deliberative rhetoric ''epideictic'' also known ceremonial concerned praise blame values right wrong demonstrating beauty skill present examples epideictic rhetoric would include eulogy wedding toast indian rhetoric india deep enriching past art rhetoric ''india 's struggle independence'' chandra et al offer vivid description culture sprang around newspaper village india early reading discussion focal point origin modern indian rhetorical movement much ancient greats


kautilya birbal likes indulged great deal discussion persuasion keith lloyd article rethinking rhetoric indian perspective implications ''nyaya sutra'' said much recital vedas likened recital ancient greek poetry lloyd proposed including ''ny ya tras'' field rhetorical studies exploring methods within historical context comparing approach traditional logical syllogism relating contemporary perspectives stephen toulmin kenneth burke chaim perelman ''nyaya'' sanskrit word

Humanities
Languages and literature
Linguistics
Rhetoric


means right refers science right wrong reasoning radhakrishnan moore p nbsp ''sutra'' also sanskrit word means string thread sutra refers collection aphorism form manual sutra short rule usually consisted one two sentences example sutra reality truth true irrespective whether know aware truth ''ny ya tras'' ancient indian sanskrit text composed aksapada gautama


foundational text nyaya school hindu philosophy date text composed biography author unknown estimated text composed th century bc nd century ad zimmer said text may composed one author period time radhakrishan moore placed origin third century bc nbsp though contents nyaya sutra certainly post christian era p nbsp vidyabhusana stated ancient school nyaya extended period


one thousand years beginning gautama bc ending vatsyayana ad nyaya provides significant insight indian rhetoric nyaya presents argumentative approach works rhetor decide argument addition proposes new approach thinking cultural tradition different western rhetoric also broadens view rhetoric relationship among human beings nyaya proposes enlightenment reality associated situations time places toulmin emphasizes situational dimension argumentative genre fundamental component


persuasive arguments rhetoric field intellectual debate aristotle 's definition rhetoric believe aristotle defines rhetoric ''on rhetoric'' art persuasion others think defines art judgment rhetoric art judgment would mean rhetor discerns available means persuasion choice aristotle also says rhetoric concerned judgment audience judges rhetor 's ethos one famous aristotelian doctrines idea topics also referred common topics commonplaces though term


wide range application memory technique compositional exercise example often referred seats argument list categories thought modes reasoning speaker could use generate arguments proofs topics thus heuristic inventional tool designed help speakers categorize thus better retain apply frequently used types argument example since often see effects like causes one way invent argument future effect discussing cause like


rhetorical topics derive aristotle 's belief certain predictable ways humans particularly non specialists draw conclusions premises based upon adapted dialectical topics rhetorical topics became central feature later rhetorical theorizing famously cicero 's work name cicero bust marcus tullius cicero romans oration became important part public life cicero bc chief among roman rhetoricians remains best known ancient orator orator spoke public produced treatises subject ''rhetorica ad herennium'' formerly


attributed cicero considered unknown authorship one significant works rhetoric still widely used reference today extensive reference use rhetoric middle ages renaissance achieved wide publication advanced school text rhetoric cicero considered one significant rhetoricians time charting middle path competing attic asiatic styles become considered second demosthenes among history 's orators works include early influential ''de inventione''


invention often read alongside ''ad herennium'' two basic texts rhetorical theory throughout middle ages renaissance ''de oratore'' fuller statement rhetorical principles dialogue form ''topics'' rhetorical treatment common topics highly influential renaissance ''brutus'' discussion famous orators ''orator'' defense cicero 's style cicero also left large body speeches letters would establish outlines latin eloquence style generations come rediscovery cicero 's speeches defense archias letters


atticus italians like petrarch part ignited cultural innovations known renaissance championed learning greek greek rhetoric contributed roman ethics linguistics philosophy politics emphasized importance forms appeal emotion humor stylistic range irony digression addition pure reasoning oratory perhaps significant contribution subsequent rhetoric education general argument orators learn specifics case ''hypothesis'' also general questions derived ''theses'' thus


giving speech defense poet whose roman citizenship questioned orator examine specifics poet 's civic status also examine role value poetry literature generally roman culture political life orator said cicero needed knowledgeable areas human life culture including law politics history literature ethics warfare medicine even arithmetic geometry cicero gave rise idea ideal orator well versed branches learning idea rendered


doctrines opinions many influential rhetoricians preceded institutes quintilian organizes rhetorical study stages education aspiring orator would undergo beginning selection nurse aspects elementary education training reading writing grammar literary criticism followed preliminary rhetorical exercises composition progymnasmata include maxims fables narratives comparisons finally full legal political speeches delivery speeches within context education entertainment purposes became widespread popular term declamation rhetorical training proper categorized


five canons would persist centuries academic circles ''inventio'' invention process leads development refinement argument arguments developed ' 'dispositio'' disposition arrangement used determine organized greatest effect usually beginning ''exordium'' speech content known structure determined next steps involve ''elocutio'' style ''pronuntiatio'' presentation ''memoria'' memory comes play speaker recalls elements speech ''actio'' delivery final step speech presented gracious


pleasing way audience nbsp grand style work available fragments medieval times discovery complete copy abbey st gall led emergence one influential works rhetoric renaissance quintilian 's work describes art rhetoric formation perfect orator politically active virtuous publicly minded citizen emphasis ethical application rhetorical training part reaction growing tendency roman schools toward standardization themes


techniques time rhetoric becoming divorced political decision making rhetoric rose culturally vibrant important mode entertainment cultural criticism movement known second sophistic development gave rise charge made quintilian others teachers emphasizing style substance rhetoric medieval enlightenment breakup western roman empire study rhetoric continued central study verbal arts study verbal arts went decline several centuries followed


eventually gradual rise formal education culminating rise medieval universities rhetoric transmuted period arts letter writing ''ars dictaminis'' sermon writing ''ars praedicandi'' part ''trivium'' rhetoric secondary study logic study highly scholastic students given repetitive exercises creation discourses historical subjects ' 'suasoriae'' classic legal questions ''controversiae'' although commonly regarded rhetorician st augustine trained rhetoric one time professor latin rhetoric


milan conversion christianity became interested using pagan arts spreading religion new use rhetoric explored fourth book ''de doctrina christiana'' laid foundation would become homiletics rhetoric sermon augustine begins book asking power eloquence efficacious pleading either erroneous cause right used righteous purposes iv one early concern medieval christian church attitude classical rhetoric jerome


complained horace psalms virgil gospels cicero apostles augustine also remembered arguing preservation pagan works fostering church tradition led conservation numerous pre christian rhetorical writings rhetoric would regain classical heights renaissance new writings advance rhetorical thought boethius brief ''overview structure rhetoric'' continues aristotle 's taxonomy placing rhetoric subordination philosophical argument dialectic introduction arab scholarship european relations muslim empire particular al andalus renewed


interest aristotle classical thought general leading historians call th century renaissance number medieval grammars studies poetry rhetoric appeared late medieval rhetorical writings include st thomas aquinas matthew vendome ''ars versificatoria'' geoffrey vinsauf ''poetria nova'' pre modern female rhetoricians outside socrates' friend aspasia rare medieval rhetoric produced women either religious orders julian norwich well connected christine de pizan occur always recorded writing


cambridge university doctoral dissertation english canadian marshall mcluhan surveys verbal arts approximately time cicero time thomas nashe dissertation still noteworthy undertaking study history verbal arts together trivium even though developments surveys studied greater detail since undertook study noted mcluhan became one widely publicized thinkers th century important note scholarly roots study history rhetoric


dialectic another interesting record medieval rhetorical thought seen many animal debate poems popular england continent middle ages owl nightingale th century geoffrey chaucer 's parliament fowls sixteenth century walter j ong 's article humanism ''new catholic encyclopedia'' surveys renaissance humanism defined broadly disfavoring medieval scholastic logic dialectic favoring instead study classical latin style grammar philology rhetoric reprinted ong 's ''faith contexts'' scholars press portrait


erasmus rotterdam one influential figure rebirth interest classical rhetoric erasmus work ''de duplici copia verborum et rerum'' also known ''copia foundations abundant style'' widely published went editions throughout europe became one basic school texts subject treatment rhetoric less comprehensive classic works antiquity provides traditional treatment ' 'res verba'' matter form first book treats subject elocutio showing student use schemes tropes second


called adoxography required pupils compose passages praise useless things juan luis vives also helped shape study rhetoric england spaniard appointed lectureship rhetoric oxford cardinal wolsey entrusted henry viii one tutors mary vives fell disfavor henry viii divorced catherine aragon left england best known work book education '''' published writings rhetoric included '''' '''' rhetoric letter


writing '''' likely many well known english writers exposed works erasmus vives well classical rhetoricians schooling conducted latin english often included study greek placed considerable emphasis rhetoric see example tw baldwin 's '''' vols university illinois press mid th century saw rise vernacular rhetorics written english rather classical languages adoption works english slow however due strong orientation toward latin greek leonard


