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IV (MIT) IV (MIT)

Description

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls files The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls files

Subjects

Unified | Unified | Unified Engineering | Unified Engineering | aerospace | aerospace | CDIO | CDIO | C-D-I-O | C-D-I-O | conceive | conceive | design | design | implement | implement | operate | operate | team | team | team-based | team-based | discipline | discipline | materials | materials | structures | structures | materials and structures | materials and structures | computers | computers | programming | programming | computers and programming | computers and programming | fluids | fluids | fluid mechanics | fluid mechanics | thermodynamics | thermodynamics | propulsion | propulsion | signals | signals | systems | systems | signals and systems | signals and systems | systems problems | systems problems | fundamentals | fundamentals | technical communication | technical communication | graphical communication | graphical communication | communication | communication | reading | reading | research | research | experimentation | experimentation | personal response system | personal response system | prs | prs | active learning | active learning | First law | First law | first law of thermodynamics | first law of thermodynamics | thermo-mechanical | thermo-mechanical | energy | energy | energy conversion | energy conversion | aerospace power systems | aerospace power systems | propulsion systems | propulsion systems | aerospace propulsion systems | aerospace propulsion systems | heat | heat | work | work | thermal efficiency | thermal efficiency | forms of energy | forms of energy | energy exchange | energy exchange | processes | processes | heat engines | heat engines | engines | engines | steady-flow energy equation | steady-flow energy equation | energy flow | energy flow | flows | flows | path-dependence | path-dependence | path-independence | path-independence | reversibility | reversibility | irreversibility | irreversibility | state | state | thermodynamic state | thermodynamic state | performance | performance | ideal cycle | ideal cycle | simple heat engine | simple heat engine | cycles | cycles | thermal pressures | thermal pressures | temperatures | temperatures | linear static networks | linear static networks | loop method | loop method | node method | node method | linear dynamic networks | linear dynamic networks | classical methods | classical methods | state methods | state methods | state concepts | state concepts | dynamic systems | dynamic systems | resistive circuits | resistive circuits | sources | sources | voltages | voltages | currents | currents | Thevinin | Thevinin | Norton | Norton | initial value problems | initial value problems | RLC networks | RLC networks | characteristic values | characteristic values | characteristic vectors | characteristic vectors | transfer function | transfer function | ada | ada | ada programming | ada programming | programming language | programming language | software systems | software systems | programming style | programming style | computer architecture | computer architecture | program language evolution | program language evolution | classification | classification | numerical computation | numerical computation | number representation systems | number representation systems | assembly | assembly | SimpleSIM | SimpleSIM | RISC | RISC | CISC | CISC | operating systems | operating systems | single user | single user | multitasking | multitasking | multiprocessing | multiprocessing | domain-specific classification | domain-specific classification | recursive | recursive | execution time | execution time | fluid dynamics | fluid dynamics | physical properties of a fluid | physical properties of a fluid | fluid flow | fluid flow | mach | mach | reynolds | reynolds | conservation | conservation | conservation principles | conservation principles | conservation of mass | conservation of mass | conservation of momentum | conservation of momentum | conservation of energy | conservation of energy | continuity | continuity | inviscid | inviscid | steady flow | steady flow | simple bodies | simple bodies | airfoils | airfoils | wings | wings | channels | channels | aerodynamics | aerodynamics | forces | forces | moments | moments | equilibrium | equilibrium | freebody diagram | freebody diagram | free-body | free-body | free body | free body | planar force systems | planar force systems | equipollent systems | equipollent systems | equipollence | equipollence | support reactions | support reactions | reactions | reactions | static determinance | static determinance | determinate systems | determinate systems | truss analysis | truss analysis | trusses | trusses | method of joints | method of joints | method of sections | method of sections | statically indeterminate | statically indeterminate | three great principles | three great principles | 3 great principles | 3 great principles | indicial notation | indicial notation | rotation of coordinates | rotation of coordinates | coordinate rotation | coordinate rotation | stress | stress | extensional stress | extensional stress | shear stress | shear stress | notation | notation | plane stress | plane stress | stress equilbrium | stress equilbrium | stress transformation | stress transformation | mohr | mohr | mohr's circle | mohr's circle | principal stress | principal stress | principal stresses | principal stresses | extreme shear stress | extreme shear stress | strain | strain | extensional strain | extensional strain | shear strain | shear strain | strain-displacement | strain-displacement | compatibility | compatibility | strain transformation | strain transformation | transformation of strain | transformation of strain | mohr's circle for strain | mohr's circle for strain | principal strain | principal strain | extreme shear strain | extreme shear strain | uniaxial stress-strain | uniaxial stress-strain | material properties | material properties | classes of materials | classes of materials | bulk material properties | bulk material properties | origin of elastic properties | origin of elastic properties | structures of materials | structures of materials | atomic bonding | atomic bonding | packing of atoms | packing of atoms | atomic packing | atomic packing | crystals | crystals | crystal structures | crystal structures | polymers | polymers | estimate of moduli | estimate of moduli | moduli | moduli | composites | composites | composite materials | composite materials | modulus limited design | modulus limited design | material selection | material selection | materials selection | materials selection | measurement of elastic properties | measurement of elastic properties | stress-strain | stress-strain | stress-strain relations | stress-strain relations | anisotropy | anisotropy | orthotropy | orthotropy | measurements | measurements | engineering notation | engineering notation | Hooke | Hooke | Hooke's law | Hooke's law | general hooke's law | general hooke's law | equations of elasticity | equations of elasticity | boundary conditions | boundary conditions | multi-disciplinary | multi-disciplinary | models | models | engineering systems | engineering systems | experiments | experiments | investigations | investigations | experimental error | experimental error | design evaluation | design evaluation | evaluation | evaluation | trade studies | trade studies | effects of engineering | effects of engineering | social context | social context | engineering drawings | engineering drawings | 16.01 | 16.01 | 16.02 | 16.02 | 16.03 | 16.03 | 16.04 | 16.04

