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Abstract Algebra

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Explore fundamental concepts of abstract algebra, including sets, relations, operations, groups, and advanced topics like homomorphisms, cosets, and group actions.
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71 Lesons
10 hours
On-Demand
Free-Video
Kimberly Brehm

Abstract Algebra

1 rewiews
Comprehensive introduction to abstract algebra, covering symmetries, groups, isomorphisms, and more. Follows Gallian's text with accompanying slide decks for in-depth understanding.
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10 Lesons
2 hours 30 minutes
On-Demand
Free-Video

Abstract Algebra

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Explore fundamental concepts of abstract algebra, including groups, rings, fields, and vector spaces, with a focus on definitions, examples, and key theorems.
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33 Lesons
3 hours 30 minutes
On-Demand
Free-Video
NPTEL

Coding Theory

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This course provides an introduction to traditional and modern coding theory. Topics covered include linear block codes, cyclic codes (BCH and RS codes), convolutional codes, turbo codes and low-density parity-check (LDPC) codes.
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38 Lesons
1 day 13 hours
On-Demand
Free-Video
NPTEL

Modern Algebra

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Explore fundamental concepts and advanced topics in modern algebra through a comprehensive series of lectures by Prof. Manindra Agrawal, covering key principles and applications.
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19 Lesons
14 hours
On-Demand
Free-Video
NPTEL

Algebra 1

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Foundational PG level course in Algebra, suitable for M.Sc and first-year Ph.D. students in Mathematics. Learn Permutations. Group Axioms. Order and Conjugacy. Subgroups. Problem solving. Group Actions. Cosets. Group Homomorphisms. Normal subgroups. Quti…
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84 Lesons
1 day 11 hours
On-Demand
Free-Video
NPTEL

Computational Commutative Algebra

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This is an introductory course in computational commutative algebra. Topics in a typical first course in commutative algebra are developed along with computations in Macaulay2. The emphasis will be on concrete computations, more than on giving complete p…
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61 Lesons
1 day 7 hours
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Polynomial Bogolyubov-Type Result for the Special Linear Group

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Explore a mathematical lecture on a polynomial Bogolyubov-type result for the special linear group. Delve into the analogy between subset properties in finite dimensional vector spaces and the special linear group over a finite field. Learn about the ach…
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
GOTO Conferences

Computation as Semigroups, Computing Semigroups

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Explore the intersection of semigroups, computation, and functional programming. Gain insights into mathematical foundations of software engineering from a unique perspective.
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1 Lesons
26 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

The Weil Conjectures and A1-homotopy Theory

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Dive into the Weil Conjectures and A1-homotopy theory, exploring connections between algebraic topology and finite field equations in this mathematical colloquium.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

Representations of Reductive Groups Over Local and Global Fields

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Dive into Langlands' theory of reductive groups and their representations in number theory, exploring local and global fields and their connections to arithmetic and geometry.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video

Abstract Algebra - Polynomial Rings

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Explora el álgebra abstracta con enfoque en anillos polinomiales, algoritmo de división, polinomios irreducibles y criterio de Eisenstein.
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8 Lesons
2 hours 30 minutes
On-Demand
Free-Video

Assorted Group Theory

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Explore the fascinating world of group theory, delving into complex orders and the intriguing connections between abstract algebra and geometric shapes.
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2 Lesons
30 minutes
On-Demand
Free-Video

Abstract Algebra Integral Domains

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Explore advanced concepts in integral domains, including fractions, primes, factorization, and various domain types. Gain deep insights into abstract algebra principles and their applications.
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11 Lesons
4 hours 30 minutes
On-Demand
Free-Video
Dr. Gajendra Purohit

Group Theory

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Comprehensive exploration of group theory, covering key concepts from basic definitions to advanced topics like Sylow theorems, ideal for mathematics and engineering students.
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62 Lesons
20 hours
On-Demand
Free-Video