cox 's ''the art crafte rhetoryke'' c second edition published considered earliest text rhetorics english part translation work philipp melanchthon successful early text thomas wilson 's '''' presents traditional treatment rhetoric instance wilson presents five canons rhetoric invention disposition elocutio memoria utterance actio notable works included angel day 's '''' george puttenham 's '''' richard rainholde 's '''' period movement began would change


organization school curriculum protestant especially puritan circles led rhetoric losing central place french scholar pierre de la ram e latin petrus ramus dissatisfied saw overly broad redundant organization trivium proposed new curriculum scheme things five components rhetoric longer lived common heading rhetoric instead invention disposition determined fall exclusively heading dialectic style delivery memory remained rhetoric see walter j ong ''ramus


method decay dialogue art discourse art reason'' harvard university press reissued university chicago press new foreword adrian johns ramus martyred french wars religion teachings seen inimical catholicism short lived france found fertile ground netherlands germany england one ramus' french followers audomarus talaeus omer talon published rhetoric ''institutiones oratoriae'' work provided simple presentation rhetoric emphasized treatment style became popular


mentioned john brinsley 's ''ludus literarius '' many ramist rhetorics followed next half century th century approach became primary method teaching rhetoric protestant especially puritan circles john milton wrote textbook logic dialectic latin based ramus' work ramism could exert influence established catholic schools universities remained loyal scholasticism new catholic schools universities founded members religious orders known society jesus


oratorians seen jesuit curriculum use right th century across christian world known ratio studiorum claude pavur sj recently translated english latin text parallel column page st louis institute jesuit sources influence cicero quintilian permeates ratio studiorum lenses devotion militancy counter reformation ''ratio'' indeed imbued sense divine incarnate logos rhetoric eloquent


humane means reach devotion action christian city absent ramist formalism ratio rhetoric answer st ignatius loyola 's practice devotion spiritual exercises complex oratorical prayer system absent ramism seventeenth century new england harvard college founded ramus followers dominated perry miller shows ''the new england mind seventeenth century'' harvard university press however england several writers influenced course rhetoric th century many carrying forward dichotomy


preoccupied style rather weight matter worth subject soundness argument life invention depth judgment matters style proposed style conform subject matter audience simple words employed whenever possible style agreeable thomas hobbes also wrote rhetoric along shortened translation aristotle 's ''rhetoric'' hobbes also produced number works subject sharply contrarian many subjects hobbes like bacon also promoted simpler natural style


used figures speech sparingly perhaps influential development english style came work royal society founded set committee improve english language among committee 's members john evelyn thomas sprat john dryden sprat regarded fine speaking disease thought proper style reject amplifications digressions swellings style instead return back primitive purity shortness ''history royal society'' work committee never went beyond planning


john dryden often credited creating exemplifying new modern english style central tenet style proper occasion subject persons advocated use english words whenever possible instead foreign ones well vernacular rather latinate syntax prose poetry became exemplars new style eighteenth century arguably one influential schools rhetoric time scottish belletristic rhetoric exemplified professors rhetoric hugh blair whose lectures rhetoric


college professor rhetoric new york central college modern turn th century revival rhetorical study manifested establishment departments rhetoric speech academic institutions well formation national international professional organizations jim kuypers andrew king suggest early interest rhetorical studies movement away elocution taught departments english united states attempt refocus rhetorical studies away delivery civic engagement collectively write twentieth


century rhetorical studies offered understanding rhetoric demonstrated rich complexity rhetorical scholars understood nature rhetoric theorists generally agree significant reason revival study rhetoric renewed importance language persuasion increasingly mediated environment th century see linguistic turn st century media focus wide variations analyses political rhetoric consequences rise advertising mass media photography telegraphy radio film brought rhetoric prominently


people 's lives recently term rhetoric applied media forms verbal language eg visual rhetoric scholars also recently highlighted importance temporal rhetorics temporal turn rhetorical theory practice notable theorists cha perelman philosopher law studied taught lived life brussels among important argumentation theorists th century chief work ''trait de l'argumentation nbsp la nouvelle rh torique'' lucie olbrechts tyteca translated english ''the new rhetoric treatise


argumentation'' john wilkinson purcell weaver perelman olbrechts tyteca move rhetoric periphery center argumentation theory among influential concepts dissociation universal audience quasi logical argument presence kenneth burke rhetorical theorist philosopher poet many works central modern rhetorical theory ''a rhetoric motives'' ''a grammar motives'' ''language symbolic action'' ''counterstatement'' among influential concepts identification consubstantiality dramatistic pentad described rhetoric use language symbolic means inducing cooperation


beings nature respond symbols relation aristotle 's theory aristotle interested constructing rhetoric burke interested debunking edwin black rhetorical critic best known book ''rhetorical criticism study method'' criticized dominant neo aristotelian tradition american rhetorical criticism little common aristotle besides recurrent topics discussion vaguely derivative view rhetorical discourse furthermore contended rhetorical scholars focusing primarily aristotelian logical forms often overlooked important alternative types discourse


also published several highly influential essays including secrecy disclosure rhetorical forms second persona note theory practice rhetorical criticism marshall mcluhan media theorist whose theories whose choice objects study important study rhetoric mcluhan 's famous dictum medium message highlights significance medium scholar history theory rhetoric widely publicized th century mcluhan richards literary critic rhetorician ''the philosophy rhetoric''


important text modern rhetorical theory work defined rhetoric study misunderstandings remedies introduced influential concepts ''tenor'' ' 'vehicle'' describe components metaphor main idea concept compared groupe interdisciplinary team contributed renovation elocutio context poetics modern linguistics significantly ''rh torique g n rale'' translated english ''a general rhetoric'' paul b burrell et edgar slotkin johns hopkins university press ''rh torique de la po sie'' stephen toulmin


anglo majority indian mexican culture ref name lunsford notable works include sinister wisdom borderlands la fronters new mestiza la prieta gertrude buck one prominent female rhetorical theorists also composition educator scholastic contributions present status rhetorical theory inspire egalitarian status hearers speakers achieve goal communication another piece edited newton scott brief english grammar troubled common prescriptive grammar book received lot praise critiques descriptive nature social responsibility


non mainstream beliefs krista ratcliffe prominent feminist critical race rhetorical theorist book ''rhetorical listening identification gender whiteness'' ratcliffe puts forward theory model rhetorical listening trope interpretive invention particularly code cross cultural conduct ref name ratcliffe k ''rhetorical listening identification gender whiteness'' southern illinois university press ref book described taking field feminist rhetoric new place movement away argumentative rhetoric towards undivided logos wherein speaking listening reintegrated reviewers also acknowledged theoretical contributions


ratcliffe makes towards model appreciating acknowledging difference instances cross cultural communication sonja k foss rhetorical scholar educator discipline communication research teaching interests contemporary rhetorical theory criticism feminist perspectives communication incorporation marginalized voices rhetorical theory practice visual rhetoric methods analysis criticism seen method rhetoric analyzed variety methods theories one method criticism using criticism analyze instances rhetoric called rhetorical criticism see section


methods admit varying degrees personality criticism whole near indeterminate contingent personal end methodological scale consequence placement neither possible desirable criticism fixed system critical techniques objectified critics interchangeable purposes scientific replication rhetorical criticism serve handmaiden quasi scientific theory idea critical method personally expressive systematized jim kuypers sums idea criticism art following manner


arguments advanced within discourse important identify specific semiotic strategies employed speaker accomplish specific persuasive goals therefore rhetorical analyst discovers use language particularly important achieving persuasion typically moves onto question work effects particular use rhetoric audience effect provide clues speaker 's writer 's objectives scholars partial rhetorical analysis defer judgments rhetorical success words


argument strategies used writing describes four argument analogy argument absurdity thought experiments inference best explanation example strategies include ethos logos pathos kairos criticism modern rhetorical criticism explores relationship text context instance rhetoric relates circumstances since aim rhetoric persuasive level rhetoric question persuades audience must analyzed later criticized determining extent text persuasive one may explore text 's


considered extant situation ie agenda spin additional theoretical approaches following neo aristotelian approaches criticism scholars began derive methods disciplines history philosophy social sciences importance critics' personal judgment decreased explicit coverage analytical dimension criticism began gain momentum throughout methodological pluralism replaced singular neo aristotelian method methodological rhetorical criticism typically done deduction broad method used examine specific case rhetoric types include ''ideological criticism'' nbsp critics engage rhetoric


interpretive lens discourse short make certain facts noticeable others particularly useful analyzing products news media ''genre criticism'' nbsp method assumes certain situations call similar needs expectations within audience therefore calling certain types rhetoric studies rhetoric different times locations looking similarities rhetorical situation rhetoric responds examples include eulogies inaugural addresses declarations war ''narrative criticism'' nbsp narratives help organize experiences order endow meaning historical events transformations narrative criticism


focuses way types discourse react situational exigencies problems demands constraints means modern rhetorical criticism based rhetorical case object persuades defines constructs audience modern terms considered rhetoric includes limited speeches scientific discourse pamphlets literary work works art pictures contemporary rhetorical criticism maintained aspects early neo aristotelian thinking close reading attempts explore organization stylistic structure rhetorical object using close textual analysis means rhetorical critics use tools