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IV (MIT) IV (MIT)

Description

Includes audio/video content: AV selected lectures, AV faculty introductions, AV special element video. The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines. Includes audio/video content: AV selected lectures, AV faculty introductions, AV special element video. The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.

Subjects

Unified | Unified | Unified Engineering | Unified Engineering | aerospace | aerospace | CDIO | CDIO | C-D-I-O | C-D-I-O | conceive | conceive | design | design | implement | implement | operate | operate | team | team | team-based | team-based | discipline | discipline | materials | materials | structures | structures | materials and structures | materials and structures | computers | computers | programming | programming | computers and programming | computers and programming | fluids | fluids | fluid mechanics | fluid mechanics | thermodynamics | thermodynamics | propulsion | propulsion | signals | signals | systems | systems | signals and systems | signals and systems | systems problems | systems problems | fundamentals | fundamentals | technical communication | technical communication | graphical communication | graphical communication | communication | communication | reading | reading | research | research | experimentation | experimentation | personal response system | personal response system | prs | prs | active learning | active learning | First law | First law | first law of thermodynamics | first law of thermodynamics | thermo-mechanical | thermo-mechanical | energy | energy | energy conversion | energy conversion | aerospace power systems | aerospace power systems | propulsion systems | propulsion systems | aerospace propulsion systems | aerospace propulsion systems | heat | heat | work | work | thermal efficiency | thermal efficiency | forms of energy | forms of energy | energy exchange | energy exchange | processes | processes | heat engines | heat engines | engines | engines | steady-flow energy equation | steady-flow energy equation | energy flow | energy flow | flows | flows | path-dependence | path-dependence | path-independence | path-independence | reversibility | reversibility | irreversibility | irreversibility | state | state | thermodynamic state | thermodynamic state | performance | performance | ideal cycle | ideal cycle | simple heat engine | simple heat engine | cycles | cycles | thermal pressures | thermal pressures | temperatures | temperatures | linear static networks | linear static networks | loop method | loop method | node method | node method | linear dynamic networks | linear dynamic networks | classical methods | classical methods | state methods | state methods | state concepts | state concepts | dynamic systems | dynamic systems | resistive circuits | resistive circuits | sources | sources | voltages | voltages | currents | currents | Thevinin | Thevinin | Norton | Norton | initial value problems | initial value problems | RLC networks | RLC networks | characteristic values | characteristic values | characteristic vectors | characteristic vectors | transfer function | transfer function | ada | ada | ada programming | ada programming | programming language | programming language | software systems | software systems | programming style | programming style | computer architecture | computer architecture | program language evolution | program language evolution | classification | classification | numerical computation | numerical computation | number representation systems | number representation systems | assembly | assembly | SimpleSIM | SimpleSIM | RISC | RISC | CISC | CISC | operating systems | operating systems | single user | single user | multitasking | multitasking | multiprocessing | multiprocessing | domain-specific classification | domain-specific classification | recursive | recursive | execution time | execution time | fluid dynamics | fluid dynamics | physical properties of a fluid | physical properties of a fluid | fluid flow | fluid flow | mach | mach | reynolds | reynolds | conservation | conservation | conservation principles | conservation principles | conservation of mass | conservation of mass | conservation of momentum | conservation of momentum | conservation of energy | conservation of energy | continuity | continuity | inviscid | inviscid | steady flow | steady flow | simple bodies | simple bodies | airfoils | airfoils | wings | wings | channels | channels | aerodynamics | aerodynamics | forces | forces | moments | moments | equilibrium | equilibrium | freebody diagram | freebody diagram | free-body | free-body | free body | free body | planar force systems | planar force systems | equipollent systems | equipollent systems | equipollence | equipollence | support reactions | support reactions | reactions | reactions | static determinance | static determinance | determinate systems | determinate systems | truss analysis | truss analysis | trusses | trusses | method of joints | method of joints | method of sections | method of sections | statically indeterminate | statically indeterminate | three great principles | three great principles | 3 great principles | 3 great principles | indicial notation | indicial notation | rotation of coordinates | rotation of coordinates | coordinate rotation | coordinate rotation | stress | stress | extensional stress | extensional stress | shear stress | shear stress | notation | notation | plane stress | plane stress | stress equilbrium | stress equilbrium | stress transformation | stress transformation | mohr | mohr | mohr's circle | mohr's circle | principal stress | principal stress | principal stresses | principal stresses | extreme shear stress | extreme shear stress | strain | strain | extensional strain | extensional strain | shear strain | shear strain | strain-displacement | strain-displacement | compatibility | compatibility | strain transformation | strain transformation | transformation of strain | transformation of strain | mohr's circle for strain | mohr's circle for strain | principal strain | principal strain | extreme shear strain | extreme shear strain | uniaxial stress-strain | uniaxial stress-strain | material properties | material properties | classes of materials | classes of materials | bulk material properties | bulk material properties | origin of elastic properties | origin of elastic properties | structures of materials | structures of materials | atomic bonding | atomic bonding | packing of atoms | packing of atoms | atomic packing | atomic packing | crystals | crystals | crystal structures | crystal structures | polymers | polymers | estimate of moduli | estimate of moduli | moduli | moduli | composites | composites | composite materials | composite materials | modulus limited design | modulus limited design | material selection | material selection | materials selection | materials selection | measurement of elastic properties | measurement of elastic properties | stress-strain | stress-strain | stress-strain relations | stress-strain relations | anisotropy | anisotropy | orthotropy | orthotropy | measurements | measurements | engineering notation | engineering notation | Hooke | Hooke | Hooke's law | Hooke's law | general hooke's law | general hooke's law | equations of elasticity | equations of elasticity | boundary conditions | boundary conditions | multi-disciplinary | multi-disciplinary | models | models | engineering systems | engineering systems | experiments | experiments | investigations | investigations | experimental error | experimental error | design evaluation | design evaluation | evaluation | evaluation | trade studies | trade studies | effects of engineering | effects of engineering | social context | social context | engineering drawings | engineering drawings

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

Includes audio/video content: AV lectures. This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include 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. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. Includes audio/video content: AV lectures. This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include 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. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Subjects

formal logic notation | formal logic notation | proof methods | proof methods | induction | induction | sets | sets | relations | relations | graph theory | graph theory | integer congruences | integer congruences | asymptotic notation | asymptotic notation | growth of functions | growth of functions | permutations | permutations | combinations | combinations | counting | counting | discrete probability | discrete probability

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 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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18.417 Introduction to Computational Molecular Biology (MIT) 18.417 Introduction to Computational Molecular Biology (MIT)

Description

This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics. This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.

