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18.06CI Linear Algebra - Communications Intensive (MIT) 18.06CI Linear Algebra - Communications Intensive (MIT)

Description

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space. This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.

Subjects

Linear Alegebra | Linear Alegebra | Latex | Latex | LaTeX2e | LaTeX2e | mathematical writing | mathematical writing | linear spaces | linear spaces | basis | basis | dimension | dimension | linear mappings | linear mappings | matrices | matrices | subspaces | subspaces | direct sums | direct sums | reflections | reflections | Euclidean space | Euclidean space | abstract root systems | abstract root systems | simple roots | simple roots | positive roots | positive roots | Cartan matrix | Cartan matrix | Dynkin diagrams | Dynkin diagrams | classification | classification | 18.06 | 18.06

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Shoe Store - Florida Shoe Store - Florida

Description

Subjects

florida | florida | shoestore | shoestore | storefronts | storefronts | quirogamariosshoes | quirogamariosshoes | reflections | reflections

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Photograph of birds on antenna supports for LORAN tower on Sand-Johnston Island, 1963.

Description

Subjects

sky | water | reflections | smithsonian | loran | sandisland | loranstation | johnsonatoll | smithsonianinstitutionarchives | longrangenavigation | lorantower | johnsonsandisland

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Satisjaure (Satihaure), Gällivare, Lappland

Description

Subjects

water | reflections | landscape | stones | riksantikvarieämbetet | theswedishnationalheritageboard

License

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Lily Pond, 1915 Panama-California Exposition

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00134 Title: Lily Pond, 1915 Panama-California Exposition Photographer: Harold A. Taylor (American, 1878-1960) Architect: Bertram Grosvenor Goodhue (American, 1869-1942) Building Date: ca. 1915 Location: North and Central America: United States; California, San Diego Materials: gelatin silver print Image: 6.125 x 8 in.; 15.5575 x 20.32 cm Provenance: Transfer from the College of Architecture, Art and Planning Persistent URI: hdl.handle.net/1813.001/5s92 There are no known U.S. copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | architecture | pools | bodiesofwater | reflections | waterlilies | plants | urns | bridges | exhibitionbuildings | panamacaliforniaexpositionsandiegocalifornia | culidentifier:value=155309000134 | culidentifier:lunafield=accessionnumber

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South Parlor, Webb House, Wethersfield, Connecticut

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00147 Title: South Parlor, Webb House, Wethersfield, Connecticut Photograph date: ca. 1925-ca. 1950 Building Date: 1752 Location: North and Central America: United States; Connecticut, Wethersfield Materials: gelatin silver print Image: 7.875 x 10 in.; 20.0025 x 25.4 cm Provenance: Transfer from the College of Architecture, Art and Planning Persistent URI: hdl.handle.net/1813.001/5s9h There are no known U.S. copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | domesticinteriors | historichousemuseums | hearths | mirrors | reflections | chairs | tables | books | josephwebbhousewethersfieldconnecticut | culidentifier:value=155309000147 | culidentifier:lunafield=accessionnumber

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Cambridge. St. John's College, Chapel Tower

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.01073 Title: Cambridge. St. John's College, Chapel Tower Architect: Sir George Gilbert Scott (English, 1811-1878) Building Date: ca. 1850-ca. 1878 Photograph date: ca. 1865-ca. 1885 Location: Europe: United Kingdom; Cambridge Materials: albumen print Image: 10 1/2 x 8 3/8 in.; 26.67 x 21.2725 cm Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5t6m There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | saintjohnscollegecambridgeengland | universitycampuses | chapels | religiousbuildings | churchtowers | rivers | bodiesofwater | rivercamcambridgeengland | willowtrees | reflections | universities | culidentifier:value=155309001073 | culidentifier:lunafield=accessionnumber

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Cambridge. Trinity College Bridge

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.01106 Title: Cambridge. Trinity College Bridge Bridge date: 1765 Photograph date: ca. 1865-ca. 1885 Location: Europe: United Kingdom; Cambridge Materials: albumen print Image: 8 1/2 x 10 3/4 in.; 21.59 x 27.305 cm Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5t7r There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | trinitycollegecambridgeengland | universitycampuses | rivers | bodiesofwater | rivercamcambridgeengland | archbridges | punts | boats | oars | reflections | willowtrees | derbies | culidentifier:value=155309001106 | culidentifier:lunafield=accessionnumber

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Durham Cathedral

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00115 Title: Durham Cathedral Building Date: 1093-1128 Photograph date: ca. 1865-ca. 1895 Location: Europe: United Kingdom; Durham Materials: albumen print Image: 8 x 6 in.; 20.32 x 15.24 cm Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5sfr There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | cathedrals | religiousbuildings | archbridges | rivers | bodiesofwater | winter | seasons | trees | riverbanks | reflections | durhamcathedraldurhamengland | riverwearcountydurhamengland | culidentifier:value=155309000115 | culidentifier:lunafield=accessionnumber

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Durham Cathedral

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00117 Title: Durham Cathedral Building Date: 1093-1128 Photograph date: ca. 1865-ca. 1895 Location: Europe: United Kingdom; Durham Materials: albumen print Image: 8 x 5 7/8 in.; 20.32 x 14.9225 cm Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5sft There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | rivers | bodiesofwater | reflections | cathedrals | religiousbuildings | churchtowers | winter | seasons | snow | clouds | townscapes | durhamcathedraldurhamengland | riverwearcountydurhamengland | culidentifier:value=155309000117 | culidentifier:lunafield=accessionnumber