Special Topics in Linear Algebra

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Explore advanced linear algebra topics including least squares approximation, error-correcting codes, functional calculus, affine transformations, stochastic maps, and C*-algebras.
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28 Lesons
5 hours
On-Demand
Free-Video
Ross Dynamics Lab

Poisson Brackets, Non-Canonical Hamiltonian Systems and Euler's Rigid Body Equations

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Explore Poisson brackets, non-canonical Hamiltonian systems, and Euler's rigid body equations in this advanced dynamics lecture. Gain insights into abstract algebra, Lie algebra, and their applications in physics and mechanics.
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10 Lesons
1 hour 11 minutes
On-Demand
Free-Video
3Blue1Brown

Group Theory, Abstraction, and the 196,883-Dimensional Monster

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Explore group theory, abstraction, and the fascinating 196,883-dimensional monster group in this engaging introduction to mathematical symmetry and classification.
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6 Lesons
22 minutes
On-Demand
Free-Video
Institute for Advanced Study

Associativity Testing - Ben Green

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Explore associativity testing in discrete mathematics, covering key concepts, theorems, and applications in group theory and additive combinatorics.
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11 Lesons
58 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Substitutions in Non-Commutative Multivariate Power Series

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Explore group laws on non-commutative formal power series, their structures, and applications in non-commutative probability theory through a Hopf algebraic approach.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Hidden Symmetries of the Work of Jan Nekovář

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Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

A Álgebra de Nós

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Explore a fascinante álgebra de nós com o pesquisador Jethro van Ekeren. Descubra como essa área da matemática conecta topologia e álgebra, revelando insights surpreendentes sobre estruturas geométricas.
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1 Lesons
41 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 15

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Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 47 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 14

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Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves em uma aula avançada de doutorado, explorando conceitos complexos e teoremas fundamentais da área.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 08

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Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 55 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 07

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 06

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 05

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves em uma aula avançada de doutorado, explorando conceitos complexos e teoremas fundamentais da área.
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1 Lesons
2 hours
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 19

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 18

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Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 59 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 17

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Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 56 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Equações de Grau Cinco

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Explore a complexidade das equações de grau cinco e suas soluções, aprofundando-se em conceitos matemáticos avançados e suas implicações teóricas.
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1 Lesons
40 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 11

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 10

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves em uma aula avançada de doutorado, explorando conceitos complexos e teoremas fundamentais da área.
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1 Lesons
2 hours
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 09

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 56 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 13

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves em uma aula avançada de doutorado, explorando conceitos complexos e teoremas fundamentais da área.
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1 Lesons
2 hours 1 minute
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 12

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Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Helly Graphs and Injective Metric Spaces - Part I

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Explorez les graphes de Helly et les espaces métriques injectifs : définitions, propriétés et exemples. Découvrez leurs caractéristiques non positives et leurs liens avec divers groupes géométriques.
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1 Lesons
46 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Universal K-matrix and Fused K-operators in Quantum Affine Algebras

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Explore universal K-matrices and fused K-operators in quantum algebras. Delve into the construction of transfer matrices and their applications to open spin-chains.
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1 Lesons
25 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 3

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Explore semisimple braided tensor categories, their structure, and classification. Delve into centralizers, non-degeneracy, equivariantizations, and the core of braided fusion categories.
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1 Lesons
53 minutes
On-Demand
Free-Video
CIMPA UCR

Contando Cuerpos de Números Algebraicos

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Explora la teoría de cuerpos de números algebraicos y sus aplicaciones en matemáticas avanzadas. Profundiza en conceptos fundamentales y técnicas de conteo.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Méthodes Galoisiennes Appliquées aux Équations Fonctionnelles

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Explorez les méthodes galoisiennes appliquées aux équations fonctionnelles en mathématiques avancées. Approfondissez vos connaissances avec cette conférence spécialisée du CIRM.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Le dernier théorème de Fermat

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Plongez dans l'histoire fascinante et la résolution du célèbre théorème de Fermat, un défi mathématique qui a intrigué les esprits pendant plus de trois siècles.
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1 Lesons
48 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

