Vector Fields, Divergence, and Curl
Explore vector fields, divergence, and curl in mathematics. Learn about the del operator and its applications with dot and cross products to analyze vector field properties.
Finding Eigenvalues and Eigenvectors
Explore eigenvalues and eigenvectors in linear algebra, their importance in math and physics, and learn how to find them through clear explanations and examples.
Oxford Linear Algebra - How to Find a Matrix Inverse Using Elementary Row Operations
Learn to calculate matrix inverses using Elementary Row Operations (ERO's) with clear explanations and worked examples for 2x2 and 4x4 matrices, including the case of non-invertible matrices.
Linear Algebra - Elementary Row Operations Explained
Comprehensive tutorial on solving linear equations using matrices and elementary row operations, with worked examples and practice resources for self-study.
Finding Opposite Terms in Elimination Method
Learn to solve Systems of Linear Equations using the Elimination Method when opposite terms are not initially provided, enhancing your problem-solving skills.
Learning-Based Low-Rank Approximations - IPAM at UCLA
Explores learning-based algorithms for low-rank matrix approximation, focusing on optimizing sketching matrices using training data to significantly reduce approximation errors in efficient computational methods.
Marie-France Vignéras- Modular Representations of P-Adic Groups
Explore modular representations of p-adic groups in the Langlands program, examining their connections to number theory and geometry using various vector spaces and modules.
The Geometry of Geometries - Matroid Theory, Old and New
Explore matroid theory's origins, connections, and recent geometric advances in combinatorial mathematics, highlighting matroid polytope, Bergman fan, and conormal fan models.
Some Comments on the Fundamental Gap of the Dirichlet Laplacian in Hyperbolic Space
Explore the fundamental gap of convex domains in hyperbolic space, comparing it with Euclidean space and examining different types of convexity in this advanced mathematical analysis.
Differential Geometry - Lecture 1
Explore fundamental concepts and principles of differential geometry in this comprehensive lecture by mathematician Claudio Arezzo.
Noise Sensitivity of the Top Eigenvector of a Wigner Matrix
Explore the noise sensitivity of Wigner matrices' top eigenvectors, delving into random matrix theory and its applications in mathematical physics and data analysis.
A Survey of Volume Inequalities - Basic Notions Seminar - 2019
Explores volume inequalities in Euclidean space, discussing identities and inequalities for convex sets and star-bodies. Covers Gromov's conjecture and is accessible to a general mathematical audience.
Algebraic Geometry - Lecture 10
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
Algebraic Geometry - Lecture 8
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
Algebraic Geometry - Lecture 7
Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
The Non-Commutative Analytic Toeplitz Algebra and Free Semigroup Algebras
Explore non-commutative analytic Toeplitz algebra and free semigroup algebras, covering topics like weak operator topology, functional calculus, and invariant subspaces.
Mini-Course on Truncated Toeplitz Operators - Part 1
Explore truncated toeplitz operators in this comprehensive lecture by Emmanuel Fricain, delving into advanced mathematical concepts and their applications in analytic function spaces.
Linear Matroid Matching in the Oracle Model
Explores linear matroid matching in the oracle model, replacing linear algebraic computation with repeated oracle-calls along alternating paths to solve challenging problems in connectivity, rigidity, and count matroids.
Algebra Review - Part 2
Comprehensive review of advanced algebra concepts, covering exponents, geometry, functions, equations, inequalities, trigonometry, and more. Ideal for strengthening mathematical foundations.
Advanced Engineering Mathematics
Comprehensive exploration of advanced mathematical concepts, including complex analysis, transforms, probability, linear algebra, and more, with applications to engineering problems.
Mathematical Methods and Its Applications
Explore linear differential equations, including solutions for homogeneous and non-homogeneous cases, Wronskian, and Euler-Cauchy equations in this comprehensive mathematical methods course.