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University of Glasgow

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.01220 Title: University of Glasgow Photographer: George Washington Wilson (Scottish, 1823-1893) Architect: Sir George Gilbert Scott (English, 1811-1878) Building Date: 1868 Photograph date: ca. 1868-ca. 1885 Location: Europe: United Kingdom; Glasgow Materials: albumen print Image: 6 1/4 x 9 1/2 in.; 15.875 x 24.13 cm Style: Gothic Revival Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5tcv There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | universityofglasgowglasgowscotland | universities | universitycampuses | towers | gazebos | fences | ponds | bodiesofwater | reflections | turrets | culidentifier:value=155309001220 | culidentifier:lunafield=accessionnumber

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Wells Cathedral

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00818 Title: Wells Cathedral Photographer: Carl Norman (British, active ca. 1870-ca. 1890) Building Date: ca. 1183-1260 Photograph date: ca. 1867-ca. 1895 Location: Europe: United Kingdom; Wells Materials: albumen print Image: 6 1/2 x 8 5/8 in.; 16.51 x 21.9075 cm Style: English Gothic Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5swj There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | wellscathedralwellsengland | cathedrals | religiousbuildings | pools | bodiesofwater | reflections | crossingtowers | churchtowers | tracery | flyingbuttresses | culidentifier:value=155309000818 | culidentifier:lunafield=accessionnumber

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Durham Cathedral

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00116 Title: Durham Cathedral Building Date: 1093-1128 Photograph date: ca. 1865-ca. 1895 Location: Europe: United Kingdom; Durham Materials: albumen print Image: 8 x 6 in.; 20.32 x 15.24 cm Provenance: Gift of Andrew Dickson White Persistent URI: hdl.handle.net/1813.001/5sfs There are no known copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | cathedrals | religiousbuildings | trees | archbridges | rivers | bodiesofwater | reflections | summer | seasons | durhamcathedraldurhamengland | riverwearcountydurhamengland | culidentifier:value=155309000116 | culidentifier:lunafield=accessionnumber | prebendsbridge

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The Silvery Margin of the Lake

Description

Subjects

autumn | sunset | reflections | islands | lakes | palmtrees | postcards | ponds | centennialpark | statelibraryofnsw | autumnglow

License

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Sunset Reflections

Description

Subjects

reflections | lakes | ducks | sunsets | autumncolours | palmtrees | postcards | ponds | centennialpark | statelibraryofnsw | autumnglow

License

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Cloud Reflections

Description

Subjects

autumn | reflections | islands | lakes | sunsets | palmtrees | postcards | ponds | centennialpark | autumncolour | statelibraryofnsw | autumnglow

License

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An Autumn Sunset

Description

Subjects

park | autumn | reflections | islands | centennial | lakes | sunsets | palmtrees | postcards | ponds | autumncolour | statelibraryofnsw | autumnglow

License

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An Autumn Afterglow

Description

Subjects

autumn | trees | sunset | reflections | islands | lakes | palm | postcards | ponds | centennialpark | statelibraryofnsw | autumnglow

License

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First Aid for Photos!

Description

Improving digital camera pictures. Activities using Powerpoint - using a digital camera, including: correcting, focusing, backgrounds, reflections, set up, lighting, and detail.

Subjects

photos | digital pictures | powerpoint activity | digital camera | correcting | focusing | backgrounds | reflections | set up | lighting and detail | ARTS and CRAFTS | J

License

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

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Photographing people

Description

A video tutorial on photographing people

Subjects

studio | film | developing | lighting | reflections | cameras | light control | portaits | portraiture | photography | design | W000

License

Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-nd/2.0/uk/ http://creativecommons.org/licenses/by-nc-nd/2.0/uk/

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Taking portrait photos

Description

A video tutorial on taking portraits

Subjects

studio | film | developing | lighting | reflections | cameras | light control | portaits | portraiture | photography | design | W000

License

Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-nd/2.0/uk/ http://creativecommons.org/licenses/by-nc-nd/2.0/uk/

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Making a home studio

Description

A video tutorial on making a photographic studio at home

Subjects

studio | film | developing | lighting | reflections | cameras | light control | portaits | portraiture | photography | design | W000

License

Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-nd/2.0/uk/ http://creativecommons.org/licenses/by-nc-nd/2.0/uk/

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Colour film processing

Description

A video tutorial on processing a colour film

Subjects

studio | film | developing | lighting | reflections | cameras | light control | portaits | portraiture | photography | design | W000

License

Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-nd/2.0/uk/ http://creativecommons.org/licenses/by-nc-nd/2.0/uk/

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18.06CI Linear Algebra - Communications Intensive (MIT)

Description

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.

Subjects

Linear Alegebra | Latex | LaTeX2e | mathematical writing | linear spaces | basis | dimension | linear mappings | matrices | subspaces | direct sums | reflections | Euclidean space | abstract root systems | simple roots | positive roots | Cartan matrix | Dynkin diagrams | classification | 18.06

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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