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

Description

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

Subjects

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

License

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

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6.003 Signals and Systems (MIT) 6.003 Signals and Systems (MIT)

Description

6.003 covers the fundamentals of signal and system analysis, focusing on representations of discrete-time and continuous-time signals (singularity functions, complex exponentials and geometrics, Fourier representations, Laplace and Z transforms, sampling) and representations of linear, time-invariant systems (difference and differential equations, block diagrams, system functions, poles and zeros, convolution, impulse and step responses, frequency responses). Applications are drawn broadly from engineering and physics, including feedback and control, communications, and signal processing. 6.003 covers the fundamentals of signal and system analysis, focusing on representations of discrete-time and continuous-time signals (singularity functions, complex exponentials and geometrics, Fourier representations, Laplace and Z transforms, sampling) and representations of linear, time-invariant systems (difference and differential equations, block diagrams, system functions, poles and zeros, convolution, impulse and step responses, frequency responses). Applications are drawn broadly from engineering and physics, including feedback and control, communications, and signal processing.

Subjects

signal and system analysis | signal and system analysis | representations of discrete-time and continuous-time signals | representations of discrete-time and continuous-time signals | representations of linear time-invariant systems | representations of linear time-invariant systems | Fourier representations | Fourier representations | Laplace and Z transforms | Laplace and Z transforms | sampling | sampling | difference and differential equations | difference and differential equations | feedback and control | feedback and control | communications | communications | signal processing | signal processing

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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18.712 Introduction to Representation Theory (MIT) 18.712 Introduction to Representation Theory (MIT)

Description

This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s Theorem

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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18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equations

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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18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail. The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.

Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equations

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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9.916 The Neural Basis of Visual Object Recognition in Monkeys and Humans (MIT) 9.916 The Neural Basis of Visual Object Recognition in Monkeys and Humans (MIT)

Description

Understanding the brain's remarkable ability for visual object recognition is one of the greatest challenges of brain research. The goal of this course is to provide an overview of key issues of object representation and to survey data from primate physiology and human fMRI that bear on those issues. Topics include the computational problems of object representation, the nature of object representations in the brain, the tolerance and selectivity of those representations, and the effects of attention and learning. Understanding the brain's remarkable ability for visual object recognition is one of the greatest challenges of brain research. The goal of this course is to provide an overview of key issues of object representation and to survey data from primate physiology and human fMRI that bear on those issues. Topics include the computational problems of object representation, the nature of object representations in the brain, the tolerance and selectivity of those representations, and the effects of attention and learning.

Subjects

vision | vision | object recognition | object recognition | monkey versus human | monkey versus human | object representations | object representations | fMRI | fMRI | temporal lobe | temporal lobe | visual cortex | visual cortex | neuronal representations | neuronal representations | neurophysiology | neurophysiology | retinal image | retinal image | pattern recognition | pattern recognition | perceptual awareness | perceptual awareness

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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18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equations

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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18.712 Introduction to Representation Theory (MIT) 18.712 Introduction to Representation Theory (MIT)

Description

The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s Theorem

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) 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 math | discrete mathematics | discrete mathematics | presentations | presentations | student presentations | student presentations | oral communication | oral communication | combinatorics | combinatorics | graph theory | graph theory | Proofs from the Book | Proofs from the Book | mathematics communication | mathematics communication

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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6.003 Signals and Systems (MIT)

Description

6.003 covers the fundamentals of signal and system analysis, focusing on representations of discrete-time and continuous-time signals (singularity functions, complex exponentials and geometrics, Fourier representations, Laplace and Z transforms, sampling) and representations of linear, time-invariant systems (difference and differential equations, block diagrams, system functions, poles and zeros, convolution, impulse and step responses, frequency responses). Applications are drawn broadly from engineering and physics, including feedback and control, communications, and signal processing.

