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How and why we do mathematical proofs

Description

This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009/10 The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs. In particular, the student will learn the following: * proofs can help you to really see why a result is true; * problems that are easy to state can be hard to solve (e.g. Fermat's Last Theorem); * sometimes statements which appear to be intuitively obvious may turn out to be false (e.g. Simpson's paradox); * the answer to a question will often depend crucially on the definitions you are working with; * how to start proofs; * how and when to use

Subjects

ukoer | proofs definitions prime number | perfect square simpson's paradox | sequence series | odd functions even functions | simpson's paradox strictly increasing | direct proofs comparison test | odd numbers multiples eight | pure maths pure mathematics pure math | convergence divergence | Computer science | I100

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Newcastle Civic Centre, March 1969

Description

A fine image of the newly completed Civic Centre with St Thomas Church in the foreground. Roads such as Simpson Street and Lovaine Crescent have been cleared to make way the Northumbria University campus buildings rising in the background. Compare this photograph with the 1963 image of the Civic Centre and surrounding area. Reference: TWAS: DT.TUR.7.11. (Copyright) We're happy for you to share this digital image within the spirit of The Commons. Please cite 'Tyne & Wear Archives & Museums' when reusing. Certain restrictions on high quality reproductions and commercial use of the original physical version apply though; if you're unsure please email archives@twmuseums.org.uk. To purchase a hi-res copy please email archives@twmuseums.org.uk quoting the title and reference number

Subjects

aerialviews | aerialphotographs | tyneandwear | newcastlecivic | centre1969st | thomas | churchsimpson | streetlovaine | crescentnorthumbria | university1963museumtwamtyne | wear | archives | museums | turner | blackwhitephotos | newcastleciviccentre | digitalimage | blackandwhitephotograph | northeastengland | land | borders | march1969 | stthomaschurch | vegetation | industry | simpsonstreet | lovainecrescent | northumbriauniversitycampus | buildings | building | surroundingareas | road | vehicle | motorcar | tree | lawn | shadow | daylight | dome | chimney | roof | wall | doorway | window | pavement | park | grid | interesting | unusual | newcastleupontyne | row | fence | carpark | aerial | abstract | unitedkingdom | ground

License

No known copyright restrictions

Site sourced from

Tyne & Wear Archives & Museums | FlickR

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Biodiversity Consortium : Measuring Ecological Diversity 1 : full version

Description

Ecological diversity can also be measured over a range of spatial scales.

Subjects

bioukoer | ukoer | biodiversity | ecology | species | biodiversity indices | abundance models | diversity models | log series model | survey | sampling | fieldwork | diversity | alpha diversity | beta diversity | gamma diversity | epsilon diversity | plant diversity | animal diversity | spatial diversity | measuring | habitats | species richness | biodiversity consortium | worlds and ecosystems | species and systematics | shannon index | shannon-weiner index | simpson index | broken stick | Biological sciences | C000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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In the eyes of the law...

Description

Subjects

ireland | dublin | tower | church | car | bicycle | pub | automobile | uniform | shaving | wallace | hackney | dye | simpson | bungalow | tramlines | policeman | bsa | glassnegative | pratts | publichouse | motorcar | stpeterschurch | leinster | haircutting | dmp | phibsboro | schoolboys | phibsborough | johndoyle | cabraroad | georgeheron | nationallibraryofireland | dublinmetropolitanpolice | doylescorner | thomasbyrne | fergusoconnor | bohemianbar | fergusoconnorcollection | le7852 | bicycleagent | georgeloconnor

License

No known copyright restrictions

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Alma Simpson, Central Park (LOC)

Description

Subjects

libraryofcongress | xmlns:dc=httppurlorgdcelements11 | dc:identifier=httphdllocgovlocpnpggbain22789 | almasimpson

License

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Man on a two way radio - Miami

Description

Subjects

men | florida | miami | inc | automobiles | twowayradios | pearcesimpson

License

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Woman on a two way radio - Miami

Description

Subjects

women | florida | miami | maps | offices | twowayradios | pearcesimpsoninc

License

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Man on a two way radio - Miami

Description

Subjects

florida | miami | automobiles | twowayradios | pearcesimpsoninc

License

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Newcastle Civic Centre, 31st July 1963

Description

The Civic Centre, under construction in this shot, was designed by the city architect, George Kenyon and completed in 1967. The building was formally opened by HM King Olav V of Norway on 14 November 1968. Note the old street pattern to the right, with Buist?s large car showroom on St Mary?s Place. Roads such as Simpson Street and Lovaine Crescent will soon be cleared to make way for Northumbria University campus buildings. Reference: TWAS: DT.TUR.7.4 (Copyright) We're happy for you to share this digital image within the spirit of The Commons. Please cite 'Tyne & Wear Archives & Museums' when reusing. Certain restrictions on high quality reproductions and commercial use of the original physical version apply though; if you're unsure please email archives@twmuseums.org.uk. To purchase a hi-res copy please email archives@twmuseums.org.uk quoting the title and reference number

Subjects

civiccentre | newcastle | 1963 | georgekenyon | hmkingolav | stmary?splace | simpsonstreet | lovainecrescent | northumbriauniversity | museum | twam | aerialviews | aerialphotographs | tyneandwear | turner | blackwhitephotos | hancockmuseum | cityhall | citypool | aerialphotograph | aerialview | blackandwhitephotograph | glimpse | digitalimage | archives | documentation | industry | industrialheritage | development | progress | construction | buildings | wall | roof | chimney | road | vehicles | street | land | design | cityarchitect | architecture | completion | 1967 | 31stjuly1963 | haymarket | newcastleupontyne | northeastofengland | unitedkingdom | newcastleciviccentre | opening | hmkingolavv | norway | 14november1968 | pattern | buist?slargecarshowroom | northumbriauniversitycampusbuildings | demolished | house | lovaineterrace | engaging | interesting | unusual | fascinating | compelling | vegetation | landscape | row | business | economy | infrastructure | shadow | daylight | pavement

License

No known copyright restrictions

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Tyne & Wear Archives & Museums | FlickR

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