classical rhetoric literary analysis evaluate style strategy used communicate argument purpose criticism rhetorical criticism serves several purposes functions first rhetorical criticism hopes help form improve public taste helps educate audiences develops better judges rhetorical situations reinforcing ideas value morality suitability rhetorical criticism thus contribute audience 's understanding society according jim kuypers dual purpose performing criticism primarily enhance appreciation understanding w e wish enhance


others' understanding rhetorical act wish share insights others enhance appreciation rhetorical act hollow goals quality life issues improving understanding appreciation critic offer new potentially exciting ways others see world understanding also produce knowledge human communication theory help us better govern interactions others criticism humanizing activity explores highlights qualities make us human animal rhetoric rhetoric practiced social


animals variety ways example birds use song various animals warn members species danger chimpanzees capacity deceive communicative keyboard systems deer stags compete attention mates might understood rhetorical actions attempts persuading meaningful actions utterances also seen rhetorical fundamentals shared humans animals study animal rhetoric described biorhetorics self awareness required practice rhetoric might difficult notice acknowledge animals however animals capable


acknowledging mirror therefore might understood self aware engaged rhetoric practicing form language therefore rhetoric anthropocentrism plays significant role human animal relationships reflecting perpetuating binaries humans assumed beings extraordinary qualities animals regarded beings lack qualities dualism manifested forms well reason sense mind body ideal phenomenon first category pair reason mind ideal represents belongs humans


animals creatures without extraordinarily qualities exist specific animals sort phr n sis confers capabilities learn receive instruction rudimentary understanding significant signs animals practice deliberative judicial epideictic rhetoric deploying ethos logos pathos gesture preen sing growl since animals offer models rhetorical behavior interaction physical even instinctual perhaps less artful getting rid accustomed focus verbal language consciousness concepts help people interested rhetoric communication matters promote human animals' rhetoric automatic detection


rhetorical figures natural language processing developed since late nineties interest automatically detecting rhetorical figures major focus detect specific figures chiasmus epanaphora epiphora using classifiers trained labeled data major shortcoming achieving high accuracy systems shortage labeled data tasks recent advances language modeling shot learning may possible detect rhetorical figures less data academic journals '' https wwwamericanforensicsassocorg argumentation advocacy argumentation advocacy '' '' https ccccncteorg cccc ccc college composition communication '' '' https ncteorg resources journals college english


college english '' '' http enculturationnet enculturation '' '' http harlotoftheartsorg indexphp harlot harlot '' '' https kairostechnorhetoricnet kairos '' '' https cfshrcorg peitho journal peitho '' '' http wwwpresenttensejournalorg present tense '' '' http relevantrhetoriccom relevant rhetoric '' '' https ojsmsupressmsuedu indexphp rpa index rhetoric public affairs '' '' https wwwtandfonlinecom loi hrhr rhetoric review '' '' https associationdatabasecom aws rsa pt sp rsq rhetoric society quarterly rsq '' '' https xchangesorg xchanges '' see also artes liberales casuistry civic humanism chironomia composition studies conversation theory critical thinking demagogy digital rhetoric discourse discourse analysis formal fallacy figure thought glossary rhetorical terms grammarian greco roman world language thought multimodality new rhetoric pedagogy persuasion technology phenomenology psychological manipulation propaganda rhetoric science rhetoric health medicine rhetorical operations rhetorical reason rogerian argument rule three semiology speechwriter technical communication


miscellaneous terms ad captandum allusion antimetabole aphesis apologue aposiopesis archaism atticism brachyology cacophony catachresis chiasmus circumlocution climax conceit dynamic formal equivalence eloquence enthymeme euphemism figure speech hendiadys hysteron proteron idiom innuendo ipse dixit kenning literary topos mediation merism metanoia negation parable paraphrase paraprosdokian pericope period perissologia praeteritio proverb representation rhetorical device rhetorical stance rhetorical velocity soundbite synchysis synesis synonymia tautology tertium comparationis truism word play political speech resources list political slogans list speeches notes references citations sources primary sources ''locus classicus'' greek


latin primary texts rhetoric loeb classical library harvard university press published english translation facing page aristotle '' https wwwperseustuftsedu cgi bin ptextlookup aristot rh rhetoric '' cicero http wwwthelatinlibrarycom cicero inventioneshtml ''de inventione '' latin nbsp '' https wwwperseustuftsedu cgi bin ptextlookup cic de orat de oratore '' latin demosthenes ''orations'' https wwwperseustuftsedu cgi bin ptextlookup dem greek http onlinebookslibraryupennedu webbin gutbook lookupnum english cornificius '' https webarchiveorg web http dobcunipvit scrineum wight herm htm de ratione dicendi '' latin isocrates '' https wwwperseustuftsedu cgi bin ptextlookup isoc sophists '' henry peacham '' https wwwperseustuftsedu cgi bin ptextdoc perseus atext garden eloquence '' george puttenham '' http rpolibraryutorontoca display displayprosecfmprosenum arte poesie '' representative poetry online quintilian '' https penelopeuchicagoedu thayer e roman texts quintilian institutio oratoria homehtml institutio oratoria '' johannes susenbrotus '' http visualiseurbnffr visualiseurdestination gallica numm epitome troporum '' thomas wilson '' https webarchiveorg web http darkwinguoregonedu rbear arte artehtm arte rhetorique '' secondary sources ralf van b hren ''die werke


''the great sophists periclean athens'' french orig english trans clarendon press oxford university press william safire ''lend ears great speeches history'' amelie oksenberg rorty ''aristotle 's rhetoric'' los angeles united states america reading andresen volker ''speak well public steps succeed'' connors robert lisa ede andrea lunsford eds ''essays classical rhetoric modern discourse'' festschrift honor edward p j corbett carbondale southern illinois univ press duffy bernard k richard leeman eds ''american voices encyclopedia contemporary orators'' westport ct


greenwood garver eugene aristotle 's rhetoric art character chicago university chicago press gunderson erik ''the cambridge companion ancient rhetoric'' cambridge uk cambridge univ press howell wilbur samuel eighteenth century british logic rhetoric princeton nj princeton univ press kieth william lundberg christian ''the essential guide rhetoric'' boston jansinski james ''sourcebook rhetoric'' sage publications inc kennedy george ''aristotle rhetoric'' oxford oxford university press kennedy george ''classical rhetoric christian secular tradition ancient modern times'' chapel hill univ north


oxford univ press steel catherine ''roman oratory'' greece rome new surveys classics cambridge uk cambridge univ press vickers brian''in defence rhetoric'' oxford clarendon walker jeffrey ''rhetoric poetics antiquity'' new york oxford univ press external links https americanrhetoriccom american rhetoric power oratory united states brian vickers rhetoric https booksgooglecom booksid pte bvhzcwc pg pa dq brian vickers rhetoric ''cambridge companion english poetry'' wikibooks rhetoric composition mitchell anthony '' http wwwcrmbuyercom story html primer business rhetoric '' discusses messages dumbed make acceptable wide audiences newall paul '' https webarchiveorg web http wwwgalilean libraryorg int html introduction


rhetoric rhetorical figures '' aimed beginners http tecnicaretoricablogspotpt cnica ret rica um blog para oradores https wwwbbccouk programmes p rhetoric bbc radio discussion angie hobbs thomas healy ceri sullivan ''in time'' oct applied linguistics communication studies critical thinking skills history logic history philosophy intellectual history narratology philosophical logic philosophy logic philosophy language


credit risk accidents natural causes disasters deliberate attack adversary events uncertain unpredictable root cause two types events ie negative events classified risks positive events classified opportunities risk management standards developed various institutions including project management institute national institute standards technology actuarial societies iso standards ref name voc ref ref name iso ref methods definitions goals vary widely according whether risk management method context project management security engineering industrial processes financial portfolios actuarial assessments public health

