methods geometry later ideas tangent spaces eventually development modern formalism subject terms tensors tensor fields classical antiquity renaissance bc ad study differential geometry least study geometry smooth shapes traced back least classical antiquity particular much known geometry earth spherical geometry


time ancient greek mathematicians famously eratosthenes calculated circumference earth around bc around ad ptolemy ''geography'' introduced stereographic projection purposes mapping shape earth ref name struik struik j outline history differential geometry isis vol pp jstor wwwjstororg stable ref implicitly throughout time principles form foundation differential geometry calculus used geodesy although much simplified form namely far back euclid 's ''elements'' understood straight line could


defined property providing shortest distance two points applying principle surface earth leads conclusion great circles locally similar straight lines flat plane provide shortest path two points earth 's surface indeed measurements distance along geodesic paths eratosthenes others considered rudimentary measure arclength curves concept see rigorous definition terms calculus around time minimal


significant development understanding differential geometry came gerardus mercator 's development mercator projection way mapping earth mercator understanding advantages pitfalls map design particular aware conformal nature projection well difference ''praga'' lines shortest distance earth ' 'directio'' straight line paths map mercator noted praga ''oblique curvatur'' projection ref name struik fact reflects lack metric preserving map earth 's surface


concepts points inflection circles osculation aid measurement curvature indeed already first paper foundations calculus leibniz notes infinitesimal condition math math indicates existence inflection point shortly time bernoulli brothers jacob johann made important early contributions use infinitesimals study geometry lectures johann bernoulli time later collated l'hopital first textbook differential calculus tangents plane curves various types computed using condition math dy math


similarly points inflection calculated ref name struik time orthogonality osculating circles plane curve tangent directions realised first analytical formula radius osculating circle essentially first analytical formula notion curvature written wake development analytic geometry plane curves alexis clairaut began study space curves age ref name struik book clairaut introduced notion tangent subtangent directions space curves relation


directions lie along surface space curve lies thus clairaut demonstrated implicit understanding tangent space surface studied idea using calculus first time importantly clairaut introduced terminology ''curvature'' ' 'double curvature'' essentially notion principal curvatures later studied gauss others around time leonhard euler originally student johann bernoulli provided many significant contributions development geometry mathematics broadly regards differential geometry euler studied notion geodesic


surface deriving first analytical geodesic equation later introduced first set intrinsic coordinate systems surface beginning theory ''intrinsic geometry'' upon modern geometric ideas based ref name struik around time euler 's study mechanics mechanica lead realization mass traveling along surface effect force would traverse geodesic path early precursor important foundational ideas einstein 's general relativity also euler lagrange equations first theory calculus variations underpins modern differential


geometry many techniques symplectic geometry geometric analysis theory used lagrange co developer calculus variations derive first differential equation describing minimal surface terms euler lagrange equation euler proved theorem expressing curvature space curve surface terms principal curvatures known euler 's theorem later new french school lead gaspard monge began make contributions differential geometry monge made important contributions theory plane curves surfaces studied surfaces revolution


envelopes plane curves space curves several students monge made contributions theory example charles dupin provided new interpretation euler 's theorem terms principle curvatures modern form equation ref name struik intrinsic geometry non euclidean geometry field differential geometry became area study considered right distinct broad idea analytic geometry primarily foundational work carl friedrich gauss bernhard riemann also important contributions


subsequent papers unpublished notes theory surfaces gauss dubbed inventor non euclidean geometry inventor intrinsic differential geometry ref name struik fundamental paper gauss introduced gauss map gaussian curvature first second fundamental forms proved theorema egregium showing intrinsic nature gaussian curvature studied geodesics computing area geodesic triangle various non euclidean geometries surfaces time gauss already opinion standard paradigm euclidean geometry discarded possession private manuscripts


non euclidean geometry informed study geodesic triangles ref name struik around time j nos bolyai lobachevsky independently discovered hyperbolic geometry thus demonstrated existence consistent geometries outside euclid 's paradigm concrete models hyperbolic geometry produced eugenio beltrami later felix klein coined term non euclidean geometry erlangen program put euclidean non euclidean geometries footing implicitly spherical geometry earth studied since antiquity non euclidean geometry elliptic geometry development intrinsic differential geometry


language gauss spurred student bernhard riemann habilitationsschrift ''on hypotheses lie foundation geometry'' work riemann introduced notion riemannian metric riemannian curvature tensor first time began systematic study differential geometry higher dimensions intrinsic point view terms riemannian metric denoted math ds math riemann development idea gauss' linear element math ds math surface time riemann began introduce systematic use linear


algebra multilinear algebra subject making great use theory quadratic forms investigation metrics curvature time riemann yet develop modern notion manifold even notion topological space encountered propose might possible investigate measure properties metric spacetime analysis masses within spacetime linking earlier observation euler masses effect forces would travel along geodesics surfaces predicting einstein 's


fundamental observation equivalence principle full years appeared scientific literature ref name struik ref name spivak wake riemann 's new description focus techniques used study differential geometry shifted ad hoc extrinsic methods study curves surfaces systematic approach terms tensor calculus klein 's erlangen program progress increased field notion groups transformations developed sophus lie jean gaston darboux leading important results theory lie groups symplectic geometry


notion differential calculus curved spaces studied elwin christoffel introduced christoffel symbols describe covariant derivative others including eugenio beltrami studied many analytic questions manifolds luigi bianchi produced ''lectures differential geometry'' studied differential geometry riemann 's perspective year later tullio levi civita gregorio ricci curbastro produced textbook systematically developing theory absolute differential calculus tensor calculus ref name spivak language differential geometry used einstein development general relativity pseudo riemannian


topological space distilled felix hausdorff many different notions manifold combinatorial differential geometric nature ref name dieudonne interest subject also focused emergence einstein 's theory general relativity importance einstein field equations einstein 's theory popularised tensor calculus ricci levi civita introduced notation math g math riemannian metric math gamma math christoffel symbols coming ''g'' ''gravitation'' lie cartan helped reformulate foundations differential geometry smooth manifolds terms exterior


calculus theory moving frames leading world physics einstein cartan theory ref name fre fr pg conceptual history space symmetry springer cham ref ref name spivak following early development many mathematicians contributed development modern theory including jean louis koszul introduced connections vector bundles shiing shen chern introduced characteristic classes subject began study complex manifolds sir william vallance douglas hodge georges de rham expanded understanding differential forms charles ehresmann introduced theory fibre bundles ehresmann connections others ref name fre ref name spivak


particular important hermann weyl made important contributions foundations general relativity introduced weyl tensor providing insight conformal geometry first defined notion gauge leading development gauge theory physics mathematics middle late th century differential geometry subject expanded scope developed links areas mathematics physics development gauge theory yang mills theory physics brought bundles connections focus leading developments gauge theory many analytical results investigated including proof


