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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 computingLicense

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.htmSite sourced from

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See all metadata4.107 MArch Portfolio Seminar (MIT) 4.107 MArch Portfolio Seminar (MIT)

Description

The aim of the Portfolio Seminar is to assist in developing a critical position in relationship to their design work. By engaging multiple forms of representation, written and visual, students will explore methods that facilitate describing and representing their design work. Through a critical assessment of their existing portfolios, students will first be challenged to articulate design theses and interests in their past projects. Different mediums of representation will then be studied in order to hone an understanding of the relationship between form and content, and more specifically, the understanding of particular modes of representation as different filters through which their work can be read. Some of the questions that will be addressed are: How does one go about describing an i The aim of the Portfolio Seminar is to assist in developing a critical position in relationship to their design work. By engaging multiple forms of representation, written and visual, students will explore methods that facilitate describing and representing their design work. Through a critical assessment of their existing portfolios, students will first be challenged to articulate design theses and interests in their past projects. Different mediums of representation will then be studied in order to hone an understanding of the relationship between form and content, and more specifically, the understanding of particular modes of representation as different filters through which their work can be read. Some of the questions that will be addressed are: How does one go about describing an iSubjects

representation | representation | portfolio | portfolio | digital | digital | written | written | communicating design | communicating design | meta-level design | meta-level design | theory | theory | representational media | representational media | words vs image | words vs image | physical vs digital | physical vs digital | design vs representation | design vs representation | multiple media | multiple media | architecture and representation | architecture and representation | design thesis | design thesis | web publishing | web publishing | architecture | architecture | description | descriptionLicense

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.htmSite sourced from

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

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

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.htmSite sourced from

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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 computingLicense

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.htmSite sourced from

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This class offers students an opportunity to experiment with various forms and practices of cellphone communication and, most importantly, to propose and develop a semester-long project using advanced A780 cellphones donated by Motorola along with access to J2ME™ source code for programming cellphone applications. Class size is limited. Students in small collaborative groups will propose, implement and report on a semester-long project. This class offers students an opportunity to experiment with various forms and practices of cellphone communication and, most importantly, to propose and develop a semester-long project using advanced A780 cellphones donated by Motorola along with access to J2ME™ source code for programming cellphone applications. Class size is limited. Students in small collaborative groups will propose, implement and report on a semester-long project.Subjects

communication | communication | contemporary engineering and science professional | contemporary engineering and science professional | analyzing how composition and publication contribute to work management and knowledge production | analyzing how composition and publication contribute to work management and knowledge production | writing specific kinds of documents in a clear style | writing specific kinds of documents in a clear style | communication as organizational process | communication as organizational process | electronic modes such as e-mail and the Internet | electronic modes such as e-mail and the Internet | the informational and social roles of specific document forms | the informational and social roles of specific document forms | writing as collaboration | writing as collaboration | the writing process | the writing process | the elements of style | the elements of style | methods of oral presentation | and communication ethics | methods of oral presentation | and communication ethics | case studies | case studies | writing assignments | writing assignments | oral presentation | oral presentation | methods of oral presentation | and communication ethics | methods of oral presentation | and communication ethicsLicense

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.htmSite sourced from

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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 TheoremLicense

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.htmSite sourced from

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See all metadataReadme file for Introduction to Artificial Intelligence

Description

This readme file contains details of links to all the Introduction to Artificial Intelligence module's material held on Jorum and information about the module as well.Subjects

