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6.441 Transmission of Information (MIT) 6.441 Transmission of Information (MIT)

Description

6.441 offers an introduction to the quantitative theory of information and its applications to reliable, efficient communication systems. Topics include: mathematical definition and properties of information; source coding theorem, lossless compression of data, optimal lossless coding; noisy communication channels, channel coding theorem, the source-channel separation theorem, multiple access channels, broadcast channels, Gaussian noise, and time-varying channels. 6.441 offers an introduction to the quantitative theory of information and its applications to reliable, efficient communication systems. Topics include: mathematical definition and properties of information; source coding theorem, lossless compression of data, optimal lossless coding; noisy communication channels, channel coding theorem, the source-channel separation theorem, multiple access channels, broadcast channels, Gaussian noise, and time-varying channels.

Subjects

transmission of information | transmission of information | quantitative theory of information | quantitative theory of information | efficient communication systems | efficient communication systems | mathematical definition of information | mathematical definition of information | properties of information | properties of information | source coding theorem | source coding theorem | lossless compression of data | lossless compression of data | optimal lossless coding | optimal lossless coding | noisy communication channels | noisy communication channels | channel coding theorem | channel coding theorem | the source-channel separation theorem | the source-channel separation theorem | multiple access channels | multiple access channels | broadcast channels | broadcast channels | gaussian noise | gaussian noise | time-varying channels | time-varying channels | lossless data compression | lossless data compression | telecommunications | telecommunications | data transmission | data transmission

License

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

Description

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

Subjects

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

License

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18.327 Wavelets, Filter Banks and Applications (MIT) 18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | Multiwavelets

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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6.441 Information Theory (MIT)

Description

This is a graduate-level introduction to mathematics of information theory. We will cover both classical and modern topics, including information entropy, lossless data compression, binary hypothesis testing, channel coding, and lossy data compression.

Subjects

properties of information | entropy | divergence | information measures | mutual information | sufficient statistic | probability of error | entropy rate | lossless data compression | fixed-length compression | ergodic sources | universal compression | binary hypothesis testing | information projection | channel coding | achievability bounds | linear codes | gaussian channels | input constraints | lattice codes | energy-per-bit | source-channel separation | feedback | forney concatenation | lossy compression | distortion | multiple-access channel | random number generator | source coding theorem | noisy communication | channel coding theorem | source channel separation theorem | broadcast channels | Gaussian noise | time-varying channels

License

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

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

Description

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

Subjects

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

License

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

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4.440 Basic Structural Design (MIT) 4.440 Basic Structural Design (MIT)

Description

This course provides students with a basic knowledge of structural analysis and design for buildings, bridges and other structures. The course emphasizes the historical development of structural form and the evolution of structural design knowledge, from Gothic cathedrals to long span suspension bridges. Students will investigate the behavior of structural systems and elements through design exercises, case studies, and load testing of models. Students will design structures using timber, masonry, steel, and concrete and will gain an appreciation of the importance of structural design today, with an emphasis on environmental impact of large scale construction. This course provides students with a basic knowledge of structural analysis and design for buildings, bridges and other structures. The course emphasizes the historical development of structural form and the evolution of structural design knowledge, from Gothic cathedrals to long span suspension bridges. Students will investigate the behavior of structural systems and elements through design exercises, case studies, and load testing of models. Students will design structures using timber, masonry, steel, and concrete and will gain an appreciation of the importance of structural design today, with an emphasis on environmental impact of large scale construction.

