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6.876J Advanced Topics in Cryptography (MIT) 6.876J Advanced Topics in Cryptography (MIT)

Description

The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge proofs of knowledge, non-interactive zero-knowledge proofs, secure protocols, two-party secure computation, multiparty secure computation, and chosen-ciphertext security. The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge proofs of knowledge, non-interactive zero-knowledge proofs, secure protocols, two-party secure computation, multiparty secure computation, and chosen-ciphertext security.

Subjects

interactive proofs | interactive proofs | zero-knowledge proofs | zero-knowledge proofs | zero-knowledge proofs of knowledge | zero-knowledge proofs of knowledge | non-interactive zero-knowledge proofs | non-interactive zero-knowledge proofs | secure protocols | secure protocols | two-party secure computation | two-party secure computation | multiparty secure computation | multiparty secure computation | chosen-ciphertext security | chosen-ciphertext security | 6.876 | 6.876 | 18.426 | 18.426

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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6.876J Advanced Topics in Cryptography (MIT)

Description

The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge proofs of knowledge, non-interactive zero-knowledge proofs, secure protocols, two-party secure computation, multiparty secure computation, and chosen-ciphertext security.

Subjects

interactive proofs | zero-knowledge proofs | zero-knowledge proofs of knowledge | non-interactive zero-knowledge proofs | secure protocols | two-party secure computation | multiparty secure computation | chosen-ciphertext security | 6.876 | 18.426

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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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

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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Testing guns at the firing range, Silloth Testing guns at the firing range, Silloth

Description

Subjects

sky | sky | industry | industry | wheel | wheel | stone | stone | standing | standing | outdoors | outdoors | interesting | interesting | gun | gun | industrial | industrial | mechanical | mechanical | unitedkingdom | unitedkingdom | drum | drum | britain | britain | crane | crane | label | label | military | military | debris | debris | pipe | pipe | platform | platform | rail | rail | testing | testing | chain | chain | northumberland | northumberland | cap | cap | pile | pile | cumbria | cumbria | archives | archives | overalls | overalls | target | target | artillery | artillery | products | products | unusual | unusual | striking | striking | armstrong | armstrong | crease | crease | cog | cog | operating | operating | attentive | attentive | weapons | weapons | firing | firing | lever | lever | newcastleupontyne | newcastleupontyne | whitworth | whitworth | fascinating | fascinating | mounting | mounting | digitalimage | digitalimage | workman | workman | factories | factories | silloth | silloth | customers | customers | firingrange | firingrange | manufacture | manufacture | nineteenthcentury | nineteenthcentury | rivertyne | rivertyne | manufacturing | manufacturing | industrialheritage | industrialheritage | armaments | armaments | blackandwhitephotograph | blackandwhitephotograph | northeastofengland | northeastofengland | armstrongwhitworth | armstrongwhitworth | lordarmstrong | lordarmstrong | ridsdale | ridsdale | elswickworks | elswickworks | williamgeorgearmstrong | williamgeorgearmstrong | workshopoftheworld | workshopoftheworld | testingguns | testingguns | scotswoodworks | scotswoodworks | sillothonsolway | sillothonsolway | proofrange | proofrange | vickersarmstrongcollection | vickersarmstrongcollection | breechloadingguns | breechloadingguns | proofranges | proofranges | 27october1926 | 27october1926 | 4inchgimbalmountings | 4inchgimbalmountings | 8inchbreechloadinggun | 8inchbreechloadinggun

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6.042J Mathematics for Computer Science (MIT) 6.042J Mathematics for Computer Science (MIT)

Description

This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science). This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science).

Subjects

mathematical definitions | mathematical definitions | proofs and applicable methods | proofs and applicable methods | formal logic notation | formal logic notation | proof methods | proof methods | induction | induction | well-ordering | well-ordering | sets | sets | relations | relations | elementary graph theory | elementary graph theory | integer congruences | integer congruences | asymptotic notation and growth of functions | asymptotic notation and growth of functions | permutations and combinations | counting principles | permutations and combinations | counting principles | discrete probability | discrete probability | recursive definition | recursive definition | structural induction | structural induction | state machines and invariants | state machines and invariants | recurrences | recurrences | generating functions | generating functions | permutations and combinations | permutations and combinations | counting principles | counting principles | discrete mathematics | discrete mathematics | computer science | computer science

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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6.042J Mathematics for Computer Science (MIT) 6.042J Mathematics for Computer Science (MIT)

Description

This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability. This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.