atiyah singer index theorem development complex geometry spurred parallel results algebraic geometry results geometry global analysis complex manifolds proven shing tung yau others latter half th century new analytic techniques developed regards curvature flows ricci flow culminated grigori perelman 's proof poincar conjecture period primarily due influence michael atiyah new links theoretical physics differential geometry formed techniques study yang mills equations


gauge theory used mathematicians develop new invariants smooth manifolds physicists edward witten physicist awarded fields medal made new impacts mathematics using topological quantum field theory string theory make predictions provide frameworks new rigorous mathematics resulted example conjectural mirror symmetry seiberg witten invariants branches riemannian geometry riemannian geometry studies riemannian manifolds smooth manifolds ''riemannian metric'' concept distance expressed means smooth positive definite symmetric bilinear form defined


riemannian manifolds distance preserving diffeomorphism riemannian manifolds called isometry notion also defined ''locally'' ie small neighborhoods points two regular curves locally isometric however theorema egregium carl friedrich gauss showed surfaces existence local isometry imposes gaussian curvatures corresponding points must higher dimensions riemann curvature tensor important pointwise invariant associated riemannian manifold measures close flat important class riemannian manifolds riemannian symmetric


cases general finsler manifolds finsler structure manifold function infinitely differentiable math t''m'' vertical hessian positive definite symplectic geometry symplectic geometry study symplectic manifolds '''almost symplectic manifold''' differentiable manifold equipped smoothly varying non degenerate skew symmetric bilinear form tangent space ie nondegenerate form '' '' called ' 'symplectic form'' symplectic manifold almost symplectic manifold symplectic


form '' '' closed diffeomorphism two symplectic manifolds preserves symplectic form called symplectomorphism non degenerate skew symmetric bilinear forms exist even dimensional vector spaces symplectic manifolds necessarily even dimension dimension symplectic manifold surface endowed area form symplectomorphism area preserving diffeomorphism phase space mechanical system symplectic manifold made implicit appearance already work joseph louis lagrange analytical mechanics later carl gustav jacobi 's william rowan hamilton 's formulations


classical mechanics contrast riemannian geometry curvature provides local invariant riemannian manifolds darboux 's theorem states symplectic manifolds locally isomorphic invariants symplectic manifold global nature topological aspects play prominent role symplectic geometry first result symplectic topology probably poincar birkhoff theorem conjectured henri poincar proved gd birkhoff claims area preserving map annulus twists boundary component opposite directions map least two fixed points contact


certain local normal form suitable choice coordinate system complex k hler geometry ''complex differential geometry'' study complex manifolds almost complex manifold ' 'real'' manifold math math endowed tensor type ie vector bundle endomorphism called ''almost complex structure'' math j tm rightarrow tm math math j math follows definition almost complex manifold even dimensional almost complex manifold called ''complex'' math n j math math n j math tensor type related math j math called nijenhuis tensor


sometimes ''torsion'' almost complex manifold complex admits holomorphic coordinate atlas ''almost hermitian structure'' given almost complex structure ''j'' along riemannian metric ''g'' satisfying compatibility condition math g jxjy g xy math almost hermitian structure defines naturally differential two form math omega jg xy g jxy math following two conditions equivalent math n j mbox omega math math nabla j math math nabla math levi civita connection math g math case math j g math called ''k hler structure'' ''k hler manifold'' manifold endowed k hler structure


vector bundles de rham differential forms beside lie algebroids also courant algebroids start playing important role lie groups lie group group category smooth manifolds beside algebraic properties enjoys also differential geometric properties obvious construction lie algebra tangent space unit endowed lie bracket left invariant vector fields beside structure theory also wide field representation theory geometric analysis geometric analysis mathematical discipline tools differential


equations especially elliptic partial differential equations used establish new results differential geometry differential topology gauge theory gauge theory study connections vector bundles principal bundles arises problems mathematical physics physical gauge theories underpin standard model particle physics gauge theory concerned study differential equations connections bundles resulting geometric moduli spaces solutions equations well invariants may derived equations often arise euler lagrange equations describing


equations motion certain physical systems quantum field theory study considerable interest physics bundles connections apparatus vector bundles principal bundles connections bundles plays extraordinarily important role modern differential geometry smooth manifold always carries natural vector bundle tangent bundle loosely speaking structure sufficient developing analysis manifold geometry requires addition way relate tangent spaces different points ie notion parallel transport important example


provided affine connections surface '''r''' sup sup tangent planes different points identified using natural path wise parallelism induced ambient euclidean space well known standard definition metric parallelism riemannian geometry levi civita connection serves similar purpose generally differential geometers consider spaces vector bundle arbitrary affine connection defined terms metric physics manifold may spacetime bundles connections related various physical fields intrinsic versus extrinsic beginning


middle th century differential geometry studied ''extrinsic'' point view curves surfaces considered lying euclidean space higher dimension example surface ambient space three dimensions simplest results differential geometry curves differential geometry surfaces starting work riemann ''intrinsic'' point view developed one cannot speak moving outside geometric object considered given free standing way fundamental result gauss 's theorema egregium


black holes differential forms used study electromagnetism differential geometry applications lagrangian mechanics hamiltonian mechanics symplectic manifolds particular used study hamiltonian systems riemannian geometry contact geometry used construct formalism geometrothermodynamics found applications classical equilibrium thermodynamics chemistry biophysics modelling cell membrane structure varying pressure economics differential geometry applications field econometrics geometric modeling including computer graphics computer aided geometric design draw ideas differential geometry engineering differential geometry applied


solve problems digital signal processing control theory differential geometry used analyze nonlinear controllers particularly geometric control probability statistics information theory one interpret various structures riemannian manifolds yields field information geometry particularly via fisher information metric structural geology differential geometry used analyze describe geologic structures computer vision differential geometry used analyze shapes image processing differential geometry used process analyse data non flat surfaces grigori perelman 's proof poincar conjecture using techniques ricci flows


demonstrated power differential geometric approach questions topology highlighted important role played analytic methods wireless communications grassmannian manifolds used beamforming techniques multiple antenna systems see also abstract differential geometry affine differential geometry analysis fractals basic introduction mathematics curved spacetime discrete differential geometry gauss glossary differential geometry topology important publications differential geometry important publications differential topology integral geometry list differential geometry topics noncommutative geometry projective differential geometry synthetic differential geometry systolic geometry gauge theory mathematics references


reading external links http mathstanfordedu conrad diffgeompage b conrad differential geometry handouts stanford university http wwwmathsadelaideeduau michaelmurray teaching oldhtml michael murray 's online differential geometry course http virtualmathmuseumorg surface bk curves surfaces palaispdf modern course curves surfaces richard palais http virtualmathmuseumorg richard palais 's dxm surfaces gallery http wwwcseltehu geometry csikos dif difhtml bal zs csik 's notes differential geometry http wwwwisdomweizmannacil yakov scanlib hickspdf n j hicks notes differential geometry van nostrand http ocwmitedu courses mathematics differential geometry fall mit opencourseware differential geometry fall geometry processing


student kerala india taking distance education covid pandemic '''distance education''' also known '' 'distance learning''' education students may always physically present school ref name kaplan haenlein ref traditionally usually involved '''correspondence courses''' wherein student corresponded school via mail today usually involves '''online education''' distance learning programme completely distance learning combination distance learning traditional classroom instruction called hybrid blended massive open online courses moocs offering large scale interactive participation open access world wide web

