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18.338J Infinite Random Matrix Theory (MIT) 18.338J Infinite Random Matrix Theory (MIT)

Description

In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices. In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices.

Subjects

Infinite Random Matrices | Infinite Random Matrices | The Hermite Ensemble | The Hermite Ensemble | Wigner's Semi-Circle Law; | Wigner's Semi-Circle Law; | The Laguerre Ensemble | The Laguerre Ensemble | Marcenko-Pastur Theorem | Marcenko-Pastur Theorem | The Jacobi Ensemble | The Jacobi Ensemble | McKay's Random Graph Theorem | McKay's Random Graph Theorem | The ?Semi-Circular? Element | The ?Semi-Circular? Element | Central Limit Theorem | Central Limit Theorem | Free Cumulants in Free Probability | Free Cumulants in Free Probability | Non-Crossing Partitionsm | Non-Crossing Partitionsm | Free Cumulants | Free Cumulants | The Semi-Circular and ?Free Poisson? distributions | The Semi-Circular and ?Free Poisson? distributions | Additive Free Convolution | Additive Free Convolution | The R-Transform and the Marcenko-Pastur Theorem | The R-Transform and the Marcenko-Pastur Theorem | Multiplicative Free Convolution | Multiplicative Free Convolution | The S-Transform | The S-Transform | Non-Crossing Partitions | Non-Crossing Partitions | Orthogonal Polynomials and the Classical Matrix Ensembles | Orthogonal Polynomials and the Classical Matrix Ensembles | Tracy Widom Distribution | Tracy Widom Distribution | Eigenvalue Spectrum Fluctuations | Eigenvalue Spectrum Fluctuations | Free Probability and Fluctuations | Free Probability and Fluctuations | Zonal Polynomials and Random Matrices | Zonal Polynomials and Random Matrices | Symmetric Group Representations and Free Probability | Symmetric Group Representations and Free Probability | 18.338 | 18.338 | 16.394 | 16.394 | Wigner's Semi-Circle Law | Wigner's Semi-Circle Law

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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Linear Álgebra Linear Álgebra

Description

Linear algebra is the study of linear equations, vector spaces, linear maps and Euclidean spaces. The subject covers all topics in a first year college in a linear algebra course. Linear Algebra finds applications in virtually every area of mathematics, including Multivariate Calculus, Differential Equations, and Probability Theory. The subject will mainly develop the theory of Linear Algebra, and will focus on the computational aspects. Linear Algebra as the structure underlying in the study of the Euclidean Geometry is developed and explained with a interesting figure description of the movements in the space. The mathematical formulas are also written with different color in order to make easier the compression of the subject. Linear algebra is the study of linear equations, vector spaces, linear maps and Euclidean spaces. The subject covers all topics in a first year college in a linear algebra course. Linear Algebra finds applications in virtually every area of mathematics, including Multivariate Calculus, Differential Equations, and Probability Theory. The subject will mainly develop the theory of Linear Algebra, and will focus on the computational aspects. Linear Algebra as the structure underlying in the study of the Euclidean Geometry is developed and explained with a interesting figure description of the movements in the space. The mathematical formulas are also written with different color in order to make easier the compression of the subject.

Subjects

Espacio Euclídeo | Espacio Euclídeo | Álgebra Lineal | Álgebra Lineal | Álgebra | Álgebra | Ecuaciones Lineales | Ecuaciones Lineales | Matrices | Matrices

License

Copyright 2009, by the Contributing Authors http://creativecommons.org/licenses/by-nc-sa/3.0/

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ticas Aplicadas a las Ciencias Sociales ticas Aplicadas a las Ciencias Sociales

Description

Curso preparatorio para asentar los conocimientos bsicos de matemticas necesarios para abordar los estudios en los grados de Economa, Administracin y Direccin de Empresas (ADE), y dobles grados de Derecho-Economa y ADE-Derecho. Curso preparatorio para asentar los conocimientos bsicos de matemticas necesarios para abordar los estudios en los grados de Economa, Administracin y Direccin de Empresas (ADE), y dobles grados de Derecho-Economa y ADE-Derecho.