Subjects

Elementary discrete mathematics for computer science and engineering | Elementary discrete mathematics for computer science and engineering | mathematical definitions | mathematical definitions | proofs and applicable methods | proofs and applicable methods | formal logic notation | formal logic notation | proof methods | proof methods | induction | induction | well-ordering | well-ordering | sets | sets | relations | relations | elementary graph theory | elementary graph theory | integer congruences | integer congruences | asymptotic notation and growth of functions | asymptotic notation and growth of functions | permutations and combinations | permutations and combinations | counting principles | counting principles | discrete probability | discrete probability | recursive definition | recursive definition | structural induction | structural induction | state machines and invariants | state machines and invariants | recurrences | recurrences | generating functions | generating functions | 6.042 | 6.042 | 18.062 | 18.062

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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How and why we do mathematical proofs How and why we do mathematical proofs

Description

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area 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; * ho 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; * ho

Subjects

UNow | UNow | UKOER | UKOER | Proofs Definitions Prime Number | Proofs Definitions Prime Number | Perfect Square Simpson's Paradox | Perfect Square Simpson's Paradox | Sequence Series | Sequence Series | Odd Functions Even Functions | Odd Functions Even Functions | Simpson's Paradox Strictly Increasing | Simpson's Paradox Strictly Increasing | Direct Proofs Comparison Test | Direct Proofs Comparison Test | Odd Numbers Multiples Eight | Odd Numbers Multiples Eight | Pure Maths Pure Mathematics Pure math | Pure Maths Pure Mathematics Pure math | Convergence Divergence | Convergence Divergence

License

Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA) Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA)

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

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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6.042J Mathematics for Computer Science (MIT) 6.042J Mathematics for Computer Science (MIT)

Description

This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability. This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.

Subjects

Elementary discrete mathematics for computer science and engineering | Elementary discrete mathematics for computer science and engineering | mathematical definitions | mathematical definitions | proofs and applicable methods | proofs and applicable methods | formal logic notation | formal logic notation | proof methods | proof methods | induction | induction | well-ordering | well-ordering | sets | sets | relations | relations | elementary graph theory | elementary graph theory | integer congruences | integer congruences | asymptotic notation and growth of functions | asymptotic notation and growth of functions | permutations and combinations | permutations and combinations | counting principles | counting principles | discrete probability | discrete probability | recursive definition | recursive definition | structural induction | structural induction | state machines and invariants | state machines and invariants | recurrences | recurrences | generating functions | generating functions | 6.042 | 6.042 | 18.062 | 18.062

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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Barn. Mansard type nr Richmond BC

Description

Subjects

Location\North America | barn | economic | gabled gambrel roof | mansard roof | roofs and spans

License

 (CC BY-NC-ND 4.0) https://creativecommons.org/licenses/by-nc-nd/4.0/ Copyright belongs to Paul Oliver Vernacular Architecture Library Copyright belongs to Paul Oliver Vernacular Architecture Library

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6.042J Mathematics for Computer Science (MIT)

Description

This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science).

Subjects

mathematical definitions | proofs and applicable methods | formal logic notation | proof methods | induction | well-ordering | sets | relations | elementary graph theory | integer congruences | asymptotic notation and growth of functions | permutations and combinations | counting principles | discrete probability | recursive definition | structural induction | state machines and invariants | recurrences | generating functions | permutations and combinations | counting principles | discrete mathematics | computer science

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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Eldon Square War Memorial on St George's Day Eldon Square War Memorial on St George's Day

Description

Subjects

door | door | flowers | flowers | 1920s | 1920s | roof | roof | chimney | chimney | sky | sky | people | people | blur | blur | window | window | glass | glass | car | car | wheel | wheel | statue | statue | wall | wall | architecture | architecture | 1932 | 1932 | buildings | buildings | square | square | interesting | interesting | chair | chair | uniform | uniform | branch | branch | lordmayor | lordmayor | dress | dress | unitedkingdom | unitedkingdom | path | path | military | military | duty | duty | grain | grain | lawn | lawn | structure | structure | historic | historic | line | line | marks | marks | event | event | step | step | fabric | fabric | frame | frame | signage | signage | gathering | gathering | archives | archives | land | land | soldiers | soldiers | service | service | unusual | unusual | sheriff | sheriff | 1912 | 1912 | remembrance | remembrance | striking | striking | warmemorial | warmemorial | eldonsquare | eldonsquare | tyneside | tyneside | crease | crease | crowds | crowds | newcastleupontyne | newcastleupontyne | fascinating | fascinating | 1877 | 1877 | digitalimage | digitalimage | blyth | blyth | citycouncil | citycouncil | commemoration | commemoration | alderman | alderman | stgeorgesday | stgeorgesday | socialhistory | socialhistory | northeastengland | northeastengland | blackandwhitephotograph | blackandwhitephotograph | 19241925 | 19241925 | northeastofengland | northeastofengland | 19361937 | 19361937 | cityofnewcastleupontyne | cityofnewcastleupontyne | servingthecity | servingthecity | thetyreshop | thetyreshop | johngrantham | johngrantham | 23april1925 | 23april1925 | cinemaproprietor | cinemaproprietor