Applied science
Education
Distance education


network technologies recent educational modes distance education ref name kaplan haenlein number terms distributed learning e learning learning online learning virtual classroom etc used roughly synonymously distance education history one earliest attempts advertised ''boston gazette'' caleb philipps teacher new method short hand sought students wanted learn weekly mailed lessons first distance education course modern sense provided sir isaac pitman taught system shorthand mailing texts


transcribed shorthand postcards receiving transcriptions students return correction element student feedback crucial innovation pitman 's system scheme made possible introduction uniform postage rates across england early beginning proved extremely successful phonographic correspondence society founded three years later establish courses formal basis society paved way later formation sir isaac pitman colleges across country ref name moorekearsley ref first correspondence school united states society encourage studies


home founded founded wolsey hall oxford first distance learning college uk university correspondence courses university london first university offer distance learning degrees establishing external programme background innovation lay fact institution later known university college london non denominational given intense religious rivalries time outcry godless university issue soon boiled institutions degree granting powers institutions ref name rothblatt


article ref ''the london university'' drawn thomas hosmer shepherd x px compromise solution emerged sole authority conduct examinations leading degrees would given new officially recognized entity called university london would act examining body university london colleges originally university college london king 's college london award students university london degrees sheldon rothblatt states thus arose nearly archetypal form famous english distinction teaching examining embodied separate institutions ref name rothblatt article


state giving examining powers separate entity groundwork laid creation programme within new university would administer examinations award qualifications students taking instruction another institution pursuing course self directed study referred people 's university charles dickens provided access higher education students less affluent backgrounds external programme chartered queen victoria making university london first university offer distance learning degrees students ref name external programme history ref ref name key facts ref enrollment increased steadily


late th century example widely copied elsewhere ref name guardian article ref programme known university london international programme includes postgraduate undergraduate diploma degrees created colleges london school economics royal holloway goldsmiths ref name key facts william rainey harper encouraged development external university courses new university chicago united states william rainey harper founder first president university chicago celebrated concept extended education research university satellite colleges elsewhere region


harper encouraged correspondence courses promote education idea put practice chicago wisconsin columbia several dozen universities enrollment largest private profit school based scranton pennsylvania international correspondence schools grew explosively founded provide training immigrant coal miners aiming become state mine inspectors foremen enrolled new students matriculated new students total enrollments reached growth due sending complete textbooks instead single lessons


use aggressive person salesmen stark contrast pedagogy education high priority progressive era american high schools colleges expanded greatly men older busy family responsibilities night schools opened ymca school boston became northeastern university outside big cities private correspondence schools offered flexible narrowly focused solution large corporations systematized training programmes new employees national association corporation schools grew starting


tuition international conference correspondence education held first meeting goal provide individualised education students low cost using pedagogy testing recording classification differentiation organization since renamed international council open distance education icde headquarters oslo norway open universities open university united kingdom founded labour government led prime minister harold wilson based vision michael young planning commenced minister state education jennie


lee established model open university ou one widening access highest standards scholarship higher education set planning committee consisting university vice chancellors educationalists television broadcasters chaired sir peter venables british broadcasting corporation bbc assistant director engineering time james redmond obtained qualifications night school natural enthusiasm project much overcome technical difficulties using television broadcast teaching programmes ref name walton hall renovated act headquarters


newly established open university '' artist hilary french '' open university revolutionised scope correspondence programme helped create respectable learning alternative traditional form education forefront developing new technologies improve distance learning service well undertaking research disciplines walter perry appointed ou 's first vice chancellor january foundation secretary anastasios christodoulou election new conservative government leadership edward heath led budget cuts chancellor exchequer iain macleod


earlier called idea open university blithering nonsense however ou accepted first students adopting radical open admissions policy time total student population conventional universities united kingdom around athabasca university canada 's open university created followed similar though independently developed pattern ref name byrne ref open university inspired creation spain 's national university distance education germany 's fernuniversit hagen many similar institutions around world often name open university english


longer able teach real time could switch asynchronous instruction significantly negatively affected coping transition ref name jelinskaparadowski ref posed various legal issues especially terms copyright recent study benefits drawbacks online learning found students harder time producing work ref name referencea ref study suggests teachers cut back amount information taught incorporate activities lesson order students create work ref name referencea technologies internet technology enabled many forms


distance learning open educational resources facilities e learning moocs although expansion internet blurs boundaries distance education technologies divided two modes delivery synchronous learning asynchronous learning synchronous learning participants present time virtual classroom traditional classroom teaching requires timetable web conferencing videoconferencing educational television instructional television examples synchronous technology direct broadcast satellite dbs internet radio live streaming telephone web based voip ref name lever duffy ref web conferencing software helps facilitate class meetings usually


contains additional interaction tools text chat polls hand raising emoticons etc tools also support asynchronous participation students listen recordings synchronous sessions immersive environments notably secondlife also used enhance participant presence distance education courses another form synchronous learning using classroom use robot proxies including allow sick students attend classes universities starting use robot proxies enable engaging synchronous hybrid classes remote person students present interact using telerobotics


devices kubi telepresence robot stand looks around double robot roams around telepresence robots remote students seat table desk instead screen wall asynchronous learning participants access course materials flexibly schedules students required together time mail correspondence oldest form distance education asynchronous delivery technology message board forums e mail video audio recordings print materials voicemail fax ref name lever duffy two methods


combined many courses offered open universities increasing number campus based institutions use periodic sessions residential day teaching supplement sessions delivered distance ref name burns ref type mixed distance campus based education recently come called blended learning less often hybrid learning many open universities use blend technologies blend learning modalities face face distance hybrid rubric distance learning distance learning also use interactive radio instruction iri interactive audio instruction iai online virtual worlds digital games webinars


webcasts referred e learning ref name burns radio television ref rapid spread film radio led proposals use distance education least city school systems state boards education many colleges universities broadcast educational programmes public schools one line thought use radio master teacher first large scale implementation radio distance education took place chicago three week school closure implemented response


polio outbreak city experiencing superintendent chicago public schools william johnson assistant superintendent minnie fallon implemented programme distance learning provided city 's elementary school students instruction radio broadcasts typical setup came kentucky john wilkinson taylor president university louisville teamed nbc use radio medium distance education chairman federal communications commission endorsed project predicted college radio would put american education nbsp years ahead university owned city local residents