Applied science
Business
Risk management


safety strategies manage threats uncertainties negative consequences typically include avoiding threat reducing negative effect probability threat transferring part threat another party even retaining potential actual consequences particular threat opposite strategies used respond opportunities uncertain future states benefits certain risk management standards criticized measurable improvement risk whereas confidence estimates decisions seems increase ref name risk management pg introduction risk management


appears scientific management literature since became formal science articles books risk management title also appear library searches research initially related finance insurance widely used vocabulary risk management defined ''iso guide '' risk management vocabulary ref name voc ideal risk management prioritization process followed whereby risks greatest loss impact greatest probability occurring handled first risks lower probability occurrence lower loss handled descending order


practice process assessing overall risk difficult balancing resources used mitigate risks high probability occurrence lower loss versus risk high loss lower probability occurrence often mishandled intangible risk management identifies new type risk probability occurring ignored organization due lack identification ability example deficient knowledge applied situation knowledge risk materializes relationship risk appears ineffective collaboration occurs process engagement risk may issue


ineffective operational procedures applied risks directly reduce productivity knowledge workers decrease cost effectiveness profitability service quality reputation brand value earnings quality intangible risk management allows risk management create immediate value identification reduction risks reduce productivity opportunity cost represents unique challenge risk managers difficult determine put resources toward risk management use resources elsewhere ideal risk management minimizes spending manpower resources also minimizes negative effects risks risk defined possibility


management''' knowledge area defined project management body knowledge pmbok consists following processes '''plan risk management''' defining conduct risk management activities '''identify risks''' identifying individual project risks well sources '''perform qualitative risk analysis''' prioritizing individual project risks assessing probability impact '''perform quantitative risk analysis''' numerical analysis effects '''plan risk responses''' developing options selecting strategies actions '''implement risk responses''' implementing agreed upon risk response plans sup th sup ed pmbok process included


activity monitor control process later separated distinct process pmbok sup th sup ed ref name morcov morcov stefan managing positive negative complexity design validation project complexity management framework ku leuven university available https liriaskuleuvenbe retrieve ref '''monitor risks''' monitoring implementation process known monitor control previous pmbok sup th sup ed also included ''implement risk responses'' process principles international organization standardization iso identifies following principles risk management ref name iso ref risk management create value resources expended mitigate


risk less consequence inaction integral part organizational processes part decision making process explicitly address uncertainty assumptions systematic structured process based best available information tailorable take human factors account transparent inclusive dynamic iterative responsive change capable continual improvement enhancement continually periodically assessed mild versus wild risk benoit mandelbrot distinguished mild wild risk argued risk assessment management must fundamentally different two types


risk mild risk follows normal near normal probability distributions subject regression mean law large numbers therefore relatively predictable wild risk follows fat tailed distributions eg pareto power law distributions subject regression tail infinite mean variance rendering law large numbers invalid ineffective therefore difficult impossible predict common error risk assessment management underestimate wildness risk assuming risk mild fact wild must avoided risk assessment management


company weather airport problem analysis risks related identified threats example threat losing money threat abuse confidential information threat human errors accidents casualties threats may exist various entities important shareholders customers legislative bodies government either source problem known events source may trigger events lead problem investigated example stakeholders withdrawing project may endanger funding project confidential


information may stolen employees even within closed network lightning striking aircraft takeoff may make people board immediate casualties chosen method identifying risks may depend culture industry practice compliance identification methods formed templates development templates identifying source problem event common risk identification methods objectives based risk identification organizations project teams objectives event may prevent objective achieved identified risk scenario based risk identification scenario analysis different scenarios created scenarios


may alternative ways achieve objective analysis interaction forces example market battle event triggers undesired scenario alternative identified risk see futures studies methodology used futurists taxonomy based risk identification taxonomy taxonomy based risk identification breakdown possible risk sources based taxonomy knowledge best practices questionnaire compiled answers questions reveal risks common risk checking several industries lists known risks available risk list


checked application particular situation risk charting method combines approaches listing resources risk threats resources modifying factors may increase decrease risk consequences wished avoid creating matrix headings enables variety approaches one begin resources consider threats exposed consequences alternatively one start threats examine resources would affect one begin consequences determine combination threats resources


risk management plan even short term positive improvement long term negative impacts take turnpike example highway widened allow traffic traffic capacity leads greater development areas surrounding improved traffic capacity time traffic thereby increases fill available capacity turnpikes thereby need expanded seemingly endless cycles many engineering examples expanded capacity function soon filled increased demand since expansion comes cost resulting growth could become unsustainable without forecasting management fundamental


management decisions may prioritized within overall company goals thus several theories attempts quantify risks numerous different risk formulae exist perhaps widely accepted formula risk quantification rate probability occurrence multiplied impact event equals risk magnitude risk options risk mitigation measures usually formulated according one following major risk options design new business process adequate built risk control containment measures start periodically assess risks accepted ongoing processes normal


feature business operations modify mitigation measures transfer risks external agency eg insurance company avoid risks altogether eg closing particular high risk business area later research shown financial benefits risk management less dependent formula used dependent frequency risk assessment performed business imperative able present findings risk assessments financial market schedule terms robert courtney jr ibm proposed formula presenting risks financial terms courtney formula


accepted official risk analysis method us governmental agencies formula proposes calculation ale annualized loss expectancy compares expected loss value security control implementation costs cost benefit analysis potential risk treatments risks identified assessed techniques manage risk fall one four major categories avoidance eliminate withdraw become involved reduction optimize mitigate sharing transfer outsource insure retention accept budget ideal use risk control strategies may possible may involve


business avoid legal liability one example avoiding airplane flights fear hijacking avoidance may seem like answer risks avoiding risks also means losing potential gain accepting retaining risk may allowed entering business avoid risk loss also avoids possibility earning profits increasing risk regulation hospitals led avoidance treating higher risk conditions favor patients presenting lower risk risk reduction risk reduction optimization involves reducing severity loss


likelihood loss occurring example sprinklers designed put fire reduce risk loss fire method may cause greater loss water damage therefore may suitable halon fire suppression systems may mitigate risk cost may prohibitive strategy acknowledging risks positive negative optimizing risks means finding balance negative risk benefit operation activity risk reduction effort applied effectively applying health safety environment


hse management standards organizations achieve tolerable levels residual risk modern software development methodologies reduce risk developing delivering software incrementally early methodologies suffered fact delivered software final phase development problems encountered earlier phases meant costly rework often jeopardized whole project developing iterations software projects limit effort wasted single iteration outsourcing could example risk sharing strategy outsourcer demonstrate higher capability managing reducing risks example company may outsource


software development manufacturing hard goods customer support needs another company handling business management way company concentrate business development without worry much manufacturing process managing development team finding physical location center risk sharing briefly defined sharing another party burden loss benefit gain risk measures reduce risk term 'risk transfer' often used place risk sharing mistaken belief


transfer risk third party insurance outsourcing practice insurance company contractor go bankrupt end court original risk likely still revert first party terminology practitioners scholars alike purchase insurance contract often described transfer risk however technically speaking buyer contract generally retains legal responsibility losses transferred meaning insurance may described accurately post event compensatory mechanism example personal injuries insurance policy


transfer risk car accident insurance company risk still lies policy holder namely person accident insurance policy simply provides accident event occurs involving policy holder compensation may payable policy holder commensurate suffering damage methods managing risk fall multiple categories risk retention pools technically retaining risk group spreading whole group involves transfer among individual members group different traditional


insurance premium exchanged members group front instead losses assessed members group risk retention risk retention involves accepting loss benefit gain risk incident occurs true self insurance falls category risk retention viable strategy small risks cost insuring risk would greater time total losses sustained risks avoided transferred retained default includes risks large


catastrophic either cannot insured premiums would infeasible war example since property risks insured war loss attributed war retained insured also amounts potential loss risk amount insured retained risk may also acceptable chance large loss small cost insure greater coverage amounts great would hinder goals organization much risk management plan select appropriate controls


countermeasures mitigate risk risk mitigation needs approved appropriate level management instance risk concerning image organization top management decision behind whereas management would authority decide computer virus risks risk management plan propose applicable effective security controls managing risks example observed high risk computer viruses could mitigated acquiring implementing antivirus software good risk management plan contain schedule control implementation responsible persons actions according


iso iec stage immediately completion risk assessment phase consists preparing risk treatment plan document decisions identified risks handled mitigation risks often means selection security controls documented statement applicability identifies particular control objectives controls standard selected implementation implementation follows planned methods mitigating effect risks purchase insurance policies risks decided transferred


risk level changes business environment example information risks good example rapidly changing business environment limitations prioritizing ''risk management processes'' highly could keep organization ever completing project even getting started especially true work suspended risk management process considered complete also important keep mind distinction risk uncertainty risk measured impacts probability risks improperly assessed prioritized time wasted dealing risk losses


likely occur spending much time assessing managing unlikely risks avoided unlikely events occur risk unlikely enough occur may better simply retain risk deal result loss fact occur qualitative risk assessment subjective lacks consistency primary justification formal risk assessment process legal bureaucratic areas finance applied financial accounting ''risk management'' technique measuring monitoring controlling financial operational risk firm 's balance


sheet traditional measure value risk var also measures like profit risk par margin risk basel ii framework breaks risks market risk price risk credit risk operational risk also specifies methods calculating capital requirements components information technology information technology risk management includes incident handling action plan dealing intrusions cyber theft denial service fire floods security related events according sans institute six step process preparation identification containment eradication recovery lessons learned contractual


risk management concept contractual risk management emphasises use risk management techniques contract deployment ie managing risks accepted entry contract norwegian academic petri keskitalo defines contractual risk management practical proactive systematical contracting method uses contract planning governance manage risks connected business activities article samuel greengard published two us legal cases mentioned emphasise importance strategy dealing risk ref name greengard greengard https wwwnxtbookcom nxtbooks acec engineeringinc indexphp p difference details engineering inc september october


pages ref udc v ch hill deals risk professional advisor signs indemnification provision including acceptance duty defend may thereby pick legal costs defending client subject claim third party witt v la gorce country club deals effectiveness limitation liability clause may certain jurisdictions found ineffective greengard recommends using industry standard contract language much possible reduce risk much possible rely clauses use