Subjects

signal and system analysis | representations of discrete-time and continuous-time signals | representations of linear time-invariant systems | Fourier representations | Laplace and Z transforms | sampling | difference and differential equations | feedback and control | communications | signal processing

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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24.901 Language and its Structure I: Phonology (MIT) 24.901 Language and its Structure I: Phonology (MIT)

Description

24.901 is designed to give you a preliminary understanding of how the sound systems of different languages are structured, how and why they may differ from each other. The course also aims to provide you with analytical tools in phonology, enough to allow you to sketch the analysis of an entire phonological system by the end of the term. On a non-linguistic level, the couse aims to teach you by example the virtues of formulating precise and explicit descriptive statements; and to develop your skills in making and evaluating arguments. 24.901 is designed to give you a preliminary understanding of how the sound systems of different languages are structured, how and why they may differ from each other. The course also aims to provide you with analytical tools in phonology, enough to allow you to sketch the analysis of an entire phonological system by the end of the term. On a non-linguistic level, the couse aims to teach you by example the virtues of formulating precise and explicit descriptive statements; and to develop your skills in making and evaluating arguments.

Subjects

fundamental concepts | fundamental concepts | phonological theory | phonological theory | philosophy | philosophy | cognitive psychology | cognitive psychology | articulatory phonetics | articulatory phonetics | acoustic phonetics | acoustic phonetics | feature systems | feature systems | underlying representations | underlying representations | underspecification | underspecification | phonological rules | phonological rules | phonological derivations | phonological derivations | syllable structure | syllable structure | accentual systems | accentual systems | morphology-phonology interface | morphology-phonology interface

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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17.869 Political Science Scope and Methods (MIT) 17.869 Political Science Scope and Methods (MIT)

Description

This course is designed to provide an introduction to a variety of empirical research methods used by political scientists. The primary aims of the course are to make you a more sophisticated consumer of diverse empirical research and to allow you to conduct sophisticated independent work in your junior and senior years. This is not a course in data analysis. Rather, it is a course on how to approach political science research. This course is designed to provide an introduction to a variety of empirical research methods used by political scientists. The primary aims of the course are to make you a more sophisticated consumer of diverse empirical research and to allow you to conduct sophisticated independent work in your junior and senior years. This is not a course in data analysis. Rather, it is a course on how to approach political science research.

Subjects

political science | political science | empirical research | empirical research | scientific method | scientific method | research design | research design | models | models | samping | samping | statistical analysis | statistical analysis | measurement | measurement | ethics | ethics | empirical | empirical | research | research | scientific | scientific | methods | methods | statistics | statistics | statistical | statistical | analysis | analysis | political | political | politics | politics | science | science | design | design | sampling | sampling | theoretical | theoretical | observation | observation | data | data | case studies | case studies | cases | cases | empirical research methods | empirical research methods | political scientists | political scientists | empirical analysis | empirical analysis | theoretical analysis | theoretical analysis | research projects | research projects | department faculty | department faculty | inference | inference | writing | writing | revision | revision | oral presentations | oral presentations | experimental method | experimental method | theories | theories | political implications | political implications

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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15.281 Advanced Managerial Communication (MIT) 15.281 Advanced Managerial Communication (MIT)

Description

This course builds on managerial communication skills developed in Management Communication for Undergraduates (15.279) or Communication for Managers (15.280). It introduces interactive oral and interpersonal communication skills important to managers, including: presenting to a hostile audience, running meetings, listening, and contributing to group decision-making. Working in teams, students present a communication topic of their choosing to the class. An individual project challenges students to address a business audience in written and oral forms. This course builds on managerial communication skills developed in Management Communication for Undergraduates (15.279) or Communication for Managers (15.280). It introduces interactive oral and interpersonal communication skills important to managers, including: presenting to a hostile audience, running meetings, listening, and contributing to group decision-making. Working in teams, students present a communication topic of their choosing to the class. An individual project challenges students to address a business audience in written and oral forms.

Subjects

interpersonal communication | interpersonal communication | business presentations | business presentations | communication strategies | communication strategies | teamwork | teamwork | running meetings | running meetings | managerial communication | managerial communication | business writing | business writing | business speaking | business speaking | group decision making | group decision making | hostile audience | hostile audience | role play exercises | role play exercises | persuasive communication | persuasive communication | persuading audiences | persuading audiences | listening | listening | nonverbal communication | nonverbal communication | A | A | question and answer | question and answer | working with media | working with media | intercultural communication | intercultural communication | communicating across cultures | communicating across cultures | cross-cultural communication | cross-cultural communication

License

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4.301 Introduction to the Visual Arts (MIT) 4.301 Introduction to the Visual Arts (MIT)

Description

This class will introduce students to a variety of contemporary art practices and ideas. The class will begin with a brief overview of 'visual language' by looking at a variety of artworks and discussing basic concepts revolving around artistic practice. The rest of the class will focus on notions of the real/unreal as explored with various mediums and practices. The class will work in video, sculpture and in public space. This class will introduce students to a variety of contemporary art practices and ideas. The class will begin with a brief overview of 'visual language' by looking at a variety of artworks and discussing basic concepts revolving around artistic practice. The rest of the class will focus on notions of the real/unreal as explored with various mediums and practices. The class will work in video, sculpture and in public space.