License

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The cargo ship 'Sir David' leaving the River Tyne The cargo ship 'Sir David' leaving the River Tyne

Description

Subjects

southshields | southshields | shipbuilding | shipbuilding | johnreadheadsonsltd | johnreadheadsonsltd | cargoship | cargoship | sirdavid | sirdavid | sea | sea | water | water | vessel | vessel | shipping | shipping | maritime | maritime | tyneside | tyneside | northeastengland | northeastengland | rivertyne | rivertyne | tynemouth | tynemouth | rivers | rivers | maritimeheritage | maritimeheritage | industrialheritage | industrialheritage | shipbuildingheritage | shipbuildingheritage | blackandwhitephotograph | blackandwhitephotograph | industry | industry | digitalimage | digitalimage | archives | archives | abstract | abstract | unitedkingdom | unitedkingdom | ship | ship | seatrials | seatrials | 1927 | 1927 | johnreadhead | johnreadhead | johnreadheadsonssouthshields | johnreadheadsonssouthshields | readheads | readheads | jsoftley | jsoftley | lawe | lawe | johnreadheadco | johnreadheadco | highwestyard | highwestyard | swanhuntergroup | swanhuntergroup | britishshipbuilders | britishshipbuilders | hainsteamshipcompanyltd | hainsteamshipcompanyltd | stricklineltd | stricklineltd | princeline | princeline | sirjamesknott | sirjamesknott | fascinating | fascinating | unusual | unusual | impressive | impressive | interesting | interesting | chimney | chimney | cylinder | cylinder | smoke | smoke | land | land | buildings | buildings | vegetation | vegetation | deck | deck | mast | mast | flags | flags | wind | wind | cabin | cabin | bar | bar | porthole | porthole | letter | letter | signage | signage | pole | pole | crew | crew | transportation | transportation | bank | bank | wall | wall | roof | roof | window | window | door | door | vent | vent | construction | construction | structure | structure | development | development | sky | sky | grain | grain | mark | mark | channel | channel

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Collecting scrap at Hetton Station Goods Yard Collecting scrap at Hetton Station Goods Yard

Description

Subjects

road | road | roof | roof | sky | sky | abstract | abstract | blur | blur | industry | industry | wheel | wheel | metal | metal | stone | stone | wall | wall | shirt | shirt | yard | yard | standing | standing | fence | fence | buildings | buildings | 1974 | 1974 | interesting | interesting | workers | workers | industrial | industrial | carriage | carriage | unitedkingdom | unitedkingdom | path | path | timber | timber | mark | mark | coat | coat | debris | debris | caps | caps | grain | grain | plate | plate | ground | ground | social | social | number | number | soil | soil | cap | cap | transportation | transportation | signage | signage | bolt | bolt | archives | archives | land | land | letter | letter | vehicle | vehicle | trousers | trousers | unusual | unusual | telegraphpole | telegraphpole | scrap | scrap | railways | railways | crease | crease | flap | flap | attentive | attentive | slope | slope | collecting | collecting | numberplate | numberplate | fascinating | fascinating | digitalimage | digitalimage | sunderland | sunderland | scrapmetal | scrapmetal | citycouncil | citycouncil | 1895 | 1895 | blackandwhitephotograph | blackandwhitephotograph | northeastofengland | northeastofengland | goodsyard | goodsyard | moorsley | moorsley | mid20thcentury | mid20thcentury | eastrainton | eastrainton | hettonlehole | hettonlehole | easingtonlane | easingtonlane | hettondowns | hettondowns | hettonurbandistrictcouncil | hettonurbandistrictcouncil | hettonstationgoodsyard | hettonstationgoodsyard | hettonleholeurbandistrict | hettonleholeurbandistrict | sunderlandmetropolitanborough | sunderlandmetropolitanborough | localgovernmentact1894 | localgovernmentact1894

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6.042J Mathematics for Computer Science (MIT)

Description

This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.