Subjects

structural analysis | structural analysis | structural design | structural design | historical structures | historical structures | environment | environment | sustainable construction | sustainable construction | graphical analysis | graphical analysis | environmental assessment | environmental assessment | beam | beam | column | column | truss | truss | frame | frame | arch | arch | structural systems | structural systems | model building | model building | design exercises | design exercises | compression | compression | tension | tension | axial forces | axial forces | structural failures | structural failures | timber | timber | steel | steel | concrete | concrete | sustainable structures | sustainable structures

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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6.450 Principles of Digital Communication - I (MIT) 6.450 Principles of Digital Communication - I (MIT)

Description

6.450 was offered in Fall 2002 as a relatively new elective on digital communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring.Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication. 6.450 was offered in Fall 2002 as a relatively new elective on digital communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring.Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | digital communication | data compression | data compression | Lempel-Ziv algorithm | Lempel-Ziv algorithm | scalar quantization | scalar quantization | vector quantization | vector quantization | sampling | sampling | aliasing | aliasing | Nyquist criterion | Nyquist criterion | PAM modulation | PAM modulation | QAM modulation | QAM modulation | signal constellations | signal constellations | finite-energy waveform spaces | finite-energy waveform spaces | detection | detection | communication system design | communication system design

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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6.050J Information and Entropy (MIT) 6.050J Information and Entropy (MIT)

Description

Includes audio/video content: AV selected lectures. This course explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include: information and computation, digital signals, codes and compression, applications such as biological representations of information, logic circuits, computer architectures, and algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, and quantum computation. The concept of entropy applied to channel capacity and to the second law of thermodynamics. Includes audio/video content: AV selected lectures. This course explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include: information and computation, digital signals, codes and compression, applications such as biological representations of information, logic circuits, computer architectures, and algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, and quantum computation. The concept of entropy applied to channel capacity and to the second law of thermodynamics.

Subjects

information and entropy | information and entropy | computing | computing | communications | communications | thermodynamics | thermodynamics | digital signals and streams | digital signals and streams | codes | codes | compression | compression | noise | noise | probability | probability | reversible operations | reversible operations | irreversible operations | irreversible operations | information in biological systems | information in biological systems | channel capacity | channel capacity | maximum-entropy formalism | maximum-entropy formalism | thermodynamic equilibrium | thermodynamic equilibrium | temperature | temperature | second law of thermodynamics quantum computation | second law of thermodynamics quantum computation

License

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6.450 Principles of Digital Communications I (MIT) 6.450 Principles of Digital Communications I (MIT)

Description

Includes audio/video content: AV lectures. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication. Includes audio/video content: AV lectures. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | digital communication | data compression | data compression | Lempel-Ziv algorithm | Lempel-Ziv algorithm | scalar quantization | scalar quantization | vector quantization | vector quantization | sampling | sampling | aliasing | aliasing | Nyquist criterion | Nyquist criterion | PAM modulation | PAM modulation | QAM modulation | QAM modulation | signal constellations | signal constellations | finite-energy waveform spaces | finite-energy waveform spaces | detection | detection | communication system design | communication system design

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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PE.210 SCUBA (MIT) PE.210 SCUBA (MIT)

Description

Includes audio/video content: AV selected lectures, AV special element video. This course will thoroughly educate the successful student with the knowledge and skills necessary to be a certified beginning SCUBA diver. The prerequisite for the course is passing the MIT SCUBA swim test and demonstrating a "comfort level" in the water. At the end of the class, students will attempt to pass the certification exam to become certified divers. The class is taught in two parts each week: a classroom session and a pool session. The classroom sessions along with the reading material will provide the student with the knowledge necessary to pass the written exam. At the pool, the water skills are taught in progressions that build on the previous skills, making the difficult skills seem easy. Includes audio/video content: AV selected lectures, AV special element video. This course will thoroughly educate the successful student with the knowledge and skills necessary to be a certified beginning SCUBA diver. The prerequisite for the course is passing the MIT SCUBA swim test and demonstrating a "comfort level" in the water. At the end of the class, students will attempt to pass the certification exam to become certified divers. The class is taught in two parts each week: a classroom session and a pool session. The classroom sessions along with the reading material will provide the student with the knowledge necessary to pass the written exam. At the pool, the water skills are taught in progressions that build on the previous skills, making the difficult skills seem easy.