Subjects

Integrales | Integrales | Ecuaciones | Ecuaciones | Polinomios | Polinomios | Derivadas | Derivadas | lgebra | lgebra | Matrices | Matrices | lculo | lculo | ticas | ticas | Sistemas lineales | Sistemas lineales | bolas | bolas | Inecuaciones | Inecuaciones | Cursos Cero | Cursos Cero | Matematica Aplicada | Matematica Aplicada | 2011 | 2011

License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/

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18.312 Algebraic Combinatorics (MIT) 18.312 Algebraic Combinatorics (MIT)

Description

This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected. This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.

Subjects

Rational Generating Functions | Rational Generating Functions | Recurrence Relations | Recurrence Relations | Radon Transform | Radon Transform | Adjacency and Laplacian Matrices of Graphs | Adjacency and Laplacian Matrices of Graphs

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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Mathematical Methods II Mathematical Methods II

Description

This course consists of a introduction to linear algebra. This course consists of a introduction to linear algebra.

Subjects

Bachelor in Statistics and Business | Bachelor in Statistics and Business | Algebra | Algebra | Prerequisites | Prerequisites | Systems of linear equations | Systems of linear equations | Eigenvalues and eigenvectors | Eigenvalues and eigenvectors | General information | General information | Orthogonality and least-square problems | Orthogonality and least-square problems | Singular value decomposition | Singular value decomposition | stica y Empresa | stica y Empresa | Real vector spaces | Real vector spaces | Matrices and determinants | Matrices and determinants | Diagonalization | Diagonalization | 2012 | 2012

License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/

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18.996 Random Matrix Theory and Its Applications (MIT) 18.996 Random Matrix Theory and Its Applications (MIT)

Description

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications. This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

Subjects

Random matrix theory | Random matrix theory | Matrix Jacobians | Matrix Jacobians | Wishart Matrices | Wishart Matrices | Wigner's Semi-Circular laws | Wigner's Semi-Circular laws | Matrix beta ensembles | Matrix beta ensembles | free probability | free probability | spherical coordinates | spherical coordinates | wedging | wedging | Plucker coordinates | Plucker coordinates | matrix factorizations | matrix factorizations | householder transformations | householder transformations | Stiefel manifold | Stiefel manifold | Cauchey-Binet theorem | Cauchey-Binet theorem | Telatar's paper | Telatar's paper | level densities | level densities | orthogonal polynomials | orthogonal polynomials | matrix integrals | matrix integrals | hypergeometric functions | hypergeometric functions | wireless communictions | wireless communictions | eigenvalue density | eigenvalue density | sample covariance matrices | sample covariance matrices | Marcenko-Pastur theorem | Marcenko-Pastur theorem | wireless communications | wireless communications

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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18.338J Infinite Random Matrix Theory (MIT)

Description

In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices.

Subjects

Infinite Random Matrices | The Hermite Ensemble | Wigner's Semi-Circle Law; | The Laguerre Ensemble | Marcenko-Pastur Theorem | The Jacobi Ensemble | McKay's Random Graph Theorem | The ?Semi-Circular? Element | Central Limit Theorem | Free Cumulants in Free Probability | Non-Crossing Partitionsm | Free Cumulants | The Semi-Circular and ?Free Poisson? distributions | Additive Free Convolution | The R-Transform and the Marcenko-Pastur Theorem | Multiplicative Free Convolution | The S-Transform | Non-Crossing Partitions | Orthogonal Polynomials and the Classical Matrix Ensembles | Tracy Widom Distribution | Eigenvalue Spectrum Fluctuations | Free Probability and Fluctuations | Zonal Polynomials and Random Matrices | Symmetric Group Representations and Free Probability | 18.338 | 16.394 | Wigner's Semi-Circle Law

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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lgebra y Matemtica Discreta (2013) lgebra y Matemtica Discreta (2013)