Subjects

basic computational methods cell on a molecular level | basic computational methods cell on a molecular level | sequence alignment algorithms | sequence alignment algorithms | dynamic programming | dynamic programming | hashing | hashing | suffix trees | suffix trees | Gibbs sampling | Gibbs sampling | genetic and physical mapping | genetic and physical mapping | genome sequencing | genome sequencing | assembly | assembly | and annotation | and annotation | RNA expression and secondary structure | RNA expression and secondary structure | protein structure and folding | protein structure and folding | and molecular interactions and dynamics | and molecular interactions and dynamics | annotation | annotation | molecular interactions and dynamics | molecular interactions and dynamics

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

Description

Includes audio/video content: AV lectures. This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042J, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.Interactive site components can be found on the Unit pages in the Includes audio/video content: AV lectures. This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042J, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.Interactive site components can be found on the Unit pages in the

Subjects

6.042 | 6.042 | 18.062 | 18.062 | formal logic notation | formal logic notation | proof methods | proof methods | induction | induction | sets | sets | relations | relations | graph theory | graph theory | integer congruences | integer congruences | asymptotic notation | asymptotic notation | growth of functions | growth of functions | permutations | permutations | combinations | combinations | counting | counting | discrete probability | discrete probability

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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IV (MIT)

Description

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.

Subjects

Unified | Unified Engineering | aerospace | CDIO | C-D-I-O | conceive | design | implement | operate | team | team-based | discipline | materials | structures | materials and structures | computers | programming | computers and programming | fluids | fluid mechanics | thermodynamics | propulsion | signals | systems | signals and systems | systems problems | fundamentals | technical communication | graphical communication | communication | reading | research | experimentation | personal response system | prs | active learning | First law | first law of thermodynamics | thermo-mechanical | energy | energy conversion | aerospace power systems | propulsion systems | aerospace propulsion systems | heat | work | thermal efficiency | forms of energy | energy exchange | processes | heat engines | engines | steady-flow energy equation | energy flow | flows | path-dependence | path-independence | reversibility | irreversibility | state | thermodynamic state | performance | ideal cycle | simple heat engine | cycles | thermal pressures | temperatures | linear static networks | loop method | node method | linear dynamic networks | classical methods | state methods | state concepts | dynamic systems | resistive circuits | sources | voltages | currents | Thevinin | Norton | initial value problems | RLC networks | characteristic values | characteristic vectors | transfer function | ada | ada programming | programming language | software systems | programming style | computer architecture | program language evolution | classification | numerical computation | number representation systems | assembly | SimpleSIM | RISC | CISC | operating systems | single user | multitasking | multiprocessing | domain-specific classification | recursive | execution time | fluid dynamics | physical properties of a fluid | fluid flow | mach | reynolds | conservation | conservation principles | conservation of mass | conservation of momentum | conservation of energy | continuity | inviscid | steady flow | simple bodies | airfoils | wings | channels | aerodynamics | forces | moments | equilibrium | freebody diagram | free-body | free body | planar force systems | equipollent systems | equipollence | support reactions | reactions | static determinance | determinate systems | truss analysis | trusses | method of joints | method of sections | statically indeterminate | three great principles | 3 great principles | indicial notation | rotation of coordinates | coordinate rotation | stress | extensional stress | shear stress | notation | plane stress | stress equilbrium | stress transformation | mohr | mohr's circle | principal stress | principal stresses | extreme shear stress | strain | extensional strain | shear strain | strain-displacement | compatibility | strain transformation | transformation of strain | mohr's circle for strain | principal strain | extreme shear strain | uniaxial stress-strain | material properties | classes of materials | bulk material properties | origin of elastic properties | structures of materials | atomic bonding | packing of atoms | atomic packing | crystals | crystal structures | polymers | estimate of moduli | moduli | composites | composite materials | modulus limited design | material selection | materials selection | measurement of elastic properties | stress-strain | stress-strain relations | anisotropy | orthotropy | measurements | engineering notation | Hooke | Hooke's law | general hooke's law | equations of elasticity | boundary conditions | multi-disciplinary | models | engineering systems | experiments | investigations | experimental error | design evaluation | evaluation | trade studies | effects of engineering | social context | engineering drawings

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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A Language for Movement: Transcript

Description

This is the transcript for the video "A Language for Movement" (1996) which is part of an Open University series entitled "Seeing through Mathematics". The 25 minute programme shows how notation can help the recording and reconstruction of dances. It focuses in particular on the work of Rudolf Laban and his system of notation known as Labanotation and how we can enjoy nowadays Nijinsky's ballet Afternoon of a Faun thanks to a notational score. Examples of other notational systems for movement and dance are also discussed. The video includes archive material, dancing and interviews with leading notators. There is a link to the video in this repository.