Subjects

SCUBA | SCUBA | diving | diving | physics | physics | water | water | ocean | ocean | neutral buoyancy | neutral buoyancy | regulator | regulator | decompression | decompression | rescue | rescue | swim techniques | swim techniques | kick cycles | kick cycles | marine life | marine life | ocean environment | ocean environment | navigation | navigation | dive tables | dive tables | air consumption | air consumption | snorkeling | snorkeling | skin diving | skin diving | NAUI | NAUI

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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PE.210 SCUBA (MIT) PE.210 SCUBA (MIT)

Description

This course will thoroughly educate the successful student with the knowledge and skills necessary to be a certified beginning SCUBA diver. The prerequisite for the course is passing the MIT SCUBA swim test and demonstrating a "comfort level" in the water. At the end of the class, students will attempt to pass the certification exam to become certified divers. The class is taught in two parts each week: a classroom session and a pool session. The classroom sessions along with the reading material will provide the student with the knowledge necessary to pass the written exam. At the pool, the water skills are taught in progressions that build on the previous skills, making the difficult skills seem easy. This course will thoroughly educate the successful student with the knowledge and skills necessary to be a certified beginning SCUBA diver. The prerequisite for the course is passing the MIT SCUBA swim test and demonstrating a "comfort level" in the water. At the end of the class, students will attempt to pass the certification exam to become certified divers. The class is taught in two parts each week: a classroom session and a pool session. The classroom sessions along with the reading material will provide the student with the knowledge necessary to pass the written exam. At the pool, the water skills are taught in progressions that build on the previous skills, making the difficult skills seem easy.

Subjects

SCUBA | SCUBA | diving | diving | physics | physics | water | water | ocean | ocean | neutral buoyancy | neutral buoyancy | regulator | regulator | decompression | decompression | rescue | rescue | swim techniques | swim techniques | kick cycles | kick cycles | marine life | marine life | ocean environment | ocean environment | navigation | navigation | dive tables | dive tables | air consumption | air consumption | snorkeling | snorkeling | skin diving | skin diving | NAUI | NAUI

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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18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

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

Subjects

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

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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6.02 Introduction to EECS II: Digital Communication Systems (MIT) 6.02 Introduction to EECS II: Digital Communication Systems (MIT)

Description

Includes audio/video content: AV lectures. An introduction to several fundamental ideas in electrical engineering and computer science, using digital communication systems as the vehicle. The three parts of the course—bits, signals, and packets—cover three corresponding layers of abstraction that form the basis of communication systems like the Internet. The course teaches ideas that are useful in other parts of EECS: abstraction, probabilistic analysis, superposition, time and frequency-domain representations, system design principles and trade-offs, and centralized and distributed algorithms. The course emphasizes connections between theoretical concepts and practice using programming tasks and some experiments with real-world communication channels. Includes audio/video content: AV lectures. An introduction to several fundamental ideas in electrical engineering and computer science, using digital communication systems as the vehicle. The three parts of the course—bits, signals, and packets—cover three corresponding layers of abstraction that form the basis of communication systems like the Internet. The course teaches ideas that are useful in other parts of EECS: abstraction, probabilistic analysis, superposition, time and frequency-domain representations, system design principles and trade-offs, and centralized and distributed algorithms. The course emphasizes connections between theoretical concepts and practice using programming tasks and some experiments with real-world communication channels.