use television along lines proved unsuccessful despite heavy funding ford foundation coordinating commission higher education california funded project outreach study potential telecourses study included university california california state university community colleges study led coordinated instructional systems legislation allowing use public funds non classroom instruction paved way emergence telecourses precursor online courses programmes today coastline community colleges dallas county community college district miami


dade community college led way ''adult learning service'' us public broadcasting service came wrapped series individually produced telecourse credit became significant part history distance education online learning internet widespread use computers internet made distance learning easier faster today virtual schools virtual universities deliver full curricula online capacity internet support voice video text immersion teaching methods made earlier distinct forms telephone videoconferencing radio television text based education somewhat redundant however


many techniques developed lessons learned earlier media used internet delivery first totally online courses graduate undergraduate credit offered starting fall connected education new school new york city students earning media studies completely online via computer conferencing person requirements ref name ref ref name new scientist ref ref name netweaver ref followed university toronto graduate school education called oise ontario institute studies education offering course women computers


education dealing gender issues educational computing first new fully online university founded open university catalonia headquartered barcelona spain jones international university launched first fully online university accredited regional accrediting association us enrollment distance education courses increased rapidly almost every country developed developing countries many private public non profit profit institutions worldwide offer distance education courses basic instruction highest levels degree doctoral


programmes new york university https iuc educa international university canada example offers online degrees engineering management related fields nyu tandon online levels accreditation vary widely respected universities stanford university harvard deliver online courses online schools receive little outside oversight actually fraudulent ie diploma mills us distance education accrediting commission deac specializes accreditation distance education institutions united states found third students enrolled postsecondary education taken accredited online course postsecondary


institution ref name lederman ref growth continued majority public private colleges offered full academic programmes online ref name lederman programmes included training mental health ref name blackmore c blackmore c van deurzen e tantam therapy training online using internet widen access training mental health issues stickley basset eds teaching mental health pgs hoboken nj john wiley sons ltd ref occupational therapy ref name jedlicka j jedlicka j brown w bunch e jaffe l e comparison distance education instructional methods


occupational therapy journal allied health ref ref name stanton stanton going distance developing shared web based learning programmes occupational therapy international ref family therapy ref name maggio l maggio l chenail r todd teaching family therapy electronic age journal systemic therapies ref art therapy ref name orr p orr p distance supervision research findings considerations art therapy arts psychotherapy ref physical therapy ref name stanton rehabilitation counseling ref name stebnicki stebnicki glover n e supervision complementary


learners commence complete course time institutions offer self paced programmes allow continuous enrollment length time complete course set learner 's time skill commitment levels self paced courses almost always offered asynchronously delivery method offers advantages disadvantages students teachers institutions kaplan haenlein classify distance education four groups according time dependency number participants moocs massive open online courses open access online course ie without specific participation restrictions allows unlimited massive participation spocs


small private online courses online course offers limited number places therefore requires form formal enrollment smocs synchronous massive online courses open access online course allows unlimited participation requires students present time synchronously ssocs synchronous private online courses online course offers limited number places requires students present time synchronously ref name kaplan haenlein paced models familiar mode since used almost exclusively campus based schools institutes offer distance campus programmes


usually use paced models teacher workload student semester planning tuition deadlines exam schedules administrative details synchronized campus delivery student familiarity pressure deadlines encourages students readily adapt usually succeed paced models however student freedom sacrificed common pace often fast students slow others additional life events professional family responsibilities interfere student 's capability complete tasks external schedule finally paced models allow students readily form communities inquiry engage


collaborative work self paced courses maximize student freedom students commence studies date complete course little time weeks year longer students often enroll self paced study pressure complete programmes able complete scheduled course need additional courses pressure precludes regular study length time self paced nature programming though unfamiliar model many students lead excessive procrastination resulting course


incompletion assessment learning also challenging exams written day making possible students share examination questions resulting loss academic integrity finally extremely challenging organize collaborative work activities though schools developing cooperative models based upon networked connectivist pedagogies use self paced programmes benefits distance learning expand access education training general populace businesses since flexible scheduling structure lessens effects many time constraints imposed personal responsibilities commitments ref name oblinger ref ref name cfp ref devolving activities


site alleviates institutional capacity constraints arising traditional demand institutional buildings infrastructure ref name oblinger furthermore potential increased access experts field students diverse geographical social cultural economic experiential backgrounds ref name maggio l ref name cfp population large becomes involved lifelong learning beyond normal schooling age institutions benefit financially adult learning business courses may particularly lucrative ref name oblinger ref name cfp distance education programmes act catalyst institutional innovation ref name oblinger least


effective face face learning programmes ref name blackmore c ref name jedlicka j ref name nguyen ref especially instructor knowledgeable skilled ref name orr p ref name cfp distance education also provide broader method communication within realm education ref name cfp many tools programmes technological advancements offer communication appears increase distance education amongst students professors well students classmates distance educational increase communication particularly communication amongst students classmates improvement made provide distance education students


many opportunities possible would receive person education improvement made distance education growing tandem constant technological advancements present day online communication allows students associate accredited schools programmes throughout world reach person learning opportunity involved global institutions via distance education diverse array thought presented students communication classmates beneficial students opportunity combine new opinions develop solid


foundation learning ref name calpoly ref shown research learners become aware variations interpretation construction meaning among range people construct individual meaning help students become knowledgeable wide array viewpoints education ref name calpoly increase likelihood students build effective ties one another course instructors use similar assignments students across different locations overcome influence co location relationship building high cost education affects students higher education distance education may


alternative order provide relief ref name nguyen ref name cfp distance education cost effective form learning sometimes save students significant amount money opposed traditional education ref name cfp distance education may able help save students considerable amount financially removing cost transportation ref name worldwidelearn ref addition distance education may able save students economic burden high priced course textbooks many textbooks available electronic textbooks known e textbooks offer digital textbooks reduced price comparison


traditional textbooks also increasing improvements technology resulted many school libraries partnership digital publishers offer course materials free help students significantly educational costs ref name worldwidelearn within class students able learn ways traditional classrooms would able provide able promote good learning experiences therefore allow students obtain higher satisfaction online learning ref name kirtman ref example students review lessons according needs students manipulate coursework fit learning


focusing weaker topics breezing concepts already easily grasp ref name kirtman course design learning environment optimal conditions distance education lead students higher satisfaction learning experiences ref name nguyen studies shown high satisfaction correlates increased learning healthcare mental health distance learning programme online based interactions potential foster deeper reflections discussions client issues ref name stanton well quicker response client issues since supervision happens regular


basis limited weekly supervision meeting ref name stebnicki ref name cfp also may contribute students feeling greater sense support since ongoing regular access instructors students ref name stanton ref name stebnicki distance learning may enable students unable attend traditional school setting due disability illness decreased mobility immune system suppression get good education children sick unable attend classes able attend person


