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6.845 Quantum Complexity Theory (MIT) 6.845 Quantum Complexity Theory (MIT)

Description

This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier. This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier.

Subjects

quantum computational complexity theory | quantum computational complexity theory | quantum computers | quantum computers | complexity classes | complexity classes | lower bounds | lower bounds | communication complexity | communication complexity | interactive proof systems | interactive proof systems | BQP | BQP | quantum algorithms | quantum algorithms | QMA | QMA | quantum Merlin Arthur | quantum Merlin Arthur

License

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6.033 Computer System Engineering (MIT) 6.033 Computer System Engineering (MIT)

Description

Includes audio/video content: AV lectures. This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Two design projects are required, and students engage in extensive written communication exercises. Includes audio/video content: AV lectures. This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Two design projects are required, and students engage in extensive written communication exercises.

Subjects

computer systems | computer systems | systems design | systems design | complexity | complexity | abstractions | abstractions | modularity | modularity | client server | client server | operating system | operating system | performance | performance | networks | networks | layering | layering | routing | routing | congestion control | congestion control | reliability | reliability | atomicity | atomicity | isolation | isolation | security | security | authentication | authentication | cryptography | cryptography | therac 25 | therac 25 | unix | unix | mapreduce | mapreduce | architecture of complexity | architecture of complexity | trusting trust | trusting trust | computer system design | computer system design

License

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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

License

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15.099 Readings in Optimization (MIT) 15.099 Readings in Optimization (MIT)

Description

In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention. In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention.

Subjects

deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization | deterministic optimization | algorithms | algorithms | stochastic processes | stochastic processes | random number generation | random number generation | simplex method | simplex method | nonlinear | nonlinear | convex | convex | complexity analysis | complexity analysis | semidefinite programming | semidefinite programming | heuristic | heuristic | global optimization | global optimization | Las Vegas algorithm | Las Vegas algorithm | randomized algorithm | randomized algorithm | linear programming | linear programming | search techniques | search techniques | hit and run | hit and run | NP-hard | NP-hard | approximation | approximation

License

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2.882 System Design and Analysis based on AD and Complexity Theories (MIT) 2.882 System Design and Analysis based on AD and Complexity Theories (MIT)

Description

This course studies what makes a good design and how one develops a good design. Students consider how the design of engineered systems (such as hardware, software, materials, and manufacturing systems) differ from the "design" of natural systems such as biological systems; discuss complexity and how one makes use of complexity theory to improve design; and discover how one uses axiomatic design theory (AD theory) in design of many different kinds of engineered systems. Questions are analyzed using Axiomatic Design Theory and Complexity Theory. Case studies are presented including the design of machines, tribological systems, materials, manufacturing systems, and recent inventions. Implications of AD and complexity theories on biological systems discussed. This course studies what makes a good design and how one develops a good design. Students consider how the design of engineered systems (such as hardware, software, materials, and manufacturing systems) differ from the "design" of natural systems such as biological systems; discuss complexity and how one makes use of complexity theory to improve design; and discover how one uses axiomatic design theory (AD theory) in design of many different kinds of engineered systems. Questions are analyzed using Axiomatic Design Theory and Complexity Theory. Case studies are presented including the design of machines, tribological systems, materials, manufacturing systems, and recent inventions. Implications of AD and complexity theories on biological systems discussed.

Subjects

information content | information content | electrical connector | electrical connector | constraint | constraint | complexity | complexity | manufacturing | manufacturing | design | design | functional requirement | functional requirement | requirement | requirement | tradeoff | tradeoff | optimization | optimization | engineered systems | engineered systems | natural systems | natural systems | complexity theory | complexity theory | axiomatic design | axiomatic design | tribology | tribology | tribological systems | tribological systems | manufacturing systems | manufacturing systems | biological systems | biological systems

License

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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

License

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6.845 Quantum Complexity Theory (MIT)

Description

This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier.

Subjects

quantum computational complexity theory | quantum computers | complexity classes | lower bounds | communication complexity | interactive proof systems | BQP | quantum algorithms | QMA | quantum Merlin Arthur

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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Readme file for Computer Science Concepts

Description

This readme file contains details of links to all the Computer Science Concepts module's material held on Jorum and information about the module as well.

