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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

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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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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

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

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

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florida | miami | automobiles | twowayradios | pearcesimpsoninc

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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

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