Subjects

dance | notation; Labanotation | Benesh notation | choreology | Nijinsky | Afternoon of a Faun | Tina Curran | Ann Hutchinson Guest | Warren Lamb | Rudolf Laban | Jean Johnson-Jones | geometry | mathematics | David Bintley | CCCEED | JISC digitisation and content | creativity

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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A Language for Movement: Video

Description

"A Language for Movement" (1996) is part of an Open University series entitled "Seeing through Mathematics". This 25 minute programme shows how notation can help the recording and reconstruction of dances. It focuses in particular on the work of Rudolf Laban and his system of notation known as Labanotation and how we can enjoy nowadays Nijinsky's ballet Afternoon of a Faun thanks to a notational score. Examples of other notational systems for movement and dance are also discussed. The video includes archive material, dancing and interviews with leading notators. A transcript of this video is available in this repository.

Subjects

dance | notation; Labanotation | Benesh notation | choreology | Nijinsky | Afternoon of a Faun | Tina Curran | Ann Hutchinson Guest | Warren Lamb | Rudolf Laban | Jean Johnson-Jones | geometry | mathematics | David Bintley | CCCEED | JISC digitisation and content | creativity

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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IV (MIT)

Description

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls files

Subjects

Unified | Unified Engineering | aerospace | CDIO | C-D-I-O | conceive | design | implement | operate | team | team-based | discipline | materials | structures | materials and structures | computers | programming | computers and programming | fluids | fluid mechanics | thermodynamics | propulsion | signals | systems | signals and systems | systems problems | fundamentals | technical communication | graphical communication | communication | reading | research | experimentation | personal response system | prs | active learning | First law | first law of thermodynamics | thermo-mechanical | energy | energy conversion | aerospace power systems | propulsion systems | aerospace propulsion systems | heat | work | thermal efficiency | forms of energy | energy exchange | processes | heat engines | engines | steady-flow energy equation | energy flow | flows | path-dependence | path-independence | reversibility | irreversibility | state | thermodynamic state | performance | ideal cycle | simple heat engine | cycles | thermal pressures | temperatures | linear static networks | loop method | node method | linear dynamic networks | classical methods | state methods | state concepts | dynamic systems | resistive circuits | sources | voltages | currents | Thevinin | Norton | initial value problems | RLC networks | characteristic values | characteristic vectors | transfer function | ada | ada programming | programming language | software systems | programming style | computer architecture | program language evolution | classification | numerical computation | number representation systems | assembly | SimpleSIM | RISC | CISC | operating systems | single user | multitasking | multiprocessing | domain-specific classification | recursive | execution time | fluid dynamics | physical properties of a fluid | fluid flow | mach | reynolds | conservation | conservation principles | conservation of mass | conservation of momentum | conservation of energy | continuity | inviscid | steady flow | simple bodies | airfoils | wings | channels | aerodynamics | forces | moments | equilibrium | freebody diagram | free-body | free body | planar force systems | equipollent systems | equipollence | support reactions | reactions | static determinance | determinate systems | truss analysis | trusses | method of joints | method of sections | statically indeterminate | three great principles | 3 great principles | indicial notation | rotation of coordinates | coordinate rotation | stress | extensional stress | shear stress | notation | plane stress | stress equilbrium | stress transformation | mohr | mohr's circle | principal stress | principal stresses | extreme shear stress | strain | extensional strain | shear strain | strain-displacement | compatibility | strain transformation | transformation of strain | mohr's circle for strain | principal strain | extreme shear strain | uniaxial stress-strain | material properties | classes of materials | bulk material properties | origin of elastic properties | structures of materials | atomic bonding | packing of atoms | atomic packing | crystals | crystal structures | polymers | estimate of moduli | moduli | composites | composite materials | modulus limited design | material selection | materials selection | measurement of elastic properties | stress-strain | stress-strain relations | anisotropy | orthotropy | measurements | engineering notation | Hooke | Hooke's law | general hooke's law | equations of elasticity | boundary conditions | multi-disciplinary | models | engineering systems | experiments | investigations | experimental error | design evaluation | evaluation | trade studies | effects of engineering | social context | engineering drawings | 16.01 | 16.02 | 16.03 | 16.04

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IV (MIT)

Description

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.