Description

Los Fundamentos matemticos de la Informtica, base esencial para los cursos de informtica Aplicada, engloban Matemtica discreta, lgica, lgebra, anlisis y estadstica El lgebra sirve para introducir los conceptos y tcnicas bsicas de trabajo con procesos lineales. Partiendo de conceptos que deberan de ser conocidos, se pasa a introducir los conceptos asociados a los Espacios Vectoriales. Dado que una gran parte de las asignaturas tanto de primer curso como de cursos posteriores usan tcnicas lineales (Codificacin, Criptografa, Optimizacin, Grficos, CAD, etc.) supone una preparacin necesaria para dichas asignaturas. Los Fundamentos matemticos de la Informtica, base esencial para los cursos de informtica Aplicada, engloban Matemtica discreta, lgica, lgebra, anlisis y estadstica El lgebra sirve para introducir los conceptos y tcnicas bsicas de trabajo con procesos lineales. Partiendo de conceptos que deberan de ser conocidos, se pasa a introducir los conceptos asociados a los Espacios Vectoriales. Dado que una gran parte de las asignaturas tanto de primer curso como de cursos posteriores usan tcnicas lineales (Codificacin, Criptografa, Optimizacin, Grficos, CAD, etc.) supone una preparacin necesaria para dichas asignaturas.

Subjects

ngulos | ngulos | lgebra Computacional | lgebra Computacional | lgebra Lineal | lgebra Lineal | gidos | gidos | tica | tica | lgebra | lgebra | Distancias | Distancias | Vectores | Vectores | Grafos | Grafos | tica Aplicada | tica Aplicada | Aplicaciones Lineales | Aplicaciones Lineales | Matrices | Matrices

License

http://creativecommons.org/licenses/by-nc-sa/3.0/

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lgebra lgebra

Description

Curso centrado en los fundamentos de los problemas lineales: algebra matricial y espacios vectoriales. Curso centrado en los fundamentos de los problemas lineales: algebra matricial y espacios vectoriales.

Subjects

a Telemtica | a Telemtica | Autovalores y autovectores | Autovalores y autovectores | Espacios vectoriales | Espacios vectoriales | 2009 | 2009 | Matrices | Matrices | nimos cuadrados | nimos cuadrados

License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/

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18.312 Algebraic Combinatorics (MIT)

Description

This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.

Subjects

Rational Generating Functions | Recurrence Relations | Radon Transform | Adjacency and Laplacian Matrices of Graphs

License

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

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18.996 Random Matrix Theory and Its Applications (MIT)

Description

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

Subjects

Random matrix theory | Matrix Jacobians | Wishart Matrices | Wigner's Semi-Circular laws | Matrix beta ensembles | free probability | spherical coordinates | wedging | Plucker coordinates | matrix factorizations | householder transformations | Stiefel manifold | Cauchey-Binet theorem | Telatar's paper | level densities | orthogonal polynomials | matrix integrals | hypergeometric functions | wireless communictions | eigenvalue density | sample covariance matrices | Marcenko-Pastur theorem | wireless communications

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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LGEBRA MATRICIAL (2008)

Description

El lgebra Lineal ha probado ser el lenguaje ms apropiado para el tratamiento moderno de muchas disciplinas. Adems, est presente en diversos pasos clave de los mtodos numricos de solucin aproximada de ecuaciones diferenciales e integrales. El programa comienza con el lgebra Matricial. Se hace especial hincapi en la resolucin de Sistemas Lineales de Ecuaciones Algebraicas y en los problemas prcticos que acarrea la resolucin de grandes sistemas de ecuaciones. Hay que recordar que muchos mtodos numricos dependen fuertemente en su solucin final de alguno de tales sistemas. En diversas asignaturas de la titulacin se pone claramente de manifiesto. Tambin se presentan las Aplicaciones Lineales y la relacin entre matrices y aplicaciones lineales entre espacios

Subjects

MATEMATICA APLICADA | Matrices | aplicaciones lineales | ecuaciones lineales | nimos cuadrados | proyecciones ortogonales | valores y vectores propios

License

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