ukoer | evolutionary algorithm lecture | algorithm tutorial | genetic algorithm lecture | genetic algorithm example | evolutionary computation tutorial | artificial intelligence lecture | artificial intelligence tutorial | random processes reading material | semantic web reading material | neural networks video | evolutionary computation test | artificial intelligence test | knowledge representation test | neural networks test | evolutionary algorithm | genetic computation | genetic programming | evolutionary computation | artificial intelligence | introduction to artificial intelligence | search | problem solving | revision | knowledge representation | semantic web | neural network | neural networks | artificial neural networks | swarm intelligence | collective intelligence | robot societies | genetic computation lecture | genetic programming lecture | evolutionary computation lecture | introduction to artificial intelligence lecture | evolutionary algorithm tutorial | genetic computation tutorial | genetic programming tutorial | introduction to artificial intelligence tutorial | evolutionary algorithm example | genetic computation example | genetic programming example | evolutionary computation example | artificial intelligence example | introduction to artificial intelligence example | search lecture | problem solving lecture | search tutorial | problem solving tutorial | search example | problem solving example | revision reading material | search reading material | artificial intelligence reading material | introduction to artificial intelligence reading material | revision lecture | knowledge representation lecture | semantic web lecture | knowledge representation practical | semantic web practical | artificial intelligence practical | introduction to artificial intelligence practical | knowledge representation reading material | knowledge representation notes | semantic web notes | artificial intelligence notes | introduction to artificial intelligence notes | neural network lecture | neural networks lecture | artificial neural networks lecture | neural network reading material | neural networks reading material | artificial neural networks reading material | neural network practical | neural networks practical | artificial neural networks practical | neural network viewing material | neural networks viewing material | artificial neural networks viewing material | artificial intelligence viewing material | introduction to artificial intelligence viewing material | swarm intelligence lecture | collective intelligence lecture | robot societies lecture | swarm intelligence tutorial | collective intelligence tutorial | robot societies tutorial | evolutionary algorithm test | genetic computation test | genetic programming test | introduction to artificial intelligence test | search test | problem solving test | semantic web test | neural network test | artificial neural networks test | g700 | ai | g700 lecture | ai lecture | g700 tutorial | ai tutorial | g700 example | ai example | g700 reading material | ai reading material | g700 practical | ai practical | g700 notes | ai notes | g700 viewing material | ai viewing material | g700 test | ai test | Computer science | I100License

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/Site sourced from

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See all metadata6.003 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 processingLicense

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.htmSite sourced from

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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 TheoremLicense

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.htmSite sourced from

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See all metadata18.702 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 equationsLicense

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.htmSite sourced from

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This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students. This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.Subjects

geometry | geometry | representation | representation | architecture | architecture | drawing | drawing | projection | projection | perspective | perspective | planes | planes | axonometric | axonometric | stereotomy | stereotomy | volume | volume | surface | surface | curvature | curvature | curves | curves | discretization | discretization | generation | generation | construction | construction | publication | publication | presentation | presentationLicense

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.htmSite sourced from

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See all metadata18.702 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 equationsLicense

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.htmSite sourced from

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See all metadata18.702 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 equationsLicense

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.htmSite sourced from

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This subject investigates the special relation of women to several musical folk traditions in the British Isles and North America. Throughout, we will be examining the implications of gender in the creation, transmission, and performance of music. Because virtually all societies operate to some extent on a gendered division of labor (and of expressive roles) the music of these societies is marked by the gendering of musical repertoires, traditions of instrumentation, performance settings, and styles. This seminar will examine the gendered dimensions of the music - the song texts, the performance styles, processes of dissemination (collection, literary representation) and issues of historiography - with respect to selected traditions within the folk musics of North America and the British I This subject investigates the special relation of women to several musical folk traditions in the British Isles and North America. Throughout, we will be examining the implications of gender in the creation, transmission, and performance of music. Because virtually all societies operate to some extent on a gendered division of labor (and of expressive roles) the music of these societies is marked by the gendering of musical repertoires, traditions of instrumentation, performance settings, and styles. This seminar will examine the gendered dimensions of the music - the song texts, the performance styles, processes of dissemination (collection, literary representation) and issues of historiography - with respect to selected traditions within the folk musics of North America and the British ISubjects

Representation | Representation | women | women | music | music | folk music | folk music | traditions | traditions | British Isles | British Isles | North America | North America | gender | gender | creation | creation | transmission | transmission | performance | performance | dissemination | dissemination | collection | collection | literary representation | literary representation | historiography | historiography | stories | stories | female identity | female identity | song texts | song texts | work | work | cultural roles | cultural rolesLicense