Subjects

digital communication | digital communication | communication systems | communication systems | information | information | entropy | entropy | compression | compression | error correction | error correction | Fourier analysis | Fourier analysis | filtering | filtering | signals | signals | media access protocols | media access protocols | networks | networks | packets | packets | data transport | data transport | internet | internet

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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18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | convolution | Fourier transform | owpass and highpass filters | Sampling rate change operations | upsampling and downsampling | ractional sampling | interpolation | Filter Banks | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | perfect reconstruction | halfband filters and possible factorizations | Modulation and polyphase representations | Noble identities | block Toeplitz matrices and block z-transforms | polyphase examples | Matlab wavelet toolbox | Orthogonal filter banks | paraunitary matrices | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | Maxflat filters | Daubechies and Meyer formulas | Spectral factorization | Multiresolution Analysis (MRA) | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | iterative and recursive solution techniques | infinite product formula | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | connection to orthogonal filters | orthogonality in the frequency domain | Biorthogonal wavelet bases | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | vanishing moments | polynomial cancellation in filter banks | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | splines | Bases vs. frames | Signal and image processing | finite length signals | boundary filters and boundary wavelets | wavelet compression algorithms | Lifting | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | Wavelets and subdivision | nonuniform grids | multiresolution for triangular meshes | representation and compression of surfaces | Numerical solution of PDEs | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | Subdivision wavelets for integral equations | Compression and convergence estimates | M-band wavelets | DFT filter banks and cosine modulated filter banks | Multiwavelets

License

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6.441 Information Theory (MIT) 6.441 Information Theory (MIT)

Description

6.441 offers an introduction to the quantitative theory of information and its applications to reliable, efficient communication systems. Topics include mathematical definition and properties of information, source coding theorem, lossless compression of data, optimal lossless coding, noisy communication channels, channel coding theorem, the source channel separation theorem, multiple access channels, broadcast channels, Gaussian noise, and time-varying channels. 6.441 offers an introduction to the quantitative theory of information and its applications to reliable, efficient communication systems. Topics include mathematical definition and properties of information, source coding theorem, lossless compression of data, optimal lossless coding, noisy communication channels, channel coding theorem, the source channel separation theorem, multiple access channels, broadcast channels, Gaussian noise, and time-varying channels.

Subjects

properties of information | properties of information | source coding theorem | source coding theorem | lossless compression | lossless compression | noisy communication | noisy communication | channel coding theorem | channel coding theorem | source channel separation theorem | source channel separation theorem | multiple access channels | multiple access channels | broadcast channels | broadcast channels | Gaussian noise | Gaussian noise | time-varying channels | time-varying channels

License

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6.450 Principles of Digital Communication I (MIT) 6.450 Principles of Digital Communication I (MIT)

Description

The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | digital communication | data compression | data compression | Lempel-Ziv algorithm | Lempel-Ziv algorithm | scalar quantization | scalar quantization | vector quantization | vector quantization | sampling | sampling | aliasing | aliasing | Nyquist criterion | Nyquist criterion | PAM modulation | PAM modulation | QAM modulation | QAM modulation | signal constellations | signal constellations | finite-energy waveform spaces | finite-energy waveform spaces | detection | detection | communication system design | communication system design | wireless | wireless | discrete source encoding | discrete source encoding | memory-less sources | memory-less sources | entropy | entropy | asymptotic equipartition property | asymptotic equipartition property | Fourier series | Fourier series | Fourier transforms | Fourier transforms | sampling theorem | sampling theorem | orthonormal expansions | orthonormal expansions | random processes | random processes | linear functionals | linear functionals | theorem of irrelevance | theorem of irrelevance | Doppler spread | Doppler spread | time spread | time spread | coherence time | coherence time | coherence frequency | coherence frequency | Rayleigh fading | Rayleigh fading | Rake receivers | Rake receivers | CDMA | CDMA | code division multiple access | code division multiple access

License

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1.103 Civil Engineering Materials Laboratory (MIT) 1.103 Civil Engineering Materials Laboratory (MIT)

Description

Includes audio/video content: AV special element video. This course introduces the concepts, techniques, and devices used to measure engineering properties of materials. There is an emphasis on measurement of load-deformation characteristics and failure modes of both natural and fabricated materials. Weekly experiments include data collection, data analysis, and interpretation and presentation of results. Includes audio/video content: AV special element video. This course introduces the concepts, techniques, and devices used to measure engineering properties of materials. There is an emphasis on measurement of load-deformation characteristics and failure modes of both natural and fabricated materials. Weekly experiments include data collection, data analysis, and interpretation and presentation of results.