Subjects

ukoer | strings lecture | induction and recursion lecture | induction lecture | recursion lecture | complexity lecture | languages lecture | computer sciences concepts test | computer science concepts test | computer science concepts assignment | computer science concepts practical | introduction | computer science concepts | computer science concept | computer science | strings and languages | strings and language | string and languages | string and language | string | language | languages | finite automata | automata | finite | push down automata | push down | prolog | data structures and algorithms | data structure and algorithms | data structures and algorithm | data structure and algorithm | data structures | data structure | algorithms | algorithm | revision exercises | revision | induction and recursion | induction | recursion | turing machines | turing machine | turing | machine | machines | complexity | grammar | grammar and languages | grammar and language | introduction lecture | computer science concepts lecture | computer science concept lecture | computer science lecture | strings and languages lecture | strings and language lecture | string and languages lecture | string and language lecture | string lecture | language lecture | finite automata lecture | automata lecture | finite lecture | push down automata lecture | push down lecture | prolog lecture | data structures and algorithms lecture | data structure and algorithms lecture | data structures and algorithm lecture | data structure and algorithm lecture | data structures lecture | data structure lecture | algorithms lecture | algorithm lecture | revision exercises lecture | revision lecture | turing machines lecture | turing machine lecture | turing lecture | machine lecture | machines lecture | computer science class test | computer science concept class test | computer science concepts class test | strings and languages class test | strings and language class test | string and languages class test | string and language class test | string class test | language class test | languages class test | introduction class test | grammar lecture | grammar and languages lecture | grammar and language lecture | computer science assignment | computer science concept assignment | strings and languages assignment | strings and language assignment | string and languages assignment | string and language assignment | string assignment | language assignment | languages assignment | finite automata class test | automata class test | finite class test | finite automata assignment | automata assignment | finite assignment | push down automata class test | push down class test | push down automata assignment | push down assignment | prolog class test | data structures and algorithms class test | data structure and algorithms class test | data structures and algorithm class test | data structure and algorithm class test | data structures class test | data structure class test | algorithms class test | algorithm class test | computer science practical | computer science concept practical | data structures and algorithms practical | data structure and algorithms practical | data structures and algorithm practical | data structure and algorithm practical | data structures practical | data structure practical | algorithms practical | algorithm practical | revision exercises class test | revision class test | induction and recursion class test | induction class test | recursion class test | induction and recursion assignment | induction assignment | recursion assignment | turing machines class test | turing machine class test | turing class test | machine class test | machines class test | turing machines assignment | turing machine assignment | turing assignment | machine assignment | machines assignment | complexity class test | grammar class test | grammar and languages class test | grammar and language class test | Computer science | I100

License

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

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6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | computability | complexity | mathematical models | computation | finite representation | infinite objects | finite automata | regular languages | context-free languages | Turing machines | partial recursive functions | Church's Thesis | undecidability | reducibility | completeness | time complexity | NP-completeness | probabilistic computation | interactive proof systems | 6.045 | 18.400

License

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2.76 Multi-Scale System Design (MIT) 2.76 Multi-Scale System Design (MIT)

Description

Multi-scale systems (MuSS) consist of components from two or more length scales (nano, micro, meso, or macro-scales). In MuSS, the engineering modeling, design principles, and fabrication processes of the components are fundamentally different. The challenge is to make these components so they are conceptually and model-wise compatible with other-scale components with which they interface. This course covers the fundamental properties of scales, design theories, modeling methods and manufacturing issues which must be addressed in these systems. Examples of MuSS include precision instruments, nanomanipulators, fiber optics, micro/nano-photonics, nanorobotics, MEMS (piezoelectric driven manipulators and optics), X-Ray telescopes and carbon nano-tube assemblies. Students master the materials Multi-scale systems (MuSS) consist of components from two or more length scales (nano, micro, meso, or macro-scales). In MuSS, the engineering modeling, design principles, and fabrication processes of the components are fundamentally different. The challenge is to make these components so they are conceptually and model-wise compatible with other-scale components with which they interface. This course covers the fundamental properties of scales, design theories, modeling methods and manufacturing issues which must be addressed in these systems. Examples of MuSS include precision instruments, nanomanipulators, fiber optics, micro/nano-photonics, nanorobotics, MEMS (piezoelectric driven manipulators and optics), X-Ray telescopes and carbon nano-tube assemblies. Students master the materials