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.htmSite sourced from

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This semester students are asked to transform the Hereshoff Museum in Bristol, Rhode Island, through processes of erasure and addition. Hereshoff Manufacturing was recognized as one of the premier builders of America's Cup racing boats between 1890's and 1930's. The studio, however, is about more than the program. It is about land, water, and wind and the search for expressing materially and tectonically the relationships between these principle conditions. That is, where the land is primarily about stasis (docking, anchoring and referencing our locus), water's fluidity holds the latent promise of movement and freedom. Movement is activated by wind, allowing for negotiating the relationship between water and land. This semester students are asked to transform the Hereshoff Museum in Bristol, Rhode Island, through processes of erasure and addition. Hereshoff Manufacturing was recognized as one of the premier builders of America's Cup racing boats between 1890's and 1930's. The studio, however, is about more than the program. It is about land, water, and wind and the search for expressing materially and tectonically the relationships between these principle conditions. That is, where the land is primarily about stasis (docking, anchoring and referencing our locus), water's fluidity holds the latent promise of movement and freedom. Movement is activated by wind, allowing for negotiating the relationship between water and land.Subjects

architecture | architecture | design | design | tectonics | tectonics | representation | representation | materials | materials | construction | construction | presentation | presentation | sketching | sketching | metaphor | metaphor | boat building | boat building | shipyard renovation | shipyard renovation | adaptive reuse | adaptive reuse | public and private space | public and private space | visual arts | visual arts | America's Cup | America's Cup | racing | racing | displacement | displacement | lightness | lightness | mass | mass | strength | strength | energy | energy | speed | speed | design studio | design studio | architectural design | architectural design | public space | public space | private space | private space | tectonic language | tectonic language | design process | design process | research | research | reading | reading | representing | representing | testing | testingLicense

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The seminar will be devoted to understanding what we're up to when we ascribe contents to a person's assertions and mental attitudes. We seek to make clear the rules of the game for the philosophy of language. We'll survey classic discussions of the issue by Field, Lewis and Stalnaker. But much of the emphasis of the class will be on getting clear about the limitations of our theoretical tools. I'd like to focus on places where our theorizing runs into trouble, or breaks down altogether. The seminar will be devoted to understanding what we're up to when we ascribe contents to a person's assertions and mental attitudes. We seek to make clear the rules of the game for the philosophy of language. We'll survey classic discussions of the issue by Field, Lewis and Stalnaker. But much of the emphasis of the class will be on getting clear about the limitations of our theoretical tools. I'd like to focus on places where our theorizing runs into trouble, or breaks down altogether.Subjects

radical interpretation | radical interpretation | mathematical truth | mathematical truth | self-location | self-location | degrees of belief | degrees of belief | incoherent belief | incoherent belief | language of thought | language of thought | representation system | representation system | modeling representation | modeling representation | intentionality | intentionality | philosophy of language | philosophy of language | Putnam's paradox | Putnam's paradox | semantics | semantics | logical omniscience | logical omniscience | epistemology | epistemology | knowledge argument | knowledge argumentLicense

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See all metadata18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

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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 computingLicense

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The goal of this course is to help students learn to communicate strategically within a professional setting. Students are asked to analyze their intended audience, the purpose of their communication, and the context in which they are operating before developing the message. The course focuses specifically on improving students’ ability to write, speak, work in a team, and communicate across cultures in their roles as future managers. The goal of this course is to help students learn to communicate strategically within a professional setting. Students are asked to analyze their intended audience, the purpose of their communication, and the context in which they are operating before developing the message. The course focuses specifically on improving students’ ability to write, speak, work in a team, and communicate across cultures in their roles as future managers.Subjects

management | management | communication | communication | oral presentation | oral presentation | presentation | presentation | leadership | leadership | writing | writing | teamwork | teamwork | business | business | professional skills | professional skillsLicense