subject established court interpretation number years ref name greengard memory institutions museums libraries archives enterprise enterprise risk management risk defined possible event circumstance negative influences enterprise question impact existence resources human capital products services customers enterprise well external impacts society markets environment financial institution enterprise risk management normally thought combination credit risk interest rate risk


asset liability management liquidity risk market risk operational risk general case every probable risk pre formulated plan deal possible consequences ensure ''contingency'' risk becomes ''liability'' information average cost per employee time cost accrual ratio project manager estimate cost associated risk arises estimated multiplying employee costs per unit time estimated time lost ''cost impact'' ''c'' ''c cost accrual ratio s'' probable increase time associated


risk'' ''rc'' rc pc pcars pscar sorting value puts highest risks budget first see concerns ' 'schedule variance'' function illustrated equation risk project process due either special cause variation common cause variation requires appropriate treatment iterate concern extremal cases equivalent list immediately enterprise security esrm security program management approach links security activities enterprise 's mission business


integral part medical device design development production processes evaluation field experience applicable types medical devices evidence application required regulatory bodies us fda management risks medical devices described international organization standardization iso iso medical devices application risk management medical devices product safety standard standard provides process framework associated requirements management responsibilities risk analysis evaluation risk controls lifecycle risk management guidance application


risks mitigated design labeling medical device ie labeling longer used mitigate risk typical risk analysis evaluation techniques adopted medical device industry include hazard analysis fault tree analysis fta failure mode effects analysis fmea hazard operability study hazop risk traceability analysis ensuring risk controls implemented effective ie tracking risks identified product requirements design specifications verification validation results etc fta analysis requires diagramming software fmea analysis done using spreadsheet program also integrated medical device


risk management solutions https wwwfdagov medicaldevices deviceregulationandguidance guidancedocuments ucm htm draft guidance fda introduced another method named safety assurance case medical device safety assurance analysis safety assurance case structured argument reasoning systems appropriate scientists engineers supported body evidence provides compelling comprehensible valid case system safe given application given environment guidance safety assurance case expected safety critical devices eg infusion devices part pre market clearance submission eg k fda introduced another draft guidance expecting


medical device manufacturers submit cybersecurity risk analysis information project management project risk management must considered different phases acquisition beginning project advancement technical developments threats presented competitor 's projects may cause risk threat assessment subsequent evaluation alternatives see analysis alternatives decision made project begun familiar project management applications used planning risk managed particular project plans include risk management tasks responsibilities activities budget assigning risk officer


team member project manager responsible foreseeing potential project problems typical characteristic risk officer healthy skepticism maintaining live project risk database risk following attributes opening date title short description probability importance optionally risk may assigned person responsible resolution date risk must resolved creating anonymous risk reporting channel team member possibility report risks foresees project preparing mitigation plans risks


chosen mitigated purpose mitigation plan describe particular risk handled done avoid minimize consequences becomes liability summarizing planned faced risks effectiveness mitigation activities effort spent risk management megaprojects infrastructure megaprojects sometimes also called major programs large scale investment projects typically costing billion per project megaprojects include major bridges tunnels highways railways airports seaports power plants dams wastewater projects coastal flood protection schemes oil natural


gas extraction projects public buildings information technology systems aerospace projects defense systems megaprojects shown particularly risky terms finance safety social environmental impacts risk management therefore particularly pertinent megaprojects special methods special education developed risk management natural disasters important assess risk regard natural disasters like floods earthquakes outcomes natural disaster risk assessment valuable considering future repair costs business interruption losses downtime effects environment insurance costs proposed costs


reducing risk sendai framework disaster risk reduction international accord set goals targets disaster risk reduction response natural disasters regular international disaster risk conferences davos deal integral risk management several tools used assess risk risk management natural disasters climate events including geospatial modeling key component land change science modeling requires understanding geographic distributions people well ability calculate likelihood natural disaster occurring wilderness


management risks persons property wilderness remote natural areas developed increases outdoor recreation participation decreased social tolerance loss organizations providing commercial wilderness experiences align national international consensus standards training equipment ansi nasbla boating uiaa ice climbing tools european norm mountaineering equipment association experiential education offers accreditation wilderness adventure programs wilderness risk management conference provides access best practices specialist organizations provide wilderness risk management consulting training book ''outdoor


leadership education'' climber outdoor educator author ari schneider notes outdoor recreation inherently risky way completely eliminate risk however explains good thing outdoor education programs according schneider optimal adventure achieved real risk managed perceived risk maintained order keep actual danger low sense adventure high ref name ref text outdoor safety risk management outdoor leaders published new zealand mountain safety council provides view wilderness risk management new zealand


due increasing awareness information security simply one facet multitude risks relevant real world processes supports cybersecurity tied closely advancement technology lags long enough incentives like black markets evolve new exploits discovered end sight advancement technology expect cybersecurity isaca 's ''risk it'' framework ties risk enterprise risk management duty care risk analysis docra evaluates risks safeguards considers


interests parties potentially affected risks petroleum natural gas offshore oil gas industry operational risk management regulated safety case regime many countries hazard identification risk assessment tools techniques described international standard iso organisations iadc international association drilling contractors publish guidelines health safety environment hse case development based iso standard diagrammatic representations hazardous events often expected governmental regulators part risk management safety case submissions


contamination relation pharmaceutical products cleanroom manufacturing environments ref name sandle ref risk communication see also enterprise risk management financial risk management operational risk management supply chain risk management project risk management risk management risk assessment risk analysis business continuity disaster risk reduction catastrophe modeling risk management security management stranded asset optimism bias pest risk analysis risk appetite roy 's safety first criterion precautionary principle representative heuristic risk management tools reference class forecasting social risk management environmental risk management authority nz international institute risk safety management loss control consultant national safety council usa references external links https wwwacqosdmil se docs riopdf dod risk issue


first four partial sums fourier series square wave fourier series important tool real analysis mathematics '' 'real analysis''' branch mathematical analysis studies behavior real numbers sequences series real numbers real functions particular properties real valued sequences functions real analysis studies include convergence limits continuity smoothness differentiability integrability real analysis distinguished complex analysis deals study complex numbers functions scope construction real numbers theorems real analysis rely

Formal science
Mathematics
Pure mathematics
Analysis
Real analysis


properties real number system must established real number system consists uncountable set math mathbb r math together two binary operations denoted order denoted operations make real numbers field along order ordered field real number system unique ''complete ordered field'' sense complete ordered field isomorphic intuitively completeness means 'gaps' real numbers property distinguishes real numbers ordered fields eg rational


numbers math mathbb q math critical proof several key properties functions real numbers completeness reals often conveniently expressed ''least upper bound property'' see order properties real numbers real numbers various lattice theoretic properties absent complex numbers also real numbers form ordered field sums products positive numbers also positive moreover ordering real numbers total real numbers least upper bound property blockquote ''every nonempty subset math mathbb r math


upper bound least upper bound also real number'' blockquote order theoretic properties lead number fundamental results real analysis monotone convergence theorem intermediate value theorem mean value theorem however results real analysis stated real numbers many results generalized mathematical objects particular many ideas functional analysis operator theory generalize properties real numbers generalizations include theories riesz spaces positive operators also mathematicians consider real imaginary parts


complex sequences pointwise evaluation operator sequences topological properties real numbers many theorems real analysis consequences topological properties real number line order properties real numbers described closely related topological properties topological space real numbers ' 'standard topology'' order topology induced order math math alternatively defining ''metric'' ' 'distance function'' math mathbb r times mathbb r mathbb r geq math using absolute value function real numbers become prototypical example metric space


bidirectional sequences indexed set integers including negative indices interest real analysis '''' 'real valued sequence''''' indexed natural numbers map math n r n mapsto n math math n n math referred '''''term''''' less commonly '''''element''''' sequence sequence rarely denoted explicitly function instead convention almost always notated ordered tuple individual terms general term enclosed parentheses math display block n n n n


chained inequalities still hold math leq math math geq math replaced given sequence math n math another sequence math b k math '''' 'subsequence''''' math n math math b k n k math positive integers math k math math n k math strictly increasing sequence natural numbers limits convergence roughly speaking '''limit''' value function sequence approaches input index approaches value value include symbols math pm infty math addressing behavior function sequence variable increases decreases without bound idea limit fundamental


calculus mathematical analysis general formal definition used turn define notions like continuity derivatives integrals fact study limiting behavior used characteristic distinguishes calculus mathematical analysis branches mathematics concept limit informally introduced functions newton leibniz end th century building infinitesimal calculus sequences concept introduced cauchy made rigorous end th century bolzano weierstrass gave modern definition


follows '''definition''' let math f math real valued function defined nowrap math e subset mathbb r math say ''''' math f x math tends math l math math x math approaches math x math ''''' '''''the limit math f x math math x math approaches math x math math l math ''''' math varepsilon math exists math delta math math x e math math x x delta math implies math f x l varepsilon math write symbolically math display block f x l text x x math math display block lim x x f x l math intuitively definition thought following way say