Subjects

Unified | Unified Engineering | aerospace | CDIO | C-D-I-O | conceive | design | implement | operate | team | team-based | discipline | materials | structures | materials and structures | computers | programming | computers and programming | fluids | fluid mechanics | thermodynamics | propulsion | signals | systems | signals and systems | systems problems | fundamentals | technical communication | graphical communication | communication | reading | research | experimentation | personal response system | prs | active learning | First law | first law of thermodynamics | thermo-mechanical | energy | energy conversion | aerospace power systems | propulsion systems | aerospace propulsion systems | heat | work | thermal efficiency | forms of energy | energy exchange | processes | heat engines | engines | steady-flow energy equation | energy flow | flows | path-dependence | path-independence | reversibility | irreversibility | state | thermodynamic state | performance | ideal cycle | simple heat engine | cycles | thermal pressures | temperatures | linear static networks | loop method | node method | linear dynamic networks | classical methods | state methods | state concepts | dynamic systems | resistive circuits | sources | voltages | currents | Thevinin | Norton | initial value problems | RLC networks | characteristic values | characteristic vectors | transfer function | ada | ada programming | programming language | software systems | programming style | computer architecture | program language evolution | classification | numerical computation | number representation systems | assembly | SimpleSIM | RISC | CISC | operating systems | single user | multitasking | multiprocessing | domain-specific classification | recursive | execution time | fluid dynamics | physical properties of a fluid | fluid flow | mach | reynolds | conservation | conservation principles | conservation of mass | conservation of momentum | conservation of energy | continuity | inviscid | steady flow | simple bodies | airfoils | wings | channels | aerodynamics | forces | moments | equilibrium | freebody diagram | free-body | free body | planar force systems | equipollent systems | equipollence | support reactions | reactions | static determinance | determinate systems | truss analysis | trusses | method of joints | method of sections | statically indeterminate | three great principles | 3 great principles | indicial notation | rotation of coordinates | coordinate rotation | stress | extensional stress | shear stress | notation | plane stress | stress equilbrium | stress transformation | mohr | mohr's circle | principal stress | principal stresses | extreme shear stress | strain | extensional strain | shear strain | strain-displacement | compatibility | strain transformation | transformation of strain | mohr's circle for strain | principal strain | extreme shear strain | uniaxial stress-strain | material properties | classes of materials | bulk material properties | origin of elastic properties | structures of materials | atomic bonding | packing of atoms | atomic packing | crystals | crystal structures | polymers | estimate of moduli | moduli | composites | composite materials | modulus limited design | material selection | materials selection | measurement of elastic properties | stress-strain | stress-strain relations | anisotropy | orthotropy | measurements | engineering notation | Hooke | Hooke's law | general hooke's law | equations of elasticity | boundary conditions | multi-disciplinary | models | engineering systems | experiments | investigations | experimental error | design evaluation | evaluation | trade studies | effects of engineering | social context | engineering drawings

License

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | coherent states | and squeezed states | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | quantum teleportation | quantum teleportation

License

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6.00 Introduction to Computer Science and Programming (MIT) 6.00 Introduction to Computer Science and Programming (MIT)

Description

This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python™ programming language. This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python™ programming language.

Subjects

computer science | computer science | computation | computation | problem solving | problem solving | Python programming | Python programming | recursion | recursion | binary search | binary search | classes | classes | inheritance | inheritance | libraries | libraries | algorithms | algorithms | optimization problems | optimization problems | modules | modules | simulation | simulation | big O notation | big O notation | control flow | control flow | exceptions | exceptions | building computational models | building computational models | software engineering | software engineering

License

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8.05 Quantum Physics II (MIT) 8.05 Quantum Physics II (MIT)

Description

This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen

Subjects

General formalism of quantum mechanics: states | General formalism of quantum mechanics: states | operators | operators | Dirac notation | Dirac notation | representations | representations | measurement theory | measurement theory | Harmonic oscillator: operator algebra | Harmonic oscillator: operator algebra | states | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | bound and scattering states | qualitative analysis of wavefunctions | qualitative analysis of wavefunctions | Angular momentum: operators | Angular momentum: operators | commutator algebra | commutator algebra | eigenvalues and eigenstates | eigenvalues and eigenstates | spherical harmonics | spherical harmonics | Spin: Stern-Gerlach devices and measurements | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | nuclear magnetic resonance | spin and statistics | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | spin systems | allotropic forms of hydrogen | allotropic forms of hydrogen | Angular momentum | Angular momentum | Harmonic oscillator | Harmonic oscillator | operator algebra | operator algebra | Spin | Spin | Stern-Gerlach devices and measurements | Stern-Gerlach devices and measurements | central potentials and the radial equation | central potentials and the radial equation | Clebsch-Gordan series and coefficients | Clebsch-Gordan series and coefficients | quantum physics | quantum physics