use robot proxies helps students experiences classroom social interaction unable receive home hospital still keeping safe learning environment last years students entering safely back classroom thanks help robots article ''new york times'' swiveling proxy even wear tutu explains positive impact virtual learning classroom another explains even simple stationary telepresence robot help distance education may provide


equal access regardless socioeconomic status income area residence gender race age cost per student applying universal design strategies distance learning courses developed rather instituting accommodations specific students needed basis increase accessibility courses students range abilities disabilities learning styles native languages distance education graduates would never associated school traditional system may donate money school distance learning may also offer final opportunity adolescents longer permitted


general education population due behavior disorders instead students academic opportunities may continue education homes earn diplomas offering another chance integral part society distance learning offers individuals unique opportunity benefit expertise resources best universities currently available moreover online environment facilitates pedagogical innovation new programme structures formats students ability collaborate share question infer suggest new methods techniques continuous improvement content ability complete


course pace appropriate individual effective manner learn given personal demands time schedule ref name cfp self paced distance learning mobile device smartphone provides maximum flexibility capability distance learning also reduce phenomenon rural exodus enabling students remote regions remain hometowns pursuing higher education eliminating distance barrier higher education also increase number alternatives open students foster greater competition institutions higher learning regardless geography criticism barriers


effective distance education include obstacles domestic distractions unreliable technology well students' programme costs adequate contact teachers support services need experience students attempt participate distance education without proper training tools needed successful programme students must provided training opportunities needed tool used throughout programme lack advanced technology skills lead unsuccessful experience schools responsibility adopt proactive policy managing technology barriers time management skills


years obstacles overcome world environment distance education continues improve dr pankaj singhm also claims debate distance education stating due lack direct face face social interaction however people become used personal social interaction online example dating chat rooms shopping blogging becoming easier learners project socializes others obstacle dissipated courses required complete degree may offered online health care profession programmes particular require


sort patient interaction fieldwork student may graduate studies also shown students pursuing medical professional graduate degree participating distance education courses favor face face communication professor mediated chat rooms independent studies however little correlation student performance comparing previous different distance learning strategies ref name jedlicka j theoretical problem application traditional teaching methods online courses online courses may upper size limit daniel barwick noted evidence large class


size always worse small class size always better although negative link established certain types instruction large classes learning outcomes argued higher education made sufficient effort experiment variety instructional methods determine whether large class size always negatively correlated reduction learning outcomes early proponents massive open online courses moocs saw type experiment barwick pointed lacking higher education although barwick never advocated moocs


may also institutional challenges distance learning new enough may challenge gain support programmes traditional brick mortar academic learning environment ref name stanton furthermore may difficult instructor organize plan distance learning programme ref name stebnicki especially since many new programmes organizational needs different traditional learning programme additionally though distance education offers industrial countries opportunity become globally informed still negative sides hellman states include cost capital


intensiveness time constraints pressures instructors isolation students instructors peers instructors' enormous difficulty adequately evaluating students never meet face face drop rates far higher classroom based courses ref name hellman judith adler hellman judith adler riddle distance education geneva june ref complex challenge distance education relates cultural differences students teachers among students distance programmes tend diverse could go beyond geographical borders regions countries continents cross cultural borders may exist respect


race gender religion requires proper understanding awareness norms differences preconceptions potential conflicting issues ref name nasiri et mafakheri ref educational technology modern use electronic educational technology also called e learning facilitates distance learning independent learning extensive use information communications technology ict ref name cfp replacing traditional content delivery postal correspondence instruction synchronous asynchronous online communication interactive learning environment virtual communities lieu physical classroom focus shifted education transaction form virtual community


learners sustainable across time one significant issues encountered mainstream correspondence model distance education transactional distance results lack appropriate communication learner teacher gap observed become wider communication learner teacher direct implications learning process future endeavors distance education distance education providers began introduce various strategies techniques procedures increase amount interaction learners teachers measures eg frequent face face tutorials increased use information


communication technologies including teleconferencing internet designed close gap transactional distance credentials online credentials learning nbsp digital credentials offered place traditional paper credentials skill educational achievement directly linked accelerated development internet communication technologies development nbsp digital badges nbsp electronic passports nbsp nbsp massive open online courses nbsp moocs direct bearing understanding learning recognition levels pose direct challenge status quo useful distinguish three forms online credentials test based credentials online badges online certificates ref name ref


see also degree completion program digital divide distance line learning advocates herbert gross linda harasim educational technology homeschooling learning environment low residency program media psychology new media open supported learning open door academic policy qualifications frameworks online learning school air distance education australia ''sunrise semester'' videotelephony virtual education sources references reading anderson ''theory practice online education'' nd ed anderson dron j three generations distance education pedagogy ''the international review research open distance learning'' bates


''technology e learning distance education'' routledgefalmer holmberg b rje ''theory practice distance education'' nd ed https wwwquestiacom library theory practice distance education online jacob ju ensign https doiorg transactional radio instruction improving educational outcomes children conflict zones palgrave macmillan cham doi https doiorg kett joseph f ''pursuit knowledge difficulties self improvement adult education america'' https wwwquestiacom library handbook distance education online edition major c h teaching online guide theory research practice johns hopkins university press moore g ''contemporary issues american distance education'' ed peters distance education industrial production comparative interpretation


courses'' princeton university press https wwwquestiacom read unlocking gates leading universities online external links http onlinebookslibraryupennedu webbin book browsetype lcsubc key radio education c x radio education full text books articles online http wwwaupressca indexphp books byseriess distanceeducation issues distance education book series athabasca university press series books related distance education research available print sale online open access http wwwwashingtonedu doit resources accessdlhtml center accessible distance learning accessdl center university washington educational television learning methods types university college education


special methods used psychological study infants conservation one many experiments used children '''developmental psychology''' scientific study human beings change course life originally concerned infants children field expanded include adolescence adult development aging entire lifespan developmental psychologists aim explain thinking feeling behaviors change throughout life field examines change across three major dimensions physical development cognitive development social emotional development within three dimensions broad range topics including