Subjects

visual art practice | visual art practice | critical analysis | critical analysis | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | aesthetic analyses | aesthetic analyses | modern art | modern art | art history | art history | body | body | phenomenology | phenomenology | personal space | personal space | installation | installation

License

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4.301 Introduction to the Visual Arts (MIT) 4.301 Introduction to the Visual Arts (MIT)

Description

This course is an introduction to artistic practice and aesthetic analysis through studio work and lectures. Students communicate ideas and experiences through various media such as sculpture, installation, performance, and video. Projects evolve through stages of conceptual and material development to final presentation. Lectures, visiting artist presentations, field trips, and readings supplement studio practice, providing an index to the historical, cultural, and environmental forces that affect both development of artistic vision and reception of works of art.Technical RequirementsSpecial software is required to use some of the files in this course: .rm. This course is an introduction to artistic practice and aesthetic analysis through studio work and lectures. Students communicate ideas and experiences through various media such as sculpture, installation, performance, and video. Projects evolve through stages of conceptual and material development to final presentation. Lectures, visiting artist presentations, field trips, and readings supplement studio practice, providing an index to the historical, cultural, and environmental forces that affect both development of artistic vision and reception of works of art.Technical RequirementsSpecial software is required to use some of the files in this course: .rm.

Subjects

visual art practice | visual art practice | critical analysis | critical analysis | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | aesthetic analyses | aesthetic analyses | modern art | modern art | art history | art history | body | body | phenomenology | phenomenology | personal space | personal space | installation | installation

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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4.301 Introduction to the Visual Arts (MIT) 4.301 Introduction to the Visual Arts (MIT)

Description

Introduction to artistic practice and aesthetic analysis through studio work and lectures. Students communicate ideas and experiences through various media such as sculpture, installation, performance, and video. Projects evolve through stages of conceptual and material development to final presentation. Lectures, visiting artist presentations, field trips, and readings supplement studio practice, providing an index to the historical, cultural, and environmental forces that affect both development of artistic vision and reception of works of art.Technical RequirementsRealOne™ Player software  is required to run the .rm files found on this course site. Introduction to artistic practice and aesthetic analysis through studio work and lectures. Students communicate ideas and experiences through various media such as sculpture, installation, performance, and video. Projects evolve through stages of conceptual and material development to final presentation. Lectures, visiting artist presentations, field trips, and readings supplement studio practice, providing an index to the historical, cultural, and environmental forces that affect both development of artistic vision and reception of works of art.Technical RequirementsRealOne™ Player software  is required to run the .rm files found on this course site.

Subjects

visual art practice | visual art practice | critical analysis | critical analysis | long-range | long-range | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | aesthetic analyses | aesthetic analyses | modern art | modern art | art history | art history | body | body | phenomenology | phenomenology | personal space | personal space | installation | installation

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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6.451 Principles of Digital Communication II (MIT) 6.451 Principles of Digital Communication II (MIT)

Description

This course is the second of a two-term sequence with 6.450. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of 6.450 and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-decision decoding. It continues with binary linear block codes, Reed-Muller codes, finite fields, Reed-Solomon and BCH codes, binary linear convolutional codes, and the Viterbi algorithm.More advanced topics include trellis representations of binary linear block codes and trellis-based decoding; codes on graphs; the sum-product and min-sum algorithms This course is the second of a two-term sequence with 6.450. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of 6.450 and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-decision decoding. It continues with binary linear block codes, Reed-Muller codes, finite fields, Reed-Solomon and BCH codes, binary linear convolutional codes, and the Viterbi algorithm.More advanced topics include trellis representations of binary linear block codes and trellis-based decoding; codes on graphs; the sum-product and min-sum algorithms