A Quick and Partial Survey on the Complexity of Query Answering

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Explore the complexity of query answering in this survey, covering key concepts and recent developments in discrete mathematics and logic.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Algebraic Attacks for the Rank Decoding Problem - Lecture 1

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Explorez les attaques algébriques pour le problème du décodage de rang dans cette conférence mathématique approfondie, mettant l'accent sur les concepts clés et les techniques avancées.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Actions on the Real Line of Some Finitely Generated Groups

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Explore finitely generated groups' actions on the real line, focusing on mathematical concepts and theories presented by Nicolás Matte Bon in this advanced mathematics conference talk.
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1 Lesons
53 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 04

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 56 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 03

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações práticas nesta aula de doutorado do IMPA.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 02

0 rewiews
Aprofunde-se na Álgebra Comutativa com o Professor Eduardo Esteves, explorando conceitos avançados e aplicações em nível de doutorado.
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1 Lesons
1 hour 59 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Doutorado: Álgebra Comutativa - Aula 01

0 rewiews
Explore os fundamentos da Álgebra Comutativa em nível de doutorado com o Professor Eduardo Esteves, abordando conceitos avançados e teorias essenciais para pesquisadores em matemática pura.
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1 Lesons
2 hours 2 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 18

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Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática e suas aplicações.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 17

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Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática com o Professor Jethro Van Ekeren.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 26

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Explore advanced concepts in Lie Algebras, focusing on doctoral-level topics and theoretical foundations in this comprehensive lecture by Jethro Van Ekeren.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Álgebra II - Aula 23

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Aprofunde-se na Álgebra II com a Profa. Carolina Araujo, explorando conceitos avançados e aplicações práticas em uma aula abrangente do programa de mestrado do IMPA.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 25

0 rewiews
Explore conceitos avançados de Álgebras de Lie em uma aula de doutorado ministrada por Jethro Van Ekeren, aprofundando o conhecimento em matemática pura.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Álgebra II - Aula 22

0 rewiews
Aprofunde-se na Álgebra II com a Profa. Carolina Araujo, explorando conceitos avançados e aplicações práticas em uma aula magistral do programa de mestrado do IMPA.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Álgebra II - Aula 21

0 rewiews
Aprofunde-se em conceitos avançados de Álgebra II com a Profa. Carolina Araujo nesta aula de mestrado do IMPA, explorando tópicos complexos e aprimorando seu conhecimento matemático.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Álgebra II - Aula 20

0 rewiews
Aprofunde-se na Álgebra II com a Profa. Carolina Araujo, explorando conceitos avançados e aplicações práticas em uma aula abrangente do programa de mestrado do IMPA.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 22

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Explore advanced concepts in Lie Algebras, focusing on doctoral-level topics and theoretical foundations in this comprehensive lecture by Jethro Van Ekeren.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Álgebra II - Aula 19

0 rewiews
Aprofunde-se na Álgebra II com a Profa. Carolina Araujo, explorando conceitos avançados e aplicações práticas em uma aula magistral do programa de mestrado do IMPA.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 20

0 rewiews
Explore conceitos avançados de Álgebras de Lie em uma aula de doutorado ministrada por Jethro Van Ekeren, aprofundando o conhecimento em matemática pura.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 19

0 rewiews
Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática com o Professor Jethro Van Ekeren.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Álgebra II - Aula 18

0 rewiews
Aprofunde-se na Álgebra II com a Profa. Carolina Araujo, explorando conceitos avançados e aplicações práticas em uma aula abrangente do programa de mestrado do IMPA.
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1 Lesons
1 hour 42 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Sharp Fourier Restriction Theory Over Finite Fields

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Explore recent developments in sharp Fourier restriction theory over finite fields, examining the intersection of two key areas in mathematical research.
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1 Lesons
52 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On the Fourier Weight of F2 Polynomials

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Explore Fourier weight of F2 polynomials, focusing on level k and degree d relationships. Gain insights into pseudorandom generators and recent mathematical proofs.
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1 Lesons
36 minutes
On-Demand
Free-Video
Institute for Advanced Study