Subjects

materials laboratory | materials laboratory | load-deformation characteristics | load-deformation characteristics | failure modes | failure modes | experiments | experiments | data collection | data collection | data analysis | data analysis | tension | tension | elastic behavior | elastic behavior | direct shear | direct shear | friction | friction | concrete | concrete | early age properties | early age properties | compression | compression | directionality | directionality | soil classification | soil classification | consolidation test | consolidation test | heat treatment | heat treatment

License

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18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | convolution | Fourier transform | owpass and highpass filters | Sampling rate change operations | upsampling and downsampling | ractional sampling | interpolation | Filter Banks | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | perfect reconstruction | halfband filters and possible factorizations | Modulation and polyphase representations | Noble identities | block Toeplitz matrices and block z-transforms | polyphase examples | Matlab wavelet toolbox | Orthogonal filter banks | paraunitary matrices | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | Maxflat filters | Daubechies and Meyer formulas | Spectral factorization | Multiresolution Analysis (MRA) | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | iterative and recursive solution techniques | infinite product formula | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | connection to orthogonal filters | orthogonality in the frequency domain | Biorthogonal wavelet bases | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | vanishing moments | polynomial cancellation in filter banks | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | splines | Bases vs. frames | Signal and image processing | finite length signals | boundary filters and boundary wavelets | wavelet compression algorithms | Lifting | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | Wavelets and subdivision | nonuniform grids | multiresolution for triangular meshes | representation and compression of surfaces | Numerical solution of PDEs | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | Subdivision wavelets for integral equations | Compression and convergence estimates | M-band wavelets | DFT filter banks and cosine modulated filter banks | Multiwavelets

License

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6.441 Transmission of Information (MIT)

Description

6.441 offers an introduction to the quantitative theory of information and its applications to reliable, efficient communication systems. Topics include: mathematical definition and properties of information; source coding theorem, lossless compression of data, optimal lossless coding; noisy communication channels, channel coding theorem, the source-channel separation theorem, multiple access channels, broadcast channels, Gaussian noise, and time-varying channels.

Subjects

transmission of information | quantitative theory of information | efficient communication systems | mathematical definition of information | properties of information | source coding theorem | lossless compression of data | optimal lossless coding | noisy communication channels | channel coding theorem | the source-channel separation theorem | multiple access channels | broadcast channels | gaussian noise | time-varying channels | lossless data compression | telecommunications | data transmission

License

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1.322 Soil Behavior (MIT) 1.322 Soil Behavior (MIT)

Description

This class presents a detailed study of soil properties with emphasis on interpretation of field and laboratory test data and their use in soft-ground construction engineering. Topics to be covered include: consolidation and secondary compression; basic strength principles; stress-strain strength behavior of clays, emphasizing effects of sample disturbance, anisotropy, and strain rate; strength and compression of granular soils; and engineering properties of compacted soils. Some knowledge of field and laboratory testing is assumed for all students. This class presents a detailed study of soil properties with emphasis on interpretation of field and laboratory test data and their use in soft-ground construction engineering. Topics to be covered include: consolidation and secondary compression; basic strength principles; stress-strain strength behavior of clays, emphasizing effects of sample disturbance, anisotropy, and strain rate; strength and compression of granular soils; and engineering properties of compacted soils. Some knowledge of field and laboratory testing is assumed for all students.