Subjects

coding techniques | coding techniques | the Shannon limit of additive white Gaussian noise channels | the Shannon limit of additive white Gaussian noise channels | performance analysis | performance analysis | Small signal constellations | Small signal constellations | coding gain | coding gain | Hard-decision and soft-decision decoding | Hard-decision and soft-decision decoding | Introduction to binary linear block codes | Introduction to binary linear block codes | Reed-Muller codes | Reed-Muller codes | finite fields | finite fields | Reed-Solomon and BCH codes | Reed-Solomon and BCH codes | binary linear convolutional codes | binary linear convolutional codes | Viterbi and BCJR algorithms | Viterbi and BCJR algorithms | Trellis representations of binary linear block codes | Trellis representations of binary linear block codes | trellis-based ML decoding | trellis-based ML decoding | Codes on graphs | Codes on graphs | sum-product | sum-product | max-product | max-product | decoding algorithms | decoding algorithms | Turbo codes | Turbo codes | LDPC codes and RA codes | LDPC codes and RA codes | Coding for the bandwidth-limited regime | Coding for the bandwidth-limited regime | Lattice codes | Lattice codes | Trellis-coded modulation | Trellis-coded modulation | Multilevel coding | Multilevel coding | Shaping | Shaping

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

Description

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

Subjects

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

License

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4.303 The Production of Space: Art, Architecture and Urbanism in Dialogue (MIT) 4.303 The Production of Space: Art, Architecture and Urbanism in Dialogue (MIT)

Description

Includes audio/video content: AV selected lectures. This seminar engages in the notion of space from various points of departure. The goal is first of all to engage in the term and secondly to examine possibilities of art, architecture within urban settings in order to produce what is your interpretation of space. Includes audio/video content: AV selected lectures. This seminar engages in the notion of space from various points of departure. The goal is first of all to engage in the term and secondly to examine possibilities of art, architecture within urban settings in order to produce what is your interpretation of space.

Subjects

architecture | architecture | urbanisml gender | urbanisml gender | space | space | visual art practice | visual art practice | critical analysis | critical analysis | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | aesthetic analyses | aesthetic analyses | modern art | modern art | art history | art history | body | body | phenomenology | phenomenology | personal space | personal space | installation | installation

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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4.367 Studio Seminar in Public Art (MIT) 4.367 Studio Seminar in Public Art (MIT)

Description

Includes audio/video content: AV special element video. How do we define Public Art? This course focuses on the production of projects for public places. Public Art is a concept that is in constant discussion and revision, as much as the evolution and transformation of public spaces and cities are. Monuments are repositories of memory and historical presences with the expectation of being permanent. Public interventions are created not to impose and be temporary, but as forms intended to activate discourse and discussion. Considering the concept of a museum as a public device and how they are searching for new ways of avoiding generic identities, we will deal with the concept of the personal imaginary museum. It should be considered as a point of departure to propose a personal individual Includes audio/video content: AV special element video. How do we define Public Art? This course focuses on the production of projects for public places. Public Art is a concept that is in constant discussion and revision, as much as the evolution and transformation of public spaces and cities are. Monuments are repositories of memory and historical presences with the expectation of being permanent. Public interventions are created not to impose and be temporary, but as forms intended to activate discourse and discussion. Considering the concept of a museum as a public device and how they are searching for new ways of avoiding generic identities, we will deal with the concept of the personal imaginary museum. It should be considered as a point of departure to propose a personal individual

Subjects

cities | cities | urbanism | urbanism | artists | artists | architects | architects | collaboration | collaboration | translation | translation | revitalization | revitalization | urban space | urban space | redistricting | redistricting | planned cities | planned cities | development | development | ground zero | ground zero | blank slate | blank slate | interventions | interventions | visual art practice | visual art practice | critical analysis | critical analysis | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | aesthetic analyses | aesthetic analyses | modern art | modern art | art history | art history | body | body | phenomenology | phenomenology | personal space | personal space | installation | installation

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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4.370 Interrogative Design Workshop (MIT) 4.370 Interrogative Design Workshop (MIT)

Description

Includes audio/video content: AV selected lectures. "Parrhesia" was an Athenian right to frank and open speaking, the right that, like the First Amendment, demands a "fearless speaker" who must challenge political powers with criticism and unsolicited advice. Can designer and artist respond today to such a democratic call and demand? Is it possible to do so despite the (increasing) restrictions imposed on our liberties today? Can the designer or public artist operate as a proactive "parrhesiatic" agent and contribute to the protection, development and dissemination of "fearless speaking" in Public Space? Includes audio/video content: AV selected lectures. "Parrhesia" was an Athenian right to frank and open speaking, the right that, like the First Amendment, demands a "fearless speaker" who must challenge political powers with criticism and unsolicited advice. Can designer and artist respond today to such a democratic call and demand? Is it possible to do so despite the (increasing) restrictions imposed on our liberties today? Can the designer or public artist operate as a proactive "parrhesiatic" agent and contribute to the protection, development and dissemination of "fearless speaking" in Public Space?