Social science
Psychology
Developmental psychology


motor skills executive functions moral understanding language acquisition social change personality emotional development self concept identity formation developmental psychology examines influences nature ''and'' nurture process human development processes change context across time many researchers interested interactions among personal characteristics individual 's behavior environmental factors including social context built environment ongoing debates regards developmental psychology include biological essentialism vs neuroplasticity stages development vs dynamic systems development developmental psychology involves range fields educational psychology child psychopathology forensic developmental


psychology child development cognitive psychology ecological psychology cultural psychology influential developmental psychologists th century include urie bronfenbrenner erik erikson sigmund freud anna freud jean piaget barbara rogoff esther thelen lev vygotsky historical antecedents jean jacques rousseau john b watson typically cited providing foundations modern developmental psychology ref name hogan ref mid th century jean jacques rousseau described three stages development ''infants'' infancy ''puer'' childhood ''adolescence'' ''emile education'' rousseau 's ideas taken strongly educators time developmental psychology generally focuses certain changes cognitive


social intellectual personality occur time course human life many theorists made profound contribution area psychology one erik erikson developed model eight stages psychological development believed humans developed stages throughout lifetimes would affect behaviors charles darwin late th century psychologists familiar evolutionary theory darwin began seeking evolutionary description psychological development ref name hogan prominent pioneering psychologist g stanley hall ref name hogan attempted correlate ages childhood


consciousness lastly unconscious includes mental processes person unaware believed tension conscious unconscious conscious tries hold back unconscious tries express explain developed three personality structures id ego superego id primitive three functions according pleasure principle seek pleasure avoid pain ref name theories ref superego plays critical moralizing role ego organized realistic part mediates desires id superego ref name snowden ref based


proposed five universal stages development characterized erogenous zone source child 's psychosexual energy first ''oral stage'' occurs birth months age oral stage libido centered baby 's mouth baby suck second ''anal stage'' one three years age anal stage child defecates anus often fascinated defecation third ''phallic stage'' occurs three five years age


materials child interact use construct used socratic questioning get children reflect tried get see contradictions explanations piaget believed intellectual development takes place series stages described theory cognitive development stage consists steps child must master moving next step believed stages separate one another rather stage builds previous one continuous learning process


children characterized reasoning based rewards punishments associated different courses action conventional moral reason occurs late childhood early adolescence characterized reasoning based rules conventions society lastly post conventional moral reasoning stage individual sees society 's rules conventions relative subjective rather authoritative ref name adolescence ref kohlberg used heinz dilemma apply stages moral development heinz dilemma involves heinz 's wife dying cancer heinz dilemma save wife stealing


drug preconventional morality conventional morality post conventional morality applies heinz 's situation stages psychosocial development erik erikson german american psychologist erik erikson collaborator wife joan erikson conceptualized eight stages psychosocial development theorized healthy individuals pass develop infancy adulthood stage person must resolve challenge existential dilemma successful resolution dilemma results person ingraining positive virtue failure resolve fundamental challenge stage reinforces negative perceptions person world around


low self esteem doubt third stage initiative vs guilt virtue gained sense purpose takes place primarily via play stage child curious many interactions kids ask many questions curiosity grows much guilt present child may slower harder time interacting world children fourth stage industry competence vs inferiority virtue stage competency result child 's early


experiences school stage child try win approval others understand value accomplishments fifth stage identity vs role confusion virtue gained fidelity takes place adolescence child ideally starts identify place society particularly terms gender role sixth stage intimacy vs isolation happens young adults virtue gained love person starts share life someone else intimately emotionally


reinforce feelings isolation seventh stage generativity vs stagnation happens adulthood virtue gained care person becomes stable starts give back raising family becoming involved community eighth stage ego integrity vs despair one grows old look back life contemplate successes failures resolve positively virtue wisdom gained also stage one gain sense closure accept death without regret fear stages based


circular sensory motor sensory motor nominal sentential preoperational primary concrete abstract formal systematic metasystematic paradigmatic cross paradigmatic meta cross paradigmatic order hierarchical complexity tasks predicts difficult performance r ranging mhc three main axioms order meet order higher order task coordinate next lower order task axioms rules followed determine mhc orders actions form hierarchy axioms defined


terms tasks next lower order hierarchical complexity task action b defined higher order task action organizes two less complex actions complex action specifies way less complex actions combine c defined lower order task actions carried non arbitrarily ecological systems theory bronfenbrenner 's ecological systems theory ecological systems theory originally formulated urie bronfenbrenner specifies four types nested environmental systems bi directional influences within systems four systems microsystem mesosystem exosystem macrosystem system


contains roles norms rules powerfully shape development microsystem direct environment lives home school mesosystem relationships connect microsystem exosystem larger social system child plays role macrosystem refers cultural values customs laws society microsystem immediate environment surrounding influencing individual example school home setting mesosystem combination two microsystems influence example sibling relationships home vs peer relationships school exosystem


mother illness longer support life ref name edpsych since publication bronfenbrenner 's major statement theory ''the ecology human development'' widespread influence way psychologists others approach study human beings environments result conceptualization development environments family economic political structures come viewed part life course childhood adulthood ref name smith et al ref zone proximal development lev vygotsky russian theorist soviet era posited


builds upon knowledge children already new knowledge adults help child learn ref name vygotsky ref vygotsky strongly focused role culture determining child 's pattern development arguing development moves social level individual level ref name vygotsky words vygotsky claimed psychology focus progress human consciousness relationship individual environment ref name vygotsky ref felt scholars continued disregard connection disregard would inhibit full comprehension human consciousness ref name vygotsky constructivism constructivism


paradigm psychology characterizes learning process actively constructing knowledge individuals create meaning make sense new information selecting organizing integrating information knowledge often context social interactions constructivism occur two ways individual social individual constructivism person constructs knowledge cognitive processes experiences rather memorizing facts provided others social constructivism individuals construct knowledge interaction knowledge bring situation social cultural exchanges within content ref


name edpsych jean piaget swiss developmental psychologist proposed learning active process children learn experience make mistakes solve problems piaget proposed learning whole helping students understand meaning constructed evolutionary developmental psychology evolutionary developmental psychology research paradigm applies basic principles darwinian evolution particularly natural selection understand development human behavior cognition involves study genetic environmental mechanisms underlie development social cognitive competencies well epigenetic gene environment interactions processes adapt


competencies local conditions ref name bjorklund et al ref edp considers reliably developing species typical features ontogeny developmental adaptations well individual differences behavior evolutionary perspective evolutionary views tend regard individual differences result either random genetic noise evolutionary byproducts idiosyncrasies example peer groups education neighborhoods chance encounters rather products natural selection edp asserts natural selection favor emergence individual differences via adaptive developmental plasticity ref name bjorklund et al ref name ref perspective human development follows alternative life history strategies


response environmental variability rather following one species typical pattern development ref name bjorklund et al edp closely linked theoretical framework evolutionary psychology ep also distinct ep several domains including research emphasis edp focuses adaptations ontogeny opposed adaptations adulthood consideration proximate ontogenetic environmental factors ie development happens addition ultimate factors ie development happens focus mainstream evolutionary psychology ref name ref attachment theory attachment theory originally developed john bowlby focuses importance open intimate


emotionally meaningful relationships attachment described biological system powerful survival impulse evolved ensure survival infant threatened stressed child move toward caregivers create sense physical emotional psychological safety individual attachment feeds body contact familiarity later mary ainsworth developed strange situation protocol concept secure base tool found help understand surveillance attachment strange situation test adult attachment interview help determine factors certain attachment styles


strange situation test help finds disturbances attachment whether certain attributes found contribute certain attachment issue ref name ref adult attachment interview tool similar strange situation test instead focuses attachment issues found adults ref name tests helped many researchers gain information risks identify ref name theorists proposed four types attachment styles ref name schacter ref secure anxious avoidant anxious resistant ref name adolescence disorganized ref name schacter secure attachment healthy attachment infant caregiver characterized