Subjects

soil | soil | soil composition | soil composition | clay | clay | interparticle forces | interparticle forces | soil strength | soil strength | laddite | laddite | Hvorslev parameters | Hvorslev parameters | plasticity | plasticity | stress history | stress history | consol | consol | conductivity | conductivity | compression | compression | consolidation | consolidation | problem soils | problem soils | sands | sands

License

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15.564 Information Technology I (MIT) 15.564 Information Technology I (MIT)

Description

Information Technology I helps students understand technical concepts underlying current and future developments in information technology. There will be a special emphasis on networks and distributed computing. Students will also gain some hands-on exposure to powerful, high-level tools for making computers do amazing things, without the need for conventional programming languages. Since 15.564 is an introductory course, no knowledge of how computers work or are programmed is assumed. Information Technology I helps students understand technical concepts underlying current and future developments in information technology. There will be a special emphasis on networks and distributed computing. Students will also gain some hands-on exposure to powerful, high-level tools for making computers do amazing things, without the need for conventional programming languages. Since 15.564 is an introductory course, no knowledge of how computers work or are programmed is assumed.

Subjects

developing-country governments; international | developing-country governments; international | computers; future developments; networks;distributed computing; programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers; future developments; networks;distributed computing; programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers;future developments;networks;distributed computing;programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers;future developments;networks;distributed computing;programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers | computers | future developments | future developments | networks | networks | distributed computing | distributed computing | programming languages | programming languages | firewall | firewall | e-business | e-business | computer architecture | computer architecture | operating | operating | software development | software development | database | database | user interface | user interface | telecommunication | telecommunication | data transmission | data transmission | local area network | local area network | wireless network | wireless network | internet | internet | world wide web | world wide web | digital security | digital security | architecture | architecture | data | data | transmission | transmission | wireless | wireless | interface | interface | user | user | software | software | development | development | programming | programming | languages | languages | distributed | distributed | computing | computing | LAN | LAN | local | local | area | area | future | future | digital | digital | security | security | technology | technology | information | information | management | management | systems | systems | relational | relational | graphical | graphical | interfaces | interfaces | client/server | client/server | enterprise | enterprise | applications | applications | cryptography | cryptography | services | services | Microsoft | Microsoft | Access | Access | Lotus Notes | Lotus Notes | processing | processing | memory | memory | I/O | I/O | CPU | CPU | OS | OS | hardware | hardware | compression | compression | SQL | SQL | queries | queries | design | design | WAN | WAN | wide | wide | Ethernet | Ethernet | packet-switched | packet-switched | peer-to-peer | peer-to-peer | WWW | WWW | public | public | key | key | mining | mining | warehousing | warehousing | concepts | concepts | conceptual | conceptual | modern computing | modern computing | information management | information management | operating systems | operating systems | relational database systems | relational database systems | graphical user interfaces | graphical user interfaces | client/server systems | client/server systems | enterprise applications | enterprise applications | web.internet services | web.internet services | Microsoft Access | Microsoft Access | database management systems | database management systems | information technology | information technology | telecommunications | telecommunications | eBusiness applications | eBusiness applications | client | client | servers | servers | wireless area network | wireless area network

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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6.050J Information and Entropy (MIT) 6.050J Information and Entropy (MIT)

Description

6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university.  6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university. 

Subjects

information and entropy | information and entropy | computing | computing | communications | communications | thermodynamics | thermodynamics | digital signals and streams | digital signals and streams | codes | codes | compression | compression | noise | noise | probability | probability | reversible operations | reversible operations | irreversible operations | irreversible operations | information in biological systems | information in biological systems | channel capacity | channel capacity | aximum-entropy formalism | aximum-entropy formalism | thermodynamic equilibrium | thermodynamic equilibrium | temperature | temperature | second law of thermodynamics quantum computation | second law of thermodynamics quantum computation | maximum-entropy formalism | maximum-entropy formalism | second law of thermodynamics | second law of thermodynamics | quantum computation | quantum computation | biological systems | biological systems | unified theory of information | unified theory of information | digital signals | digital signals | digital streams | digital streams | bits | bits | errors | errors | processes | processes | inference | inference | maximum entropy | maximum entropy | physical systems | physical systems | energy | energy | quantum information | quantum information | 6.050 | 6.050 | 2.110 | 2.110

License

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TALAT Lecture 2301: Design of Members

Description

This lecture gives background to calculation methods for aluminium members in order to understand the specific behavior of statically loaded aluminium alloy structures. Basic structural mechanic, design philosophy and structural aluminium alloys and product forms is assumed.