Subjects

visual art practice | visual art practice | critical analysis | critical analysis | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | aesthetic analyses | aesthetic analyses | modern art | modern art | art history | art history | body | body | phenomenology | phenomenology | personal space | personal space | installation | installation

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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4.302 BSAD Foundations in the Visual Arts (MIT) 4.302 BSAD Foundations in the Visual Arts (MIT)

Description

This class offers a foundation in the visual art practice and its critical analysis for beginning architecture students. Emphasis is on long-range artistic development and its analogies to architectural thinking and practice. Students will learn to communicate ideas and experiences through various two-dimensional, and three-dimensional, and time-based media, including installations, performance and video. Lectures, visiting artist presentations, field trips, and readings supplement studio practice. This class offers a foundation in the visual art practice and its critical analysis for beginning architecture students. Emphasis is on long-range artistic development and its analogies to architectural thinking and practice. Students will learn to communicate ideas and experiences through various two-dimensional, and three-dimensional, and time-based media, including installations, performance and video. Lectures, visiting artist presentations, field trips, and readings supplement studio practice.

Subjects

visual art practice | visual art practice | critical analysis | critical analysis | long-range artistic development | long-range artistic development | two-dimensional | two-dimensional | three-dimensional | three-dimensional | time-based media | time-based media | installations | installations | performance and video | performance and video | visiting artist presentations | visiting artist presentations | field trips | field trips | studio practice | studio practice | architecture | architecture | architectural practice | architectural practice | two-dimensional media | two-dimensional media | three-dimensional media | three-dimensional media | 2D media | 2D media | 3D media | 3D media | sculpture | sculpture | performance | performance | video | video

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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6.451 Principles of Digital Communication II (MIT) 6.451 Principles of Digital Communication II (MIT)

Description

Includes audio/video content: AV lectures. This course is the second of a two-term sequence with 6.450. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of 6.450 and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-decision decoding. It continues with binary linear block codes, Reed-Muller codes, finite fields, Reed-Solomon and BCH codes, binary linear convolutional codes, and the Viterbi algorithm. More advanced topics include trellis representations of binary linear block codes and trellis-based decoding; codes on graphs; the sum-product and Includes audio/video content: AV lectures. This course is the second of a two-term sequence with 6.450. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of 6.450 and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-decision decoding. It continues with binary linear block codes, Reed-Muller codes, finite fields, Reed-Solomon and BCH codes, binary linear convolutional codes, and the Viterbi algorithm. More advanced topics include trellis representations of binary linear block codes and trellis-based decoding; codes on graphs; the sum-product and

Subjects

coding techniques | coding techniques | the Shannon limit of additive white Gaussian noise channels | the Shannon limit of additive white Gaussian noise channels | performance analysis | performance analysis | Small signal constellations | Small signal constellations | coding gain | coding gain | Hard-decision and soft-decision decoding | Hard-decision and soft-decision decoding | Introduction to binary linear block codes | Introduction to binary linear block codes | Reed-Muller codes | Reed-Muller codes | finite fields | finite fields | Reed-Solomon and BCH codes | Reed-Solomon and BCH codes | binary linear convolutional codes | binary linear convolutional codes | Viterbi and BCJR algorithms | Viterbi and BCJR algorithms | Trellis representations of binary linear block codes | Trellis representations of binary linear block codes | trellis-based ML decoding | trellis-based ML decoding | Codes on graphs | Codes on graphs | sum-product | sum-product | max-product | max-product | decoding algorithms | decoding algorithms | Turbo codes | Turbo codes | LDPC codes and RA codes | LDPC codes and RA codes | Coding for the bandwidth-limited regime | Coding for the bandwidth-limited regime | Lattice codes. | Lattice codes. | Trellis-coded modulation | Trellis-coded modulation | Multilevel coding | Multilevel coding | Shaping | Shaping | Lattice codes | Lattice codes

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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