Subjects

Elementary discrete mathematics for computer science and engineering | mathematical definitions | proofs and applicable methods | formal logic notation | proof methods | induction | well-ordering | sets | relations | elementary graph theory | integer congruences | asymptotic notation and growth of functions | permutations and combinations | counting principles | discrete probability | recursive definition | structural induction | state machines and invariants | recurrences | generating functions | 6.042 | 18.062

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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Why do we do proofs? Why do we do proofs?

Description

The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. 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 (Fermat's Last Theorem); sometimes statements which appear to be intuitively obvious may turn out to be false (the Hospitals paradox); the answer to a question will often depend crucially on the definitions you are working with. Target audience: suitable for anyone with a knowledge of elementary algebra and prime numbers, as may be obtained by studying A level mathematics. The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. 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 (Fermat's Last Theorem); sometimes statements which appear to be intuitively obvious may turn out to be false (the Hospitals paradox); the answer to a question will often depend crucially on the definitions you are working with. Target audience: suitable for anyone with a knowledge of elementary algebra and prime numbers, as may be obtained by studying A level mathematics.

Subjects

UNow | UNow | Mathematical proofs | Mathematical proofs | UKOER | UKOER

License

Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA) Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA)

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Château de Blois, Exterior Detail of the Grand Staircase Tower (Louis XII Wing)

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.01296 Title: Château de Blois, Exterior Detail of the Grand Staircase Tower (Louis XII Wing) Photographer: Neurdein Frères (French, active ca. 1863-1912) Building Date: 1498-1503 Photograph date: ca. 1865-ca. 1895 Location: Europe: France; Blois Materials: albumen print Image: 10.4331 x 7.8346 in.; 26.5 x 19.9 cm Style: Flamboyant Gothic Provenance: Transfer from the College of Architecture, Art and Planning Persistent URI: hdl.handle.net/1813.001/5tgh 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 | châteaudebloisbloisfrance | châteaux | palaces | towers | mansardroofs | wroughtiron | dormers | egganddartmoldings | stairways | grilledwindows | porcupines | animals | crowns | symbolsofoffice | escutcheonscoatsofarms | fleursdelis | plantderivedmotifs | rooftops | culidentifier:value=155309001296 | culidentifier:lunafield=accessionnumber

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View of 'Naess Crusader' from across the River Wear View of 'Naess Crusader' from across the River Wear

Description

Subjects

roof | roof | sky | sky | cloud | cloud | abstract | abstract | building | building | industry | industry | window | window | water | water | wall | wall | daylight | daylight | interesting | interesting | construction | construction | marine | marine | industrial | industrial | ship | ship | unitedkingdom | unitedkingdom | crane | crane | platform | platform | bank | bank | rail | rail | vessel | vessel | rope | rope | structure | structure | historic | historic | riverwear | riverwear | beam | beam | cranes | cranes | deck | deck | walkway | walkway | bow | bow | land | land | unusual | unusual | shipyard | shipyard | shipping | shipping | majestic | majestic | stern | stern | development | development | carrier | carrier | fascinating | fascinating | digitalimage | digitalimage | sunderland | sunderland | landcape | landcape | shipbuilding | shipbuilding | industrialheritage | industrialheritage | wearside | wearside | northeastengland | northeastengland | blackandwhitephotograph | blackandwhitephotograph | northeastofengland | northeastofengland | shipbuildingheritage | shipbuildingheritage | maritimeheritage | maritimeheritage | obocarrier | obocarrier | northsandsshipyard | northsandsshipyard | oilbulkore | oilbulkore | sunderlandshipbuildersltd | sunderlandshipbuildersltd | northsandssunderland | northsandssunderland | naesscrusader | naesscrusader | turnersphotographyltd | turnersphotographyltd | 14august1972 | 14august1972 | sunderlandkeelline | sunderlandkeelline | naesscrusadersunderlandslargestship | naesscrusadersunderlandslargestship | angloeasternbulkshipsltd | angloeasternbulkshipsltd