License

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4.123 Architectural Design, Level I: Perceptions and Processes (MIT) 4.123 Architectural Design, Level I: Perceptions and Processes (MIT)

Description

This studio explores the notion of in-between by engaging several relationships; the relationship between intervention and perception, between representation and notation and between the fixed and the temporal. In the Exactitude in Science, Jorge Luis Borges tells the perverse tale of the one to one scale map, where the desire for precision and power leads to the escalating production of larger and more accurate maps of the territory. For Jean Baudrillard, "The territory no longer precedes the map nor survives it. …it is the map that precedes the territory... and thus, it would be the territory whose shreds are slowly rotting across the map." The map or the territory, left to ruin-shredding across the 'other', beautifully captures the tension between reality and representati This studio explores the notion of in-between by engaging several relationships; the relationship between intervention and perception, between representation and notation and between the fixed and the temporal. In the Exactitude in Science, Jorge Luis Borges tells the perverse tale of the one to one scale map, where the desire for precision and power leads to the escalating production of larger and more accurate maps of the territory. For Jean Baudrillard, "The territory no longer precedes the map nor survives it. …it is the map that precedes the territory... and thus, it would be the territory whose shreds are slowly rotting across the map." The map or the territory, left to ruin-shredding across the 'other', beautifully captures the tension between reality and representati

Subjects

in-between | in-between | relationships | relationships | intervention and perception | intervention and perception | representation and notation | representation and notation | fixed and temporal | fixed and temporal | Borges | Borges | mapping | mapping | territory | territory | Baudrillard | Baudrillard | the 'other' | the 'other' | reality and representation | reality and representation | collective desire and territorial surface | collective desire and territorial surface | filter | filter | create | create | frame | frame | scale | scale | orient | orient | project | project | agency | agency | landscape | landscape | architecture | architecture | urbanism | urbanism | representation versus real | representation versus real | design | design | perception | perception | representation | representation | fixed | fixed | temporal | temporal | map | map | reality | reality | collective desire | collective desire | territorial surface | territorial surface

License

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6.00 Introduction to Computer Science and Programming (MIT) 6.00 Introduction to Computer Science and Programming (MIT)

Description

Includes audio/video content: AV lectures. This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python™ programming language. Includes audio/video content: AV lectures. This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python™ programming language.

Subjects

computer science | computer science | computation | computation | problem solving | problem solving | Python programming | Python programming | recursion | recursion | binary search | binary search | classes | classes | inheritance | inheritance | libraries | libraries | algorithms | algorithms | optimization problems | optimization problems | modules | modules | simulation | simulation | big O notation | big O notation | control flow | control flow | exceptions | exceptions | building computational models | building computational models | software engineering | software engineering

License

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.

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6.821 Programming Languages (MIT) 6.821 Programming Languages (MIT)

Description

6.821 teaches the principles of functional, imperative, and logic programming languages. Topics covered include: meta-circular interpreters, semantics (operational and denotational), type systems (polymorphism, inference, and abstract types), object oriented programming, modules, and multiprocessing. The course involves substantial programming assignments and problem sets as well as a significant amount of reading. The course uses the Scheme+ programming language for all of its assignments. 6.821 teaches the principles of functional, imperative, and logic programming languages. Topics covered include: meta-circular interpreters, semantics (operational and denotational), type systems (polymorphism, inference, and abstract types), object oriented programming, modules, and multiprocessing. The course involves substantial programming assignments and problem sets as well as a significant amount of reading. The course uses the Scheme+ programming language for all of its assignments.

Subjects

Scheme | Scheme | Scheme+ | Scheme+ | programming | programming | programming language | programming language | functional programming language | functional programming language | imperative programming language | imperative programming language | ogic programming languages | ogic programming languages | meta-circular interpreters | meta-circular interpreters | operational semantics | operational semantics | denotational semantics | denotational semantics | type systems | type systems | polymorphism | polymorphism | inference | inference | abstract types | abstract types | object oriented programming | object oriented programming | modules | modules | multiprocessing | multiprocessing

License

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20.181 Computation for Biological Engineers (MIT) 20.181 Computation for Biological Engineers (MIT)

Description

This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition. An official course Web site and Wiki is maintained on OpenWetWare: 20.181 Computation for Biological Engineers. This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition. An official course Web site and Wiki is maintained on OpenWetWare: 20.181 Computation for Biological Engineers.