Subjects

aluminium | aluminum | european aluminium association | eaa | talat | training in aluminium application technologies | training | metallurgy | technology | lecture | design | product | member | joint | static | safety | serviceability | geometrical imperfections | extruded profiles | welded profiles | residual stresses | mechanical properties | bauschinger effect | heat affected zones | stress-strain relationship | strength | reduced strength | partial coefficients | resistance factors | gross section | net section | local buckling | cross section classes | slender plates | effective cross section | class 4 cross sections | deflections of beams | breathing | bending moment | yielding | slenderness parameter | element classification | effective thickness | welded section | section with holes | lateral torsional buckling | axial force | tensile force | compressive force | euler load | squash load | flexural buckling | reduction factor | buckling length | splices | end connections | welded columns | columns with bolt holes | cut-outs | longitudinal welds | transverse welds | columns with unfilled bolt-holes | built-up members | intermediate stiffeners | edge stiffeners | single-sided rib | multi-stiffened plates | orthotropic plates | shear force | plate girder webs | shear buckling | shear resistance | webs with stiffeners | plate girders with intermediate stiffeners | corrugated webs | closely stiffened webs | concentrated loads | beam webs without stiffeners | beam webs with stiffeners | shear centre | closed sections | open sections | torsion without warping | torsion with warpin | bending and axial tension | bending and axial compression | strength of beam-column segments | rectangular section | strain hardening | plastic theory | i-section | h-section | thin walled cross sections | t-section | biaxial bending | linear stress distribution | shear lag | flange curling | lateral deflection | non-symmetrical flanges | corematerials | ukoer | Engineering | H000

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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6.450 Principles of Digital Communication I (MIT)

Description

The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | data compression | Lempel-Ziv algorithm | scalar quantization | vector quantization | sampling | aliasing | Nyquist criterion | PAM modulation | QAM modulation | signal constellations | finite-energy waveform spaces | detection | communication system design | wireless | discrete source encoding | memory-less sources | entropy | asymptotic equipartition property | Fourier series | Fourier transforms | sampling theorem | orthonormal expansions | random processes | linear functionals | theorem of irrelevance | Doppler spread | time spread | coherence time | coherence frequency | Rayleigh fading | Rake receivers | CDMA | code division multiple access

License

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15.564 Information Technology I (MIT)

Description

Information Technology I helps students understand technical concepts underlying current and future developments in information technology. There will be a special emphasis on networks and distributed computing. Students will also gain some hands-on exposure to powerful, high-level tools for making computers do amazing things, without the need for conventional programming languages. Since 15.564 is an introductory course, no knowledge of how computers work or are programmed is assumed.

Subjects

developing-country governments; international | computers; future developments; networks;distributed computing; programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers;future developments;networks;distributed computing;programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers | future developments | networks | distributed computing | programming languages | firewall | e-business | computer architecture | operating | software development | database | user interface | telecommunication | data transmission | local area network | wireless network | internet | world wide web | digital security | architecture | data | transmission | wireless | interface | user | software | development | programming | languages | distributed | computing | LAN | local | area | future | digital | security | technology | information | management | systems | relational | graphical | interfaces | client/server | enterprise | applications | cryptography | services | Microsoft | Access | Lotus Notes | processing | memory | I/O | CPU | OS | hardware | compression | SQL | queries | design | WAN | wide | Ethernet | packet-switched | peer-to-peer | WWW | public | key | mining | warehousing | concepts | conceptual | modern computing | information management | operating systems | relational database systems | graphical user interfaces | client/server systems | enterprise applications | web.internet services | Microsoft Access | database management systems | information technology | telecommunications | eBusiness applications | client | servers | wireless area network

License

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