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Sons Sons

Description

Subjects

road | road | houses | houses | roof | roof | chimney | chimney | abstract | abstract | reflection | reflection | heritage | heritage | industry | industry | window | window | water | water | glass | glass | grass | grass | wall | wall | buildings | buildings | daylight | daylight | construction | construction | cabin | cabin | industrial | industrial | ship | ship | name | name | ships | ships | border | border | platform | platform | bank | bank | rail | rail | vessel | vessel | row | row | cranes | cranes | deck | deck | transportation | transportation | frame | frame | cylinder | cylinder | land | land | vegetation | vegetation | letter | letter | vehicle | vehicle | unusual | unusual | mast | mast | coal | coal | shipyard | shipyard | striking | striking | brand | brand | southshields | southshields | partnership | partnership | vessels | vessels | fascinating | fascinating | digitalimage | digitalimage | 1865 | 1865 | staithes | staithes | rivertyne | rivertyne | shipbuilding | shipbuilding | aerialphotograph | aerialphotograph | tyneandwear | tyneandwear | industrialheritage | industrialheritage | southtyneside | southtyneside | tyneriver | tyneriver | blackandwhitephotograph | blackandwhitephotograph | lawe | lawe | northeastofengland | northeastofengland | maritimeheritage | maritimeheritage | sirjamesknott | sirjamesknott | johnreadhead | johnreadhead | stricklineltd | stricklineltd | shipbuildinghistory | shipbuildinghistory | princeline | princeline | britishshipbuilders | britishshipbuilders | hainsteamshipcompanyltd | hainsteamshipcompanyltd | johnreadheadsonsltd | johnreadheadsonsltd | highwestyard | highwestyard | johnreadheadsonssouthshields | johnreadheadsonssouthshields | jsoftley | jsoftley | swanhuntergroup | swanhuntergroup | johnreadheadco | johnreadheadco | 10may1963 | 10may1963

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Estate and property outside Clonmel Estate and property outside Clonmel

Description

Subjects

ireland | ireland | stream | stream | smith | smith | hills | hills | valley | valley | blacksmith | blacksmith | 1906 | 1906 | waterford | waterford | munster | munster | glassnegative | glassnegative | smithy | smithy | slateroof | slateroof | cowaterford | cowaterford | ruralscene | ruralscene | nationallibraryofireland | nationallibraryofireland | johnfarrell | johnfarrell | ahpoole | ahpoole | locationidentified | locationidentified | peopleidentified | peopleidentified | poolecollection | poolecollection | arthurhenripoole | arthurhenripoole | graignagower | graignagower | knockatrellane | knockatrellane | parishofknockatrellane | parishofknockatrellane | johannafarrell | johannafarrell | 17thjanuary1906 | 17thjanuary1906

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18.100A Introduction to Analysis (MIT) 18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | estimations | estimations | limit of a sequence | limit of a sequence | limit theorems | limit theorems | subsequences | subsequences | cluster points | cluster points | infinite series | infinite series | power series | power series | local and global properties | local and global properties | continuity | continuity | intermediate-value theorem | intermediate-value theorem | convexity | convexity | integrability | integrability | Riemann integral | Riemann integral | calculus | calculus | convergence | convergence | Gamma function | Gamma function | Stirling | Stirling | quantifiers and negation | quantifiers and negation | Leibniz | Leibniz | Fubini | Fubini | improper integrals | improper integrals | Lebesgue integral | Lebesgue integral | mathematical proofs | mathematical proofs | differentiation | differentiation | integration | integration

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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CALVisual Images : Loughborough University Busines School Development

Description

A collection of 68 images of Loughborough Business School development for use in teaching civil engineering.

Subjects

development | preparation of foundations | laying foundations | reinforced concrete columns | structural frame assembly | cement mixer | concrete cast in situ | waterproofing to in situ concrete | ceiling supports | tower crane | falsework | staircase | concrete floor slab | access panels | structural steelwork | profiled roof sheeting | wall cladding | ukoer | engscoer | loughboroughunioer | loughborough university business school | construction site | fencing off | Engineering | H000

License

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

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Presentation at the launch of 'Armanistan' Presentation at the launch of 'Armanistan'

Description

Subjects

flowers | flowers | roof | roof | shadow | shadow | sky | sky | abstract | abstract | flower | flower | men | men | industry | industry | window | window | smile | smile | hat | hat | stone | stone | wall | wall | shirt | shirt | yard | yard | standing | standing | buildings | buildings | beard | beard | shoe | shoe | daylight | daylight | interesting | interesting | wire | wire | construction | construction | women | women | industrial | industrial | timber | timber | coat | coat | debris | debris | grain | grain | hats | hats | tie | tie | ground | ground | vessel | vessel | social | social | furcoat | furcoat | petal | petal | moustache | moustache | frame | frame | gathering | gathering | trousers | trousers | worker | worker | presentation | presentation | unusual | unusual | launch | launch | shipyard | shipyard | telegraphpole | telegraphpole | southshields | southshields | crease | crease | wrinkle | wrinkle | development | development | partnership | partnership | readhead | readhead | fascinating | fascinating | digitalimage | digitalimage | shipbuilding | shipbuilding | shiplaunch | shiplaunch | cargoship | cargoship | blackandwhitephotograph | blackandwhitephotograph | lawe | lawe | northeastofengland | northeastofengland | maritimeheritage | maritimeheritage | johnreadhead | johnreadhead | strickline | strickline | britishshipbuilders | britishshipbuilders | shipyardworker | shipyardworker | armanistan | armanistan | johnreadheadsonsltd | johnreadheadsonsltd | johnreadheadsons | johnreadheadsons | highwestyard | highwestyard | johnreadheadsonssouthshields | johnreadheadsonssouthshields | jsoftley | jsoftley | swanhuntergroup | swanhuntergroup | 30november1948 | 30november1948 | johnreadheadco | johnreadheadco

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Looking up Dean Street, Newcastle upon Tyne Looking up Dean Street, Newcastle upon Tyne

Description

Subjects

road | road | street | street | door | door | city | city | bridge | bridge | roof | roof | shadow | shadow | sky | sky | people | people | abstract | abstract | reflection | reflection | cars | cars | industry | industry | window | window | glass | glass | hat | hat | wheel | wheel | stone | stone | wall | wall | buildings | buildings | paper | paper | walking | walking | advertising | advertising | handle | handle | daylight | daylight | clothing | clothing | interesting | interesting | construction | construction | arch | arch | unitedkingdom | unitedkingdom | seat | seat | curtain | curtain | tie | tie | pedestrian | pedestrian | billboard | billboard | suit | suit | shade | shade | transportation | transportation | frame | frame | signage | signage | archives | archives | land | land | vehicle | vehicle | products | products | gutter | gutter | 1960s | 1960s | unusual | unusual | cigarettes | cigarettes | striking | striking | tyneside | tyneside | development | development | consumerism | consumerism | impressive | impressive | streetview | streetview | businesses | businesses | newcastleupontyne | newcastleupontyne | fascinating | fascinating | digitalimage | digitalimage | deanstreet | deanstreet | heritagebuildings | heritagebuildings | sidestreet | sidestreet | premises | premises | industrialheritage | industrialheritage | motorist | motorist | theside | theside | northeastengland | northeastengland | blackandwhitephotograph | blackandwhitephotograph | northeastofengland | northeastofengland | artanddesign | artanddesign | dailylives | dailylives | northbritish | northbritish | november1963 | november1963 | curvedstructure | curvedstructure | turnersltd | turnersltd | scenicviewsofnewcastle | scenicviewsofnewcastle

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Official inauguration of the South Pier, Sunderland Official inauguration of the South Pier, Sunderland

Description

Subjects

portofsunderland | portofsunderland | sunderland | sunderland | riverwear | riverwear | southpier | southpier | crane | crane | victorian | victorian | ceremony | ceremony | piers | piers | harbour | harbour | marine | marine | wearside | wearside | historic | historic | sepiaphotograph | sepiaphotograph | digitalimage | digitalimage | archives | archives | industrialheritage | industrialheritage | shipbuildingheritage | shipbuildingheritage | maritimeheritage | maritimeheritage | abstract | abstract | northeastofengland | northeastofengland | unitedkingdom | unitedkingdom | officialinauguration | officialinauguration | blocklayingceremony | blocklayingceremony | newsouthpier | newsouthpier | construction | construction | structure | structure | riverwearcommissioners | riverwearcommissioners | 12september1893 | 12september1893 | 300thanniversary | 300thanniversary | portauthority | portauthority | 1717 | 1717 | actofparliament | actofparliament | management | management | river | river | port | port | development | development | changes | changes | docks | docks | quays | quays | dredging | dredging | coaltrade | coaltrade | region | region | alliedindustries | alliedindustries | marineengineering | marineengineering | shiprepairing | shiprepairing | crease | crease | grain | grain | mark | mark | block | block | stone | stone | pole | pole | flag | flag | platform | platform | men | men | workers | workers | cabin | cabin | window | window | sky | sky | water | water | wall | wall | roof | roof | stairs | stairs | debris | debris | land | land | bank | bank | blur | blur | buildings | buildings | lighthouse | lighthouse | slope | slope | cog | cog | wire | wire | fascinating | fascinating | interesting | interesting | unusual | unusual | standing | standing

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