Sheaves on Graphs, the Hanna Neumann Conjecture, and Algebraic Geometry Applications

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Explore advanced graph theory concepts through sheaf theory and the Hanna Neumann conjecture, featuring innovative problem-solving approaches and applications in discrete mathematics.
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1 Lesons
2 hours 6 minutes
On-Demand
Free-Video
BunG Seminar

Algebraic D-Modules: A Basic Review - Talk 12

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Dive into the fundamentals of algebraic D-modules through a comprehensive review based on J. Bernstein's notes, exploring key concepts and theoretical foundations.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
BunG Seminar

The Stacks of n-Truncated Barsotti-Tate Groups - Part 2

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Delve into advanced algebraic geometry concepts, focusing on n-truncated Barsotti-Tate groups and n-smooth group schemes over F_p-algebras, with emphasis on their structural properties and relationships.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Class Field Theory Standpoint and Its Three Fundamental Generalisations - Lecture 2

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Delve into advanced class field theory concepts, exploring Takagi's existence theory, Mochizuki's IUT theory, and modern perspectives on Langlands program and anabelian geometry.
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1 Lesons
2 hours 2 minutes
On-Demand
Free-Video
Freya Holmér

Math for Game Devs - Abstract Algebra, Procedural Animation & Splines

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Explore advanced math concepts for game development, including abstract algebra, procedural animation, and splines. Learn about complex numbers, quaternions, and geometric algebra for enhanced game design and animation techniques.
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24 Lesons
3 hours 47 minutes
On-Demand
Free-Video
TheIACR

Cryptanalysis 2

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Explore cryptanalysis techniques, focusing on discrete logarithm problems in finite fields. Learn about L notation, historical developments, and computational complexity.
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14 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Differential Geometry With Finite Fields - Differential Geometry

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Exploring differential geometry in finite fields, introducing arithmetic in prime fields, polynomial operations, and tangent conics to cubics. Highlights unique patterns and combinatorial structures in finite calculus.
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11 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

Infinitesimal Calculus with Finite Fields - Famous Math Problems

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Explore infinitesimal calculus in finite fields through the semi-cubical parabola over F_7, challenging traditional real number analysis and emphasizing polynumbers and de Casteljau Bezier curves.
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9 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

How to Construct the True Complex Numbers I - Famous Math Problems

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Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.
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8 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

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Exploring finite field geometry: isometries, rotations, and reflections on the projective line, revealing connections to relativistic geometry and offering a new perspective on Euclidean concepts.
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8 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Ptolemy's Theorem and Generalizations - Rational Geometry Math Foundations

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Explores Ptolemy's theorem in rational geometry, extending it to finite fields and relativistic planar geometry. Demonstrates how classical results can yield broader insights when formulated without infinite processes.
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9 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

Bases and Dimension for Integral Linear Spaces - Abstract Algebra Math Foundations

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Explore spanning sets, bases, and dimensions in integral linear spaces. Learn convenient notations for vexels and discover a multiset-oriented approach to mathematical structures.
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6 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

An Introduction to Abstract Algebra - Abstract Algebra Math Foundations

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Explore fundamental algebraic structures like groups, rings, fields, and vector spaces through intuitive examples, providing a bird's-eye view of abstract algebra's foundational concepts.
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5 Lesons
26 minutes
On-Demand
Free-Video
Ryan O'Donnell

Polynomials

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Explore polynomials, from formal definitions to applications in finite fields, interpolation, and error-correcting codes for noisy communication channels.
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17 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Insights into Mathematics

An Informal Introduction to Abstract Algebra

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Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.
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12 Lesons
49 minutes
On-Demand
Free-Video
Simons Institute

Randomness in Number Theory

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Explore randomness in number theory, covering topics like finite fields, graphs, quantum gates, and the Riemann Hypothesis with Princeton's Peter Sarnak.
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11 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Michael Penn

Lots of Group Isomorphism Examples

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Explore group homomorphisms and isomorphisms through practical examples, applying the first isomorphism theorem to deepen understanding of abstract algebra concepts.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Michael Penn

What Is It Like to Be a Pure Mathematician?