trust anxious avoidant insecure attachment infant caregiver characterized infant 's indifference toward caregiver anxious resistant insecure attachment infant caregiver characterized distress infant separated anger reunited ref name adolescence disorganized attachment style without consistent pattern responses upon return parent ref name schacter child hindered natural tendency form attachments babies raised without stimulation attention regular caregiver locked away conditions abuse extreme


neglect possible short term effects deprivation anger despair detachment temporary delay intellectual development long term effects include increased aggression clinging behavior detachment psychosomatic disorders increased risk depression adult attachment established early childhood attachment continues adulthood involved intimate relationships way adults able handle relationship issues depends attachment styles formed childhood ref name ref example secure attachment continuing adulthood would person feels confident able meet needs secure


attachment allows adult healthy trusting relationship ref name example anxious attachment adulthood adult chooses partner anxious avoidant attachment anxious ambivalent attachment style affect adult 's trust issues committed relationship ref name understanding attachment style individual formed caregiver children better understand interpersonal relationships adults nature vs nurture significant issue developmental psychology relationship innateness environmental influence regard particular aspect development often referred


nature nurture nativism versus empiricism nativist account development would argue processes question innate specified organism 's genes empiricist perspective would argue processes acquired interaction environment today developmental psychologists rarely take polarised positions regard aspects development rather investigate among many things relationship innate environmental influences one ways relationship explored recent years emerging field evolutionary developmental psychology one area


innateness debate prominently portrayed research language acquisition major question area whether certain properties human language specified genetically acquired learning empiricist position issue language acquisition suggests language input provides necessary information required learning structure language infants acquire language process statistical learning perspective language acquired via general learning methods also apply aspects development perceptual learning nativist position argues


input language impoverished infants children acquire structure language linguist noam chomsky asserts evidenced lack sufficient information language input universal grammar applies human languages pre specified led idea special cognitive module suited learning language often called language acquisition device chomsky 's critique behaviorist model language acquisition regarded many key turning point decline prominence theory behaviorism


improvement propose improvement includes slow progressing changes life span behavior within prior stages advancement giving premise abilities capacities required stages many concept continuous quantifiable measurement seems essence science ref name crain william c psychologists may concur advancement could continuous process see advancement discontinuous process accept advancement includes unmistakable partitioned stages diverse sorts behavior happening organize proposes development


certain capacities arrange particular feelings ways considering definite beginning finishing point may 's correct time capacity abruptly shows disappears although sorts considering feeling carrying could seem seem abruptly likely developing gradually time stage theories development rest suspicion development may discontinuous process including particular stages characterized subjective contrasts behavior moreover assume structure


stages n't variable concurring person case time arrange may shift separately stage theories differentiated ceaseless hypotheses set development incremental process stability vs change issue involves degree one becomes older renditions early experience whether develop something different earlier point development considers extent early experiences especially infancy later experiences key determinants person 's development lifespan developmentalists recognize extreme positions unwise therefore


key comprehensive understanding development stage requires interaction different factors one mathematical models developmental psychology concerned describing characteristics psychological change time also seeks explain principles internal workings underlying changes psychologists attempted better understand factors using models model must simply account means process takes place sometimes done reference changes brain may correspond changes behavior course development


mathematical modeling useful developmental psychology implementing theory precise easy study manner allowing generation explanation integration prediction diverse phenomena several modeling techniques applied development symbolic connectionist neural network dynamical systems models dynamic systems models illustrate many different features complex system may interact yield emergent behaviors abilities nonlinear dynamics applied human systems specifically address issues require attention temporality life transitions human development behavioral emotional change time nonlinear dynamic systems currently explored way


explain discrete phenomena human development affect second language acquisition locomotion research areas cognitive development cognitive development primarily concerned ways infants children acquire develop use internal mental capabilities problem solving memory language major topics cognitive development study language acquisition development perceptual motor skills piaget one influential early psychologists study development cognitive abilities theory suggests development proceeds set stages infancy adulthood end point


considerations cognitive psychology psychology individual differences interpretation modeling development ref name demetriou demetriou cognitive development demetriou w doise kfm van lieshout eds ''life span developmental psychology'' pp london wiley ref specifically neo piagetian theories cognitive development showed successive levels stages cognitive development associated increasing processing efficiency working memory capacity increases explain differences stages progression higher stages individual differences children age grade level however theories moved away piagetian stage theories


influenced accounts domain specific information processing posit development guided innate evolutionarily specified content specific information processing mechanisms social emotional development developmental psychologists interested social development examine individuals develop social emotional competencies example study children form friendships understand deal emotions identity develops research area may involve study relationship cognition cognitive development social behavior emotional regulation er refers individual 's ability modulate emotional responses across variety contexts young children


modulation part controlled externally parents authority figures children develop take responsibility internal state studies shown development er affected emotional regulation children observe parents caretakers emotional climate home reaction parents caretakers child 's emotions music also influence stimulating enhancing senses child self expression child 's social emotional development disrupted motor coordination problems evidenced environmental stress hypothesis


environmental hypothesis explains children coordination problems developmental coordination disorder exposed several psychosocial consequences act secondary stressors leading increase internalizing symptoms depression anxiety ref name referencea ref motor coordination problems affect fine gross motor movement well perceptual motor skills secondary stressors commonly identified include tendency children poor motor skills less likely participate organized play children likely feel socially isolated ref name referencea social emotional development focuses five keys areas self awareness self management social


awareness relationship skills responsible decision making physical development physical development concerns physical maturation individual 's body reaches adult stature although physical growth highly regular process children differ tremendously timing growth spurts ref name eaton eaton warren physical maturation university manitoba winnipeg canada retrieved ref studies done analyze differences timings affect related variables developmental psychology information processing speed traditional measures physical maturity using x rays less practice nowadays compared simple measurements


body parts height weight head circumference arm span ref name eaton studies practices physical developmental psychology phonological abilities mature year olds controversial hypotheses left handers maturationally delayed compared right handers study eaton chipperfield ritchot kostiuk found three different samples difference right left handers ref name eaton memory development researchers interested memory development look way memory develops childhood onward according fuzzy trace theory people two separate memory processes verbatim


gist two traces begin develop different times well different pace children young four years old verbatim memory memory surface information increases early adulthood point begins decline hand capacity gist memory memory semantic information increases early adulthood point consistent old age furthermore one 's reliance gist memory traces increases one ages ref name fuzzy trace theory children 's false memories ref research methods designs main research methods developmental psychology employs many


research methods used areas psychology however infants children cannot tested ways adults different methods often used study development developmental psychologists number methods study changes individuals time common research methods include systematic observation including naturalistic observation structured observation self reports could clinical interviews structured interviews clinical case study method ethnography participant observation ref name berk ref methods differ extent control researchers impose study conditions construct ideas variables