math f x l math math x x math given positive number math varepsilon math matter small always find math delta math guarantee math f x math math l math less math varepsilon math apart long math x math domain math f math real number less math delta math away math x math distinct math x math purpose last stipulation corresponds condition math x x math definition ensure math display inline lim x x f x l math imply anything value math f x math actually math x math


even need domain math f math order math display inline lim x x f x math exist slightly different related context concept limit applies behavior sequence math n math math n math becomes large '''definition''' let math n math real valued sequence say math n math '''''converges to''''' math math math varepsilon math exists natural number math n math math n geq n math implies math n varepsilon math write symbolically math display block n text n infty math math display block lim n


infty n math math n math fails converge say math n math '''' 'diverges''''' generalizing real valued function real variable slight modification definition replacement sequence math n math term math n math function math f math value math f x math natural numbers math n math math n math real numbers math math math x math respectively yields definition '''''limit math f x math math x math increases without bound''''' notated math display inline lim x infty f x math reversing inequality math x geq math math x leq math gives corresponding definition limit math f x math math x math ' 'decreases'' ''without bound''


nowrap math display inline lim x infty f x math sometimes useful conclude sequence converges even though value converges unknown irrelevant cases concept cauchy sequence useful '''definition''' let math n math real valued sequence say math n math '''''cauchy sequence''''' math varepsilon math exists natural number math n math math mn geq n math implies math n varepsilon math shown real valued sequence cauchy convergent property real


numbers expressed saying real numbers endowed standard metric math r cdot math '''''complete metric space''''' general metric space however cauchy sequence need converge addition real valued sequences monotonic shown sequence bounded convergent uniform pointwise convergence sequences functions addition sequences numbers one may also speak ' 'sequences functions'' ''on'' math e subset mathbb r math infinite ordered families functions math f n e mathbb r math denoted math f n n infty math convergence properties


however case sequences functions two kinds convergence known ''pointwise convergence'' ''uniform convergence'' need distinguished roughly speaking pointwise convergence functions math f n math limiting function math f e mathbb r math denoted math f n rightarrow f math simply means given math x e math math f n x f x math math n infty math contrast uniform convergence stronger type convergence sense uniformly convergent sequence functions also converges pointwise conversely uniform convergence requires members family functions math f n math fall within error math varepsilon math


math f math ''every value math x e math '' whenever math n geq n math integer math n math family functions uniformly converge sometimes denoted math f n rightrightarrows f math value math n math must exist math varepsilon math given matter small intuitively visualize situation imagining large enough math n math functions math f n f n f n ldots math confined within 'tube' width math varepsilon math math f math math f varepsilon math math f varepsilon math ''for every value domain'' math e math distinction pointwise uniform convergence important exchanging


order two limiting operations eg taking limit derivative integral desired order exchange well behaved many theorems real analysis call uniform convergence example sequence continuous functions see guaranteed converge continuous limiting function convergence uniform limiting function may continuous convergence pointwise karl weierstrass generally credited clearly defining concept uniform convergence fully investigating implications compactness compactness concept general topology plays


important role many theorems real analysis property compactness generalization notion set ''closed'' ''bounded'' context real analysis notions equivalent set euclidean space compact closed bounded briefly closed set contains boundary points set bounded exists real number distance two points set less number math mathbb r math sets closed


bounded therefore compact include empty set finite number points closed intervals finite unions however list exhaustive instance set math n n mathbb n cup math compact set cantor ternary set math mathcal c subset math another example compact set hand set math n n mathbb n math compact bounded closed boundary point member set set math infty math also compact closed bounded subsets real numbers


convergent subsequence particular property known ' 'subsequential compactness'' math mathbb r math set subsequentially compact closed bounded making definition equivalent one given subsequential compactness equivalent definition compactness based subcovers metric spaces topological spaces general general definition compactness relies notion ''open covers'' ' 'subcovers'' applicable topological spaces thus metric spaces math mathbb r math special cases brief collection open sets math u alpha math said


''open cover'' set math x math union sets superset math x math open cover said ''finite subcover'' finite subcollection math u alpha math could found also covers math x math '''definition''' set math x math topological space compact every open cover math x math finite subcover compact sets well behaved respect properties like convergence continuity instance cauchy sequence compact metric space convergent another example image compact metric space


continuous map also compact continuity function set real numbers real numbers represented graph cartesian plane function continuous roughly speaking graph single unbroken curve holes jumps several ways make intuition mathematically rigorous several definitions varying levels generality given cases two definitions applicable readily shown equivalent one another convenient definition used determine whether


given function continuous first definition given math f r math function defined non degenerate interval math math set real numbers domain possibilities include math r math whole set real numbers open interval math b x r mid x b math closed interval math b x r mid leq x leq b math math math math b math distinct real numbers exclude case math math empty consisting


one point particular '''definition''' math subset mathbb r math non degenerate interval say math f r math '''''continuous at''''' math p math math display inline lim x p f x f p math say math f math '''''continuous map''''' math f math continuous every math p math contrast requirements math f math limit point math p math constrain behavior math f math math p math following two conditions addition existence math display inline lim x p f x math must also hold order math f math continuous


math p math ''' ''' math f math must defined math p math ie math p math domain math f math ''and'' ''' ii ''' math f x f p math math x p math definition actually applies domain math e math contain isolated point equivalently math e math every math p e math limit point math e math general definition applying math f x mathbb r math general domain math x subset mathbb r math following '''definition''' math x math arbitrary subset math mathbb r math say math f x mathbb r math '''''continuous at''''' math p x math math varepsilon math exists math delta math


math x x math math x p delta math implies math f x f p varepsilon math say math f math '''''continuous map''''' math f math continuous every math p x math consequence definition math f math ''trivially continuous isolated point'' math p x math somewhat unintuitive treatment isolated points necessary ensure definition continuity functions real line consistent general definition continuity maps topological spaces includes metric spaces math mathbb r math particular special cases definition extends beyond scope


discussion real analysis given completeness '''definition''' math x math math math topological spaces say math f x math '''''continuous at''''' math p x math math f v math neighborhood math p math math x math every neighborhood math v math math f p math math math say math f math '''''continuous map''''' math f u math open math x math every math u math open math math math f math refers preimage math subset math math f math uniform continuity '''definition''' math x math subset real numbers say function math f x mathbb r math '''''uniformly continuous''''' '''''on'''''


math x math math varepsilon math exists math delta math math xy x math math x delta math implies math f x f varepsilon math explicitly function uniformly continuous math x math choice math delta math needed fulfill definition must work ''all of'' math x math given math varepsilon math contrast function continuous every point math p x math said continuous math x math choice math delta math may depend math varepsilon math ''and'' math p math contrast simple continuity uniform continuity property function makes sense


specified domain speak uniform continuity single point math p math meaningless compact set easily shown continuous functions uniformly continuous math e math bounded noncompact subset math mathbb r math exists math f e mathbb r math continuous uniformly continuous simple example consider math f mathbb r math defined math f x x math choosing points close always make math f x f varepsilon math single choice math delta math given math varepsilon math absolute continuity '''definition''' let math subset mathbb r math interval real line


generalized version fundamental theorem calculus applies lebesgue integral differentiation notion ' 'derivative'' function ' 'differentiability'' originates concept approximating function near given point using best linear approximation approximation exists unique given line tangent function given point math math slope line derivative function math math function math f mathbb r mathbb r math '''' 'differentiable math math ''''' limit math f' lim h frac f h f h math exists limit


set continuous functions declaring '' math c k math '' positive integer math k math set differentiable functions whose derivative math c k math particular '' math c k math '' contained math c k math every math k math examples show containment strict class math c infty math intersection sets '' math c k math '' '' math k math '' varies non negative integers members class known '''' 'smooth functions''''' class math c omega math consists analytic functions strictly contained math c infty math see bump function smooth function


analytic series series formalizes imprecise notion taking sum endless sequence numbers idea taking sum infinite number terms lead finite result counterintuitive ancient greeks led formulation number paradoxes zeno philosophers modern notion assigning value series avoids dealing ill defined notion adding infinite number terms instead finite sum first math n math terms sequence known partial


sum considered concept limit applied sequence partial sums math n math grows without bound series assigned value limit exists given infinite sequence math n math define associated '''' 'series''''' formal mathematical object nowrap math display inline cdots sum n infty n math sometimes simply written math display inline sum n math '''''partial sums''''' series math display inline sum n math numbers math display inline n sum j n j math series math display inline sum n math said '''''convergent''''' sequence consisting


partial sums math n math convergent otherwise '''' 'divergent''''' '''' 'sum''''' convergent series defined number nowrap math display inline lim n infty n math word sum used metaphorical sense shorthand taking limit sequence partial sums interpreted simply adding infinite number terms instance contrast behavior finite sums rearranging terms infinite series may result convergence different number see article ''riemann rearrangement theorem''


discussion example convergent series geometric series forms basis one zeno 's famous paradoxes math sum n infty frac n frac frac frac cdots math contrast harmonic series known since middle ages divergent series math sum n infty frac n frac frac cdots infty math math infty math merely notational convention indicate partial sums series grow without bound series math display inline sum n math said '''''converge absolutely''''' math display inline sum n math