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Explore the life of a pure mathematician, delving into abstract algebra, group theory, and partitions. Gain insights into the field's challenges, problem-solving approaches, and the beauty of elegant proofs.
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17 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Every PID is a UFD

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Explore the connection between principal ideal domains and unique factorization domains, introducing key concepts like ascending chain condition and Noetherian rings.
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1 Lesons
26 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - The Field of Fractions of an Integral Domain

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Explore the concept of field fractions in integral domains, with examples and proofs demonstrating the construction of the smallest containing field.
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1 Lesons
30 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Eisenstein's Criterion

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Proof and examples of Eisenstein's criterion in abstract algebra, demonstrating its application in determining polynomial irreducibility over rational numbers.
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1 Lesons
23 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - The Division Algorithm for Polynomials

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Explore the division algorithm for polynomials over a field, including its statement and proof, in this concise abstract algebra lesson.
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1 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Polynomial Rings

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Explore polynomial rings, their properties, and key theorems, including the proof that R[x] is an integral domain when R is one.
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1 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - More Ring Theory Examples

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Explore advanced ring theory concepts, including ideals and homomorphisms in matrix and polynomial rings, with in-depth examples and proofs.
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1 Lesons
40 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Properties and Examples of Ring Homomorphisms

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Explore ring homomorphisms' properties and examples, including proofs and comparisons of isomorphic groups versus rings in abstract algebra.
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5 Lesons
24 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Ring Homomorphisms

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Explore ring homomorphisms in abstract algebra, including definitions, examples, and key properties like multiplicative behavior and kernels.
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7 Lesons
20 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Units and Zero Divisors of a Ring

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Explore units and zero divisors in Zn and 2x2 real matrices, classifying elements and proving key properties in abstract algebra.
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7 Lesons
23 minutes
On-Demand
Free-Video
Michael Penn

Representations of Finite Groups - A Few More Common Examples

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Explore representations of finite groups including cyclic, dihedral, quaternions, and symmetric groups. Gain insights into advanced abstract algebra concepts and their applications.
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1 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Ideals of Quotients of PIDs

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Explore the proof that ideals in quotients of principal ideal domains are principal, delving into the intricacies of abstract algebra and ring theory.
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1 Lesons
24 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - A PID That Is Not a Euclidean Domain

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Explore a principal ideal domain that's not Euclidean, using Dedekind-Hasse Norm and universal side divisor concepts to demonstrate this intriguing algebraic property.
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1 Lesons
37 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - If D is a UFD then D[x] is a UFD

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Explore the proof that polynomial rings over unique factorization domains are also UFDs, covering key concepts like Gauss' lemma and polynomial factorization in integral domains.
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6 Lesons
26 minutes
On-Demand
Free-Video
Michael Penn

No Simple Groups of Order 66 or 144

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Explore advanced group theory using Sylow's Theorems to prove the non-existence of simple groups with specific orders, demonstrating powerful algebraic techniques.
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1 Lesons
29 minutes
On-Demand
Free-Video
Michael Penn

Some Important Facts About Congruence Modulo N

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Explore key properties of congruence modulo n, a fundamental equivalence relation in number theory. Learn arithmetic properties and computational techniques for this important concept.
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5 Lesons
25 minutes
On-Demand
Free-Video
Michael Penn

The Number Theory You Need to Learn Abstract Algebra

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Explore essential number theory concepts like division algorithm, Euclidean algorithm, and congruence modulo n, laying the foundation for abstract algebra studies.
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6 Lesons
44 minutes
On-Demand
Free-Video
IMSA

Braids and Configuration Spaces

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Explore topology, homotopy, and braid groups in this talk on configuration spaces. Discover connections between fundamental groups, loop spaces, and unordered configurations in mathematics.
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19 Lesons
56 minutes
On-Demand
Free-Video