Subjects

scale | scale | complexity | complexity | nano | micro | meso | or macro-scale | nano | micro | meso | or macro-scale | kinematics | kinematics | metrology | metrology | engineering modeling | motion | engineering modeling | motion | modeling | modeling | design | design | manufacture | manufacture | design principles | design principles | fabrication process | fabrication process | functional requirements | functional requirements | precision instruments | precision instruments | nanomanipulators | fiber optics | micro- photonics | nano-photonics | nanorobotics | MEMS | nanomanipulators | fiber optics | micro- photonics | nano-photonics | nanorobotics | MEMS | piezoelectric | transducer | actuator | sensor | piezoelectric | transducer | actuator | sensor | constraint | rigid constraint | flexible constraint | ride-flexible constraint | constraint | rigid constraint | flexible constraint | ride-flexible constraint | constaint-based design | constaint-based design | carbon nanotube | carbon nanotube | nanowire | nanowire | scanning tunneling microscope | scanning tunneling microscope | flexure | flexure | protein structure | protein structure | polymer structure | polymer structure | nanopelleting | nanopipette | nanowire | nanopelleting | nanopipette | nanowire | TMA pixel array | TMA pixel array | error modeling | error modeling | repeatability | repeatability

License

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RES.6-011 The Art of Insight in Science and Engineering: Mastering Complexity (MIT) RES.6-011 The Art of Insight in Science and Engineering: Mastering Complexity (MIT)

Description

In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering. (Description courtesy of MIT Press.) In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering. (Description courtesy of MIT Press.)

Subjects

approximation | approximation | science | science | engineering | engineering | complexity | complexity | divide and conquer | divide and conquer | abstraction | abstraction | symmetry | symmetry | proportion | proportion | dimension | dimension | lumping | lumping | probabalistic reasoning | probabalistic reasoning

License

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2.A35 Biomimetic Principles and Design (MIT) 2.A35 Biomimetic Principles and Design (MIT)

Description

Biomimetics is based on the belief that nature, at least at times, is a good engineer. Biomimesis is the scientific method of learning new principles and processes based on systematic study, observation and experimentation with live animals and organisms. This Freshman Advising Seminar on the topic is a way for freshmen to explore some of MIT's richness and learn more about what they may want to study in later years. Biomimetics is based on the belief that nature, at least at times, is a good engineer. Biomimesis is the scientific method of learning new principles and processes based on systematic study, observation and experimentation with live animals and organisms. This Freshman Advising Seminar on the topic is a way for freshmen to explore some of MIT's richness and learn more about what they may want to study in later years.

Subjects

biomimetics | biomimetics | biomimicry | biomimicry | biomimesis | biomimesis | nature | nature | reverse engineering | reverse engineering | bionics | bionics | adaptation | adaptation | genetic algorithms | genetic algorithms | politics | politics | design | design | imitate | imitate | robot | robot | robotics | robotics | robotuna | robotuna | fluid mechanics | fluid mechanics | fish | fish | swim | swim | submarine | submarine | complexity | complexity

License

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Computer Science Concepts - Complexity

Description

This lecture forms part of the "Complexity" topic of the Computer Science Concepts module.

Subjects

ukoer | complexity lecture | computer science | computer science concept | computer science concepts | complexity | computer science lecture | computer science concept lecture | computer science concepts lecture | Computer science | I100

License

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Computer Science Concepts - Complexity

Description

This class test forms part of the "Complexity" topic of the Computer Science Concepts module.

Subjects

ukoer | computer science concepts test | computer science | computer science concept | computer science concepts | complexity | computer science class test | computer science concept class test | computer science concepts class test | complexity class test | Computer science | I100

License

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

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Computer Science Concepts - Complexity

Description

This class test forms part of the "Complexity" topic of the Computer Science Concepts module.