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See all metadata18.091 Mathematical Exposition (MIT) 18.091 Mathematical Exposition (MIT)

Description

This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems. This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.Subjects

oral presentation | oral presentation | mathematics writing | mathematics writing | mathematics presentation | mathematics presentation | 17.881 | 17.881 | 17.882 | 17.882License

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See all metadata4.107 MArch Portfolio Seminar (MIT)

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The aim of the Portfolio Seminar is to assist in developing a critical position in relationship to their design work. By engaging multiple forms of representation, written and visual, students will explore methods that facilitate describing and representing their design work. Through a critical assessment of their existing portfolios, students will first be challenged to articulate design theses and interests in their past projects. Different mediums of representation will then be studied in order to hone an understanding of the relationship between form and content, and more specifically, the understanding of particular modes of representation as different filters through which their work can be read. Some of the questions that will be addressed are: How does one go about describing an iSubjects

representation | portfolio | digital | written | communicating design | meta-level design | theory | representational media | words vs image | physical vs digital | design vs representation | multiple media | architecture and representation | design thesis | web publishing | architecture | descriptionLicense

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See all metadata4.123 Architectural Design, Level I: Perceptions and Processes (MIT)

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

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

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This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field. This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field.Subjects

computational theories of human cognition | computational theories of human cognition | principles of inductive learning and inference | principles of inductive learning and inference | representation of knowledge | representation of knowledge | computational frameworks | computational frameworks | Bayesian models | Bayesian models | hierarchical Bayesian models | hierarchical Bayesian models | probabilistic graphical models | probabilistic graphical models | nonparametric statistical models | nonparametric statistical models | Bayesian Occam's razor | Bayesian Occam's razor | sampling algorithms for approximate learning and inference | sampling algorithms for approximate learning and inference | probabilistic models defined over structured representations such as first-order logic | probabilistic models defined over structured representations such as first-order logic | grammars | grammars | relational schemas | relational schemas | core aspects of cognition | core aspects of cognition | concept learning | concept learning | concept categorization | concept categorization | causal reasoning | causal reasoning | theory formation | theory formation | language acquisition | language acquisition | social inference | social inferenceLicense

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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 awarenessLicense

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See all metadata15.280 Communication for Managers (MIT) 15.280 Communication for Managers (MIT)

Description

Writing and speaking skills necessary for a career in management. Students polish communication strategies and methods through discussion, examples, and practice. Several written and oral assignments, most based on material from other subjects and from career development activities. Schedule and curriculum coordinated with 15.311 Organizational Processes class. Restricted to first-year Sloan School of Management graduate students. Students may also enroll in 15.277 Special Seminar in Communication: Leadership and Personal Effectiveness Coaching. 15.280 is offered for 6 units and 15.277 provides an additional 3 units for a total of 9 units in Managerial Communication. 15.277 acts as a lab component to 15.280 and provides students additional opportunities to hone their communication skills t Writing and speaking skills necessary for a career in management. Students polish communication strategies and methods through discussion, examples, and practice. Several written and oral assignments, most based on material from other subjects and from career development activities. Schedule and curriculum coordinated with 15.311 Organizational Processes class. Restricted to first-year Sloan School of Management graduate students. Students may also enroll in 15.277 Special Seminar in Communication: Leadership and Personal Effectiveness Coaching. 15.280 is offered for 6 units and 15.277 provides an additional 3 units for a total of 9 units in Managerial Communication. 15.277 acts as a lab component to 15.280 and provides students additional opportunities to hone their communication skills tSubjects

management communication | management communication | communication strategy | communication strategy | Minto pyramid | Minto pyramid | persuasive communication | persuasive communication | managing feedback | managing feedback | visual aids | visual aids | effective presentation strategies | effective presentation strategies | business communication | business communication | memo format | memo format | intercultural communication | intercultural communication | active listening | active listening | reflective listening | reflective listening | group presentations | group presentations | business e-mail | business e-mailLicense

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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 | MultiwaveletsLicense

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