The Number `E' by Tanvi Jain
Explore the mathematical constant 'e', its history, applications in compound interest, logarithms, calculus, and complex numbers. Discover its irrationality and significance in various mathematical contexts.
Beyond Lazy Training for Over-parameterized Tensor Decomposition
Explore over-parameterization in tensor decomposition, comparing lazy training and gradient descent approaches. Discover how gradient descent can leverage low-rank data structure beyond lazy training regimes.
Matroid Tautological Classes in Types A and B
Explore matroid tautological classes in Types A and B, covering definitions, examples, applications, and connections to root systems and Hodge theory.
On Conjugacy of Cartan Subalgebras in Extended Affine Lie Algebras and Classification of Torsors
Explore advanced concepts in extended affine Lie algebras and torsors over Laurent polynomial rings in this mathematical lecture by Vladimir Chernousov at the Fields Institute.
Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary
Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.
Symmetry, Almost
Explore the beauty