Subjects

ukoer | computer science concepts test | computer science | computer science concept | computer science concepts | complexity | computer science class test | computer science concept class test | computer science concepts class test | complexity class test | Computer science | I100

License

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

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Computer Science Concepts - Complexity

Description

This class test forms part of the "Complexity" topic of the Computer Science Concepts module.

Subjects

ukoer | computer science concepts test | computer science | computer science concept | computer science concepts | complexity | computer science class test | computer science concept class test | computer science concepts class test | complexity class test | Computer science | I100

License

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

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2.882 System Design and Analysis based on AD and Complexity Theories (MIT)

Description

This course studies what makes a good design and how one develops a good design. Students consider how the design of engineered systems (such as hardware, software, materials, and manufacturing systems) differ from the "design" of natural systems such as biological systems; discuss complexity and how one makes use of complexity theory to improve design; and discover how one uses axiomatic design theory (AD theory) in design of many different kinds of engineered systems. Questions are analyzed using Axiomatic Design Theory and Complexity Theory. Case studies are presented including the design of machines, tribological systems, materials, manufacturing systems, and recent inventions. Implications of AD and complexity theories on biological systems discussed.

Subjects

information content | electrical connector | constraint | complexity | manufacturing | design | functional requirement | requirement | tradeoff | optimization | engineered systems | natural systems | complexity theory | axiomatic design | tribology | tribological systems | manufacturing systems | biological systems

License

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ESD.932 Engineering Ethics (MIT) ESD.932 Engineering Ethics (MIT)

Description

Includes audio/video content: AV lectures, AV faculty introductions. This course introduces the theory and the practice of engineering ethics using a multi-disciplinary and cross-cultural approach. Theory includes ethics and philosophy of engineering. Historical cases are taken primarily from the scholarly literatures on engineering ethics, and hypothetical cases are written by students. Each student will write a story by selecting an ancestor or mythic hero as a substitute for a character in a historical case. Students will compare these cases and recommend action. Includes audio/video content: AV lectures, AV faculty introductions. This course introduces the theory and the practice of engineering ethics using a multi-disciplinary and cross-cultural approach. Theory includes ethics and philosophy of engineering. Historical cases are taken primarily from the scholarly literatures on engineering ethics, and hypothetical cases are written by students. Each student will write a story by selecting an ancestor or mythic hero as a substitute for a character in a historical case. Students will compare these cases and recommend action.

Subjects

philosophy | philosophy | myth | myth | Kant | Kant | John Stuart Mill | John Stuart Mill | Kierkegaard | Kierkegaard | Augustine | Augustine | Joseph Campbell | Joseph Campbell | risk | risk | disaster | disaster | honesty | honesty | whisteblower | whisteblower | social responsibility | social responsibility | Pugwash | Pugwash | environment | environment | bioethics | bioethics | lawsuit | lawsuit | praxistics | praxistics | decision making | decision making | management | management | accident | accident | choice | choice | morals | morals | complexity | complexity | judgement | judgement | consequence | consequence

License

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ESD.84 Engineering Systems Doctoral Seminar (MIT) ESD.84 Engineering Systems Doctoral Seminar (MIT)

Description

Examines core theory and contextual applications of the emerging field of Engineering Systems. The focus is on doctoral-level analysis of scholarship on key concepts such as complexity, uncertainty, fragility, and robustness, as well as a critical look at the historical roots of the field and related areas such as systems engineering, systems dynamics, agent modeling, and systems simulations. Contextual applications range from aerospace to technology implementation to regulatory systems to large-scale systems change. Special attention is given to the interdependence of social and technical dimensions of engineering systems. Examines core theory and contextual applications of the emerging field of Engineering Systems. The focus is on doctoral-level analysis of scholarship on key concepts such as complexity, uncertainty, fragility, and robustness, as well as a critical look at the historical roots of the field and related areas such as systems engineering, systems dynamics, agent modeling, and systems simulations. Contextual applications range from aerospace to technology implementation to regulatory systems to large-scale systems change. Special attention is given to the interdependence of social and technical dimensions of engineering systems.

Subjects

engineering systems | engineering systems | complexity | complexity | fragility | fragility | robustness | robustness | systems engineering | systems engineering | systems dynamics | systems dynamics | agent modeling | agent modeling | systems simulations | systems simulations | large-scale systems change | large-scale systems change | uncertainty | uncertainty

License

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6.033 Computer System Engineering (MIT)

Description

This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Two design projects are required, and students engage in extensive written communication exercises.