Subjects

Phylogenetic Inference | Phylogenetic Inference | Molecular Modeling | Molecular Modeling | Protein Design | Protein Design | Discrete Reaction Event Network Modeling | Discrete Reaction Event Network Modeling | Python | Python | genetics | genetics | DNA sequence | DNA sequence | genomics | genomics | gene sequencing | gene sequencing | UPGMA | UPGMA | Newick notation | Newick notation | parsimony | parsimony | downpass | downpass | uppass | uppass | jukes-cantor | jukes-cantor | invertase | invertase | genetic memory | genetic memory

License

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21M.065 Introduction to Musical Composition (MIT) 21M.065 Introduction to Musical Composition (MIT)

Description

Through a progressive series of composition projects, this course investigates the sonic organization of musical works and performances, focusing on fundamental questions of unity and variety. Aesthetic issues are considered in the pragmatic context of the instructions that composers provide to achieve a desired musical result, whether these instructions are notated in prose, as graphic images, or in symbolic notation. No formal training is required. Weekly listening, reading, and composition assignments draw on a broad range of musical styles and intellectual traditions, from various cultures and historical periods. Through a progressive series of composition projects, this course investigates the sonic organization of musical works and performances, focusing on fundamental questions of unity and variety. Aesthetic issues are considered in the pragmatic context of the instructions that composers provide to achieve a desired musical result, whether these instructions are notated in prose, as graphic images, or in symbolic notation. No formal training is required. Weekly listening, reading, and composition assignments draw on a broad range of musical styles and intellectual traditions, from various cultures and historical periods.

Subjects

music | music | improvision | improvision | form | form | structure | structure | notation | notation | musical score | musical score | performance | performance | composer | composer | listening | listening | melody | melody | rhythm | rhythm | harmony | harmony | sound | sound | meter | meter | syncopation | syncopation | consonance | consonance | dissonance | dissonance

License

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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

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8.05 Quantum Physics II (MIT) 8.05 Quantum Physics II (MIT)

Description

Includes audio/video content: AV lectures. Together, this course and 8.06 Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum. Includes audio/video content: AV lectures. Together, this course and 8.06 Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

Subjects

quantum physics | quantum physics | quantum mechanics | quantum mechanics | Schrodinger equation | Schrodinger equation | Dirac's notation | Dirac's notation | Harmonic oscillator | Harmonic oscillator | wave functions | wave functions | angular momentum | angular momentum | eigenvalues | eigenvalues | eigenstates | eigenstates | spherical harmonics | spherical harmonics | spin systems | spin systems

License

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21M.065 Introduction to Musical Composition (MIT) 21M.065 Introduction to Musical Composition (MIT)

Description

Through a progressive series of composition projects, students investigate the sonic organization of musical works and performances, focusing on fundamental questions of unity and variety. Aesthetic issues are considered in the pragmatic context of the instructions that composers provide to achieve a desired musical result, whether these instructions are notated in prose, as graphic images, or in symbolic notation. No formal training is required. Weekly listening, reading, and composition assignments draw on a broad range of musical styles and intellectual traditions, from various cultures and historical periods. Through a progressive series of composition projects, students investigate the sonic organization of musical works and performances, focusing on fundamental questions of unity and variety. Aesthetic issues are considered in the pragmatic context of the instructions that composers provide to achieve a desired musical result, whether these instructions are notated in prose, as graphic images, or in symbolic notation. No formal training is required. Weekly listening, reading, and composition assignments draw on a broad range of musical styles and intellectual traditions, from various cultures and historical periods.

Subjects

form | form | structure | structure | notation | notation | musical score | musical score | composer | composer | composing | composing | music history | music history | deep listening | deep listening | sound | sound | soundwalk | soundwalk | instrument building | instrument building | contemporary music | contemporary music | avant-garde music | avant-garde music | experimental music | experimental music | graphic score | graphic score | Musique Concrete | Musique Concrete | vocal music | vocal music

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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