convergent convergent series math display inline sum n math math display inline sum n math diverges said '''''converge''''' '''''non absolutely''''' easily shown absolute convergence series implies convergence hand example series converges non absolutely math sum n infty frac n n frac frac frac cdots ln math taylor series taylor series real complex valued function '' '' ''x'' infinitely differentiable real complex number ''a'' power series math f frac f' x frac f'' x frac f x


largest ''r'' convergence guaranteed called ''radius convergence'' converge entire real line even converging taylor series may converge value different value function point taylor series point nonzero radius convergence sums function disc convergence function analytic analytic functions many fundamental properties particular analytic function real variable extends naturally function complex variable


enclosed surface basic strategy solving problems type known ancient greeks chinese known ''method exhaustion'' generally speaking desired area bounded respectively increasingly accurate circumscribing inscribing polygonal approximations whose exact areas computed considering approximations consisting larger larger infinite number smaller smaller infinitesimal pieces area bound curve deduced upper lower bounds defined approximations converge around common value spirit


basic strategy easily seen definition riemann integral integral said exist upper lower riemann darboux sums converge common value thinner thinner rectangular slices refinements considered though machinery used define much elaborate compared riemann integral lebesgue integral defined similar basic ideas mind compared riemann integral sophisticated lebesgue integral allows area length volume etc termed measure general defined computed


much complicated irregular subsets euclidean space although still exist non measurable subsets area cannot assigned riemann integration riemann integral defined terms riemann sums functions respect tagged partitions interval let math ab math closed interval real line '''''tagged partition''''' math cal p math math ab math finite sequence math x le le x le le x le cdots le x n le n le x n b math partitions interval math ab math math n math sub intervals math x x math indexed


math ldots n math tagged distinguished point math x x math function math f math bounded math ab math define '''''riemann sum''''' math f math respect tagged partition math cal p math math sum n f delta math math delta x x math width sub interval math math thus term sum area rectangle height equal function value distinguished point given sub interval width sub interval width '''''mesh''''' tagged partition width largest sub interval formed


partition math display inline delta max ldots n delta math say '''''riemann integral''''' math f math math ab math math math math varepsilon math exists math delta math tagged partition math cal p math mesh math delta delta math math left sum n f delta right varepsilon math sometimes denoted math display inline mathcal r int b f math chosen tags give maximum respectively minimum value interval riemann sum known upper respectively lower '''''darboux sum''''' function '''''darboux integrable''''' upper lower darboux sums made arbitrarily


close sufficiently small mesh although definition gives darboux integral appearance special case riemann integral fact equivalent sense function darboux integrable riemann integrable values integrals equal fact calculus real analysis textbooks often conflate two introducing definition darboux integral riemann integral due slightly easier apply definition former fundamental theorem calculus asserts


integration differentiation inverse operations certain sense lebesgue integration measure '''lebesgue integration''' mathematical construction extends integral larger class functions also extends domains functions defined concept '''''measure''''' abstraction length area volume central lebesgue integral probability theory distributions '''distributions''' '''generalized functions''' objects generalize functions distributions make possible differentiate functions whose derivatives exist classical sense particular locally integrable function distributional derivative


relation complex analysis real analysis area analysis studies concepts sequences limits continuity differentiation integration sequences functions definition real analysis focuses real numbers often including positive negative infinity form extended real line real analysis closely related complex analysis studies broadly properties complex numbers complex analysis natural define differentiation via holomorphic functions number useful properties repeated differentiability expressibility power series satisfying cauchy integral formula real


analysis usually natural consider differentiable smooth harmonic functions widely applicable may lack powerful properties holomorphic functions however results fundamental theorem algebra simpler expressed terms complex numbers techniques theory analytic functions complex variable often used real analysis evaluation real integrals residue calculus important results important results include bolzano weierstrass heine borel theorems intermediate value theorem mean value theorem taylor 's theorem fundamental theorem calculus arzel ascoli


theorem stone weierstrass theorem fatou 's lemma monotone convergence dominated convergence theorems generalizations related areas mathematics various ideas real analysis generalized real line broader abstract contexts generalizations link real analysis disciplines subdisciplines instance generalization ideas like continuous functions compactness real analysis metric spaces topological spaces connects real analysis field general topology generalization finite dimensional euclidean spaces infinite dimensional analogs led concepts banach spaces hilbert spaces


generally functional analysis georg cantor 's investigation sets sequence real numbers mappings foundational issues real analysis gave birth naive set theory study issues convergence sequences functions eventually gave rise fourier analysis subdiscipline mathematical analysis investigation consequences generalizing differentiability functions real variable ones complex variable gave rise concept holomorphic functions inception complex analysis another distinct subdiscipline analysis hand


real analysis calculus finite differences real multivariable function real coordinate space complex analysis references bibliography external links https textbooksopensunyorg got story real analysis got story real analysis robert rogers eugene boman http wwwworldscientificcom worldscibooks first course analysis donald yau http wwwanalysiswebnotescom analysis webnotes john lindsay orr http wwwmathcsorg analysis reals indexhtml interactive real analysis bert g wachsmuth http www groupsmcsst andrewsacuk john analysis indexhtml first analysis course john o'connor http wwwtrilliacom zakon analysisihtml mathematical analysis elias zakon http wwwtrilliacom zakon analysisiihtml mathematical analysis ii elias zakon http wwweconomicssotonacuk staff aldrich calculus analysis earliest useshtm earliest known uses words mathematics calculus analysis


http wwwjirkaorg ra basic analysis introduction real analysis jiri lebl https wwwmatunivieacat gerald ftp book fa indexhtml topics real functional analysis gerald teschl university vienna


'''regression''' '' 'regressions''' may refer science marine regression coastal advance due falling sea level opposite marine transgression regression medicine characteristic diseases express lighter symptoms less extent mainly tumors without disappearing totally regression psychology defensive reaction unaccepted impulses statistics regression analysis statistical technique estimating relationships among variables several types regression linear regression simple linear regression logistic regression nonlinear regression nonparametric regression robust regression stepwise regression regression toward mean common statistical phenomenon computing software regression appearance bug

Applied science
Library and museum studies
Statistics
Regression


absent previous revision regression testing software testing method seeks uncover regression bugs hypnosis age regression therapy process claiming retrieve memories past life regression process claiming retrieve memories previous lives uses infinite regress problem epistemology ''regression'' film horror film directed written alejandro amen bar starring ethan hawke emma watson ''regressions'' album album cleric see also regress disambiguation


sport childhood association football shown team sport also provides opportunities nurture physical fitness social interaction skills '''sport''' pertains form competitive physical activity game ref name sportaccord ref aims use maintain improve physical ability skills providing enjoyment participants cases entertainment spectators ref name council ref sports casual organized participation improve one 's physical health hundreds sports exist single contestants hundreds simultaneous participants either teams competing individuals certain sports

Human physical performance and recreation


racing many contestants may compete simultaneously consecutively one winner others contest ''match'' two sides attempting exceed sports allow tie draw single winner others provide tie breaking methods ensure one winner one loser number contests may arranged tournament producing champion many sports leagues make annual champion arranging games regular sports season followed cases playoffs sport generally recognised system activities based physical athleticism physical


dexterity major competitions olympic games admitting sports meeting definition organisations council europe preclude activities without physical element classification sports ref name council however number competitive non physical activities claim recognition mind sports international olympic committee arisf recognises chess bridge ''bona fide'' sports sportaccord international sports federation association recognises five non physical sports bridge chess draughts checkers go xiangqi limits number mind games admitted sports ref name sportaccord sport usually governed


set rules customs serve ensure fair competition allow consistent adjudication winner winning determined physical events scoring goals crossing line first also determined judges scoring elements sporting performance including objective subjective measures technical performance artistic impression records performance often kept popular sports information may widely announced reported sport news sport also major source entertainment non participants spectator sport drawing large crowds sport


purpose gambling hunting games diversions including ones require exercise roget 's defines noun sport activity engaged relaxation amusement synonyms including diversion recreation nomenclature singular term sport used english dialects describe overall concept eg children taking part sport sports used describe multiple activities eg football rugby popular sports england american english uses sports terms definition international olympic committee recognises board games sports including chess show jumping equestrian sport


mind sports increase application term sport wider set non physical challenges video games also called esports electronic sports especially due large scale participation organised competition widely recognised mainstream sports organisations according council europe european sports charter article sport' means forms physical activity casual organised participation aim expressing improving physical fitness mental well forming social relationships obtaining results competition levels competition race record


holder usain bolt yellow right runners moscow opposing views necessity competition defining element sport almost professional sports involving competition governing bodies requiring competition prerequisite recognition international olympic committee ioc sportaccord ref name sportaccord bodies advocate widening definition sport include physical activity instance council europe include forms physical exercise including competed fun order widen participation reduce impact losing less able participants