cause effect relationships among variables ref name shaffer hand limitation data obtained artificial environment may lack generalizability ref name shaffer correlational method explores relationship two events gathering information variables without researcher intervention ref name prentice hall ref name shaffer advantage using correlational design estimates strength direction relationships among variables natural environment ref name shaffer however limitation permit determination cause effect relationships among variables ref name shaffer case study approach allows investigations obtain


depth understanding individual participant collecting data based interviews structured questionnaires observations test scores ref name shaffer methods strengths weaknesses experimental method appropriate preferred method developmental scientists provides controlled situation conclusions drawn cause effect relationships ref name prentice hall research designs developmental studies regardless whether employ experimental correlational case study method also constructed using research designs ref name bruning research designs logical frameworks used make key comparisons within research studies cross sectional


design longitudinal design sequential design microgenetic design longitudinal study researcher observes many individuals born around time cohort carries new observations members cohort age method used draw conclusions types development universal normative occur members cohort example longitudinal study early literacy development examined detail early literacy experiences one child families researchers may also observe ways development varies individuals hypothesize


causes variation data longitudinal studies often require large amounts time funding making unfeasible situations also members cohort experience historical events unique generation apparently normative developmental trends may fact universal cohort ref name berk cross sectional study researcher observes differences individuals different ages time generally requires fewer resources longitudinal method individuals come different cohorts shared historical events much confounding factor token


however cross sectional research may effective way study differences participants differences may result different ages exposure ' 'different'' historical events ref name berk third study design sequential design combines methodologies researcher observes members different birth cohorts time tracks participants time charting changes groups much resource intensive format aids clearer distinction changes attributed individual historical environment truly universal ref name berk


every method weaknesses developmental psychologists rarely rely one study even one method reach conclusions finding consistent evidence many converging sources possible ref name prentice hall life stages psychological development prenatal development prenatal development interest psychologists investigating context early psychological development whole prenatal development involves three main stages germinal stage embryonic stage fetal stage germinal stage begins conception weeks embryonic stage means development weeks weeks fetal stage represents weeks birth baby


senses develop womb fetus see hear second trimester weeks age sense touch develops embryonic stage weeks ref name berk brain 's billions neurons also developed second trimester ref name berk babies hence born odor taste sound preferences largely related mother 's environment ref name berk primitive reflexes arise birth still present newborns one hypothesis reflexes vestigial limited use early


neurodevelopmental disorders example schizophrenia advent cognitive neuroscience embryology neuroscience prenatal development increasing interest developmental psychology research several environmental agents teratogens cause damage prenatal period include prescription nonprescription drugs illegal drugs tobacco alcohol environmental pollutants infectious disease agents rubella virus toxoplasmosis parasite maternal malnutrition maternal emotional stress rh factor blood incompatibility mother child ref name berk many statistics prove effects aforementioned substances leading example would america alone


approximately 'cocaine babies' born annual basis result expectant mother abusing drug pregnant 'cocaine babies' proven quite severe lasting difficulties persist throughout infancy right throughout childhood drug also encourages behavioural problems affected children defects various vital organs infancy birth first year child referred infant ref name berk developmental psychologists vary widely assessment infant psychology influence outside world upon certain aspects relatively clear


majority newborn infant 's time spent sleep first sleep evenly spread throughout day night couple months infants generally become diurnal infants seen six states grouped pairs quiet sleep active sleep dreaming rem sleep occurs quiet waking active waking fussing crying infant perception infant perception newborn see hear smell taste touch five features better known one 's five senses infants respond stimuli differently different states ref name bremner vision


significantly worse infants older children infant sight tends blurry early stages improves time color perception similar seen adults demonstrated infants young four months using habituation methods ref name butterworth infants attain adult like vision six months ref name berk hearing well developed prior birth unlike vision newborns prefer complex sounds pure tones human speech sounds mother 's voice voices native language languages scientist believe features probably learned womb ref name berk infants


fairly good detecting direction sound comes months hearing ability approximately equal adult 's smell taste present infants showing different expressions disgust pleasure presented pleasant odors honey milk etc unpleasant odors rotten egg tastes eg sour taste newborns born odor taste preferences acquired womb smell taste amniotic fluid turn influenced mother eats breast bottle fed babies around three days old prefer smell human milk


formula indicating innate preference ref name berk good evidence older infants preferring smell mother others ref name butterworth touch feel one better developed senses birth one first senses develop inside womb evidenced primitive reflexes described relatively advanced development somatosensory cortex ref name slater ref pain infants feel pain similarly strongly older children pain relief infants received much attention area research ref


name matthewmatthew ref glucose known relieve pain newborns ref name dilenelseviers ref language babies born ability discriminate virtually sounds human languages ref name berk infants around six months differentiate phonemes language similar phonemes another language stage infants also start babble producing phonemes infant cognition piagetian era piaget suggested infant 's perception understanding world depended motor development required infant link visual tactile motor representations objects according view


touching handling objects infants develop object permanence understanding objects solid permanent continue exist sight ref name bremner piaget 's sensorimotor stage comprised six sub stages see sensorimotor stages detail early stages development arises movements caused primitive reflexes ref name gruber ref discovery new behaviors results classical operant conditioning formation habits ref name gruber eight months infant able uncover hidden object persevere object moved piaget came conclusion infants lacked


new methods assessing infants' understanding world far precision subtlety piaget able time since many studies based methods suggest young infants understand far world first thought based recent findings researchers elizabeth spelke renee baillargeon proposed understanding object permanence learned rather comprises part innate cognitive capacities species research suggested young infants first six months life may possess


understanding numerous aspects world around including early numerical cognition ability represent number even compute outcomes addition subtraction operations ability infer goals people environment ability engage simple causal reasoning critical periods development critical periods infancy childhood development certain perceptual sensorimotor social language systems depends crucially environmental stimulation ref name siegler ref feral children genie deprived adequate stimulation fail acquire important skills unable learn later


childhood concept critical periods also well established neurophysiology work hubel wiesel among others developmental delays studies done look differences children developmental delays versus typical development normally compared one another mental age taken consideration still may differences developmentally delayed dd children vs typical development td behavioral emotional mental disorders compared children bigger difference normal developmental behaviors overall dds cause lower comparing dds tds


may accurate pairing dds specifically td children similar accurate levels behavioral differences considered normal certain ages look dds kids want see dds larger amount behavior normal group developmental delays tend contribute disorders difficulties td counterparts toddlerhood infants shift ages one two developmental stage known toddlerhood stage infant 's transition toddlerhood


highlighted self awareness developing maturity language use presence memory imagination toddlerhood babies begin learning walk talk make decisions important characteristic age period development language children learning communicate express emotions desires use vocal sounds babbling eventually words ref name upton ref self control also begins develop age children take initiative explore experiment learn making mistakes caretakers encourage toddlers try new things test limits help child become