Subjects

computer systems | systems design | complexity | abstractions | modularity | client server | operating system | performance | networks | layering | routing | congestion control | reliability | atomicity | isolation | security | authentication | cryptography | therac 25 | unix | mapreduce | architecture of complexity | trusting trust | computer system design

License

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18.404J Theory of Computation (MIT) 18.404J Theory of Computation (MIT)

Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory. This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Computability | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

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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6.033 Computer System Engineering (SMA 5501) (MIT) 6.033 Computer System Engineering (SMA 5501) (MIT)

Description

This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. We will also look at case studies of working systems and readings from the current literature provide comparisons and contrasts, and do two design projects. Students engage in extensive written communication exercises. Enrollment may be limited. This course is worth 4 Engineering Design Points.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5501 (Computer System Engineering). This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. We will also look at case studies of working systems and readings from the current literature provide comparisons and contrasts, and do two design projects. Students engage in extensive written communication exercises. Enrollment may be limited. This course is worth 4 Engineering Design Points.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5501 (Computer System Engineering).

Subjects

computer software | computer software | hardware systems | hardware systems | controlling complexity | controlling complexity | strong modularity | strong modularity | client-server design | client-server design | virtual memory | virtual memory | threads | threads | networks | networks | atomicity | atomicity | coordination | coordination | parallel activities | parallel activities | recovery | recovery | reliability | reliability | privacy | privacy | security | security | encryption | encryption | impact on society | impact on society | computer systems | computer systems | case studies | case studies

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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18.404J Theory of Computation (MIT) 18.404J Theory of Computation (MIT)

Description

A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems. A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Subjects

computability | computability | computational complexity theory | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | Decidable and undecidable problems | reducibility | reducibility | recursive function theory | recursive function theory | Time and space measures on computation | Time and space measures on computation | completeness | completeness | hierarchy theorems | hierarchy theorems | inherently complex problems | inherently complex problems | oracles | oracles | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 18.404 | 18.404 | 6.840 | 6.840

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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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power. This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Subjects

finite automata | finite automata | Turing machine | Turing machine | halting problem | halting problem | computability | computability | computational complexity | computational complexity | polynomial time | polynomial time | P | P | NP | NP | NP complete | NP complete | probabilistic algorithms | probabilistic algorithms | private-key cryptography | private-key cryptography | public-key cryptography | public-key cryptography | randomness | randomness

License

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3.012 Fundamentals of Materials Science (MIT) 3.012 Fundamentals of Materials Science (MIT)

Description

This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all

Subjects

fundamentals of bonding | energetics | and structure | fundamentals of bonding | energetics | and structure | Quantum mechanical descriptions of interacting electrons and atoms | Quantum mechanical descriptions of interacting electrons and atoms | Symmetry properties of molecules and solids | Symmetry properties of molecules and solids | complex and disordered materials | complex and disordered materials | thermodynamic functions | thermodynamic functions | equilibrium properties | equilibrium properties | macroscopic behavior | macroscopic behavior | molecular models | molecular models | heat capacities | heat capacities | phase transformations | phase transformations | multiphase equilibria | multiphase equilibria | chemical reactions | chemical reactions | magnetism | magnetism | engineered alloys | engineered alloys | electronic and magnetic materials | electronic and magnetic materials | ionic and network solids | ionic and network solids | polymers | polymers | biomaterials | biomaterials | energetics | energetics | structure | structure | materials science | materials science | electrons | electrons | silicon | silicon | DNA | DNA | electronic bonding | electronic bonding | energy | energy | stability | stability | quantum mechanics | quantum mechanics | atoms | atoms | interactions | interactions | symmetry | symmetry | molecules | molecules | solids | solids | complex material | complex material | disorderd materials | disorderd materials | thermodynamic laws | thermodynamic laws | electronic materials | electronic materials | magnetic materials | magnetic materials | ionic solids | ionic solids | network solids | network solids | statistical mechanics | statistical mechanics | microstates | microstates | microscopic complexity | microscopic complexity | entropy | entropy

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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