introduction non competitive physical activity traditionally competitive events school sports days although moves like often controversial competitive events participants graded classified based result often divided groups comparable performance eg gender weight age measurement result may objective subjective corrected handicaps penalties race example time complete course objective measurement gymnastics diving result decided panel judges therefore subjective many shades


traditional iranian martial art zoorkhaneh close connection warfare skills among sports originated ancient persia polo jousting motorised sports appeared since advent modern age squats warm exercise prior entering pool us military base wide range sports already established time ancient greece military culture development sport greece influenced one another considerably sport became prominent part culture greeks created olympic games ancient times


st nbsp century increasing debate whether transgender sports persons able participate sport events conform post transition gender identity fair play sportsmanship sportsmanship attitude strives fair play courtesy toward teammates opponents ethical behaviour integrity grace victory defeat sportsmanship expresses aspiration ethos activity enjoyed sake well known sentiment sports journalist grantland rice 's lost played game modern olympic creed expressed


founder pierre de coubertin important thing winning taking part typical expressions sentiment cheating key principles sport include result predetermined sides equal opportunity win rules place ensure fair play participants break rules order gain advantage participants may cheat order unfairly increase chance winning order achieve advantages financial gains widespread existence gambling results sports fixtures creates motivation


crossing line fair competition intentional aggressive violence athletes coaches fans parents sometimes unleash violent behaviour people property misguided shows loyalty dominance anger celebration rioting hooliganism fans particular problem national international sporting contests participation gender participation international level female athletes istaf berlin female participation sports continues rise alongside opportunity involvement value sports child development physical fitness despite increases female participation last three decades gap persists enrolment figures


male female players sports related teams female players account total participation us interscholastic athletics youth participation youth sport presents children opportunities fun socialisation forming peer relationships physical fitness athletic scholarships activists education war drugs encourage youth sport means increase educational participation fight illegal drug trade according center injury research policy nationwide children 's hospital biggest risk youth sport death serious injury including concussion risks come running basketball association football volleyball


gridiron gymnastics ice hockey youth sport us billion industry including equipment private coaching disabled participation ''marathon international de paris'' paris marathon '''disabled sports''' also '''adaptive sports''' '''parasports''' sports played persons disability including physical intellectual disabilities many based existing sports modified meet needs persons disability sometimes referred ''adapted sports'' however disabled sports adapted several sports specifically created persons disability equivalent


able bodied sports spectator involvement spectators unofficial olympic games competition element sport along aesthetic appeal sports result popularity people attending watch sport played led specific phenomenon spectator sport amateur professional sports attract spectators person sport venue broadcast media including radio television internet broadcast attendance person viewing remotely incur sometimes substantial charge entrance ticket pay per view television broadcast common popular sports


attract large broadcast audiences leading rival broadcasters bidding large amounts money rights show certain fixtures football world cup attracts global television audience hundreds millions final alone attracted estimated worldwide audience well nbsp million cricket world cup final attracted estimated audience nbsp million india alone united states championship game nfl super bowl become one watched television broadcasts year ref name sb ref super bowl sunday ' 'de facto'' national holiday america


high paying professional sport culture high performing participants rewarded pay far excess average wages run millions dollars sports individual competitions within sport retain policy allowing amateur sport olympic games started principle amateur competition practised sport professionally considered unfair advantage practised merely hobby ref name oideology ref olympic athletes allowed receive compensation sponsorship ref name infoplease ref ioc decided make professional athletes eligible


shoes competitive swimwear sports engineering emerged discipline increasing focus materials design also use technology sport analytics big data wearable technology ref name gaining steam sports technology ref order control impact technology fair play governing bodies frequently specific rules set control impact technical advantage participants example full body non textile swimsuits banned fina enhancing swimmers' performances increase technology also allowed many decisions sports matches


taken reviewed field another official using instant replays make decisions sports players challenge decisions made officials association football goal line technology makes decisions whether ball crossed goal line technology compulsory ref name ifabofficial ref used fifa world cup brazil fifa women 's world cup canada well premier league ref name bbc premier ref bundesliga nfl referee ask review replay booth


broadcaster number different technologies used umpire player review including instant replays hawk eye hot spot real time snickometer hawk eye also used tennis challenge umpiring decisions ref name tind ref sports education research suggests sports capacity connect youth positive adult role models provide positive development opportunities well promote learning application life skills ref name ref recent years use sport reduce crime well prevent violent extremism radicalization become widespread especially tool


winter olympics held garmisch partenkirchen promote nazi ideology superiority aryan race inferiority jews undesirables ref name world fascism ref name sociology sport ref germany used olympics give peaceful image secretly preparing war apartheid official policy south africa many sports people particularly rugby union adopted conscientious approach appear competitive sports feel effective contribution eventual demolition policy apartheid others feel may prolonged reinforced worst


effects history ireland gaelic sports connected cultural nationalism mid th nbsp century person could banned playing gaelic football hurling sports administered gaelic athletic association gaa played supported association football games seen british origin recently gaa continued ban playing football rugby union gaelic venues ban also known rule still enforced modified allow football rugby played croke park lansdowne road redeveloped


aviva stadium recently rule nbsp gaa also banned members british security forces members ruc playing gaelic games advent good friday agreement led eventual removal ban nationalism often evident pursuit sport reporting people compete national teams commentators audiences adopt partisan view occasion tensions lead violent confrontation among players spectators within beyond sporting venue football war trends seen many


contrary fundamental ethos sport carried sake enjoyment participants sport politics collided olympics munich masked men entered hotel israeli olympic team killed many men known munich massacre study us elections shown result sports events affect results study published proceedings national academy sciences showed home team wins game election incumbent candidates


distracting blockquote imagine bird easily caught decoy fish sooner fixed hook wormy bait poor fools neatly tricked servitude slightest feather passed speak mouths truly marvellous thing let caught quickly slightest tickling fancy plays farces spectacles gladiators strange beasts medals pictures opiates ancient peoples bait toward slavery price liberty instruments tyranny


practices enticements ancient dictators successfully lulled subjects yoke stupefied peoples fascinated pastimes vain pleasures flashed eyes learned subservience na vely creditably little children learn read looking bright picture books blockquote religious views foot race one events dedicated zeus panathenaic amphora kleophrades painter circa bc louvre museum sport important form worship ancient greek religion ancient olympic games called olympiad held honour head deity zeus


featured various forms religious dedication gods many greeks travelled see games combination religion sport also served way uniting practice athletic competitions criticised christian thinkers form idolatry human beings extol adore sacrifice reward ref name watson ''sports christianity historical contemporary perspectives'' nick j watson ed routledge p ref sports seen critics manifestation collective pride national self deification feats human power


pleasure keenness feeling giving pleasure zest keenness feeling rivalry giving turn zest rivalry rage bitterness wrath grief bad things flow nbsp whole entirely keeping religion christ blockquote christian clerics wesleyan holiness movement oppose viewing participation professional sports believing professional sports leagues profane sabbath modern era certain associations hold games lord 's day ref name handel also


criticize professional sports fostering commitment competes christian 's primary commitment god opposition perceive lack modesty players' cheerleaders' uniforms conformity methodistic doctrine outward holiness association violence opposition perceive extensive use profanity among many players contravenes frequent presence gambling well alcohol drugs sporting events go commitment teetotalism ref name handel ref popularity popularity


major sports size fan base ref name wa ref class wikitable rank sport estimated global following sphere influence association football soccer billion globally cricket billion primarly uk commonwealth hockey ice field billion europe north america africa asia australia tennis billion globally volleyball along beach volleyball million americas europe asia oceania table tennis million globally basketball million


globally baseball million primarly united states caribbean japan rugby union million primarly uk commonwealth golf million primarly western europe east asia north america see also outline sports list sports list sportspeople list sports attendance figures list professional sports leagues new media sports '''related topics''' athletic sports animals sport combat sport disabled sports electronic sports fan person handedness advantage sports international sport lawn game mind sport motor sports multi sport events national sport nationalism


normal distribution common probability density useful central limit theorem scatter plots used descriptive statistics show observed relationships different variables using iris flower data set '''statistics''' discipline concerns collection organization analysis interpretation presentation data ref name ox ref applying statistics scientific industrial social problem conventional begin statistical population statistical model studied populations diverse groups people objects people living country every atom

Applied science
Library and museum studies
Statistics


composing crystal statistics deals every aspect data including planning data collection terms design surveys experiments ref name dodge dodge ''the oxford dictionary statistical terms'' oxford university press ref census data cannot collected statisticians collect data developing specific experiment designs survey samples representative sampling assures inferences conclusions reasonably extend sample population whole experimental study involves taking measurements system study manipulating system taking additional measurements using procedure determine


manipulation modified values measurements contrast observational study involve experimental manipulation two main statistical methods used data analysis descriptive statistics summarize data sample using indexes mean standard deviation inferential statistics draw conclusions data subject random variation eg observational errors sampling variation ref name lundresearchltd ref descriptive statistics often concerned two sets properties ' 'distribution'' sample population ''central tendency'' ''location'' seeks characterize distribution 's central typical value ' 'dispersion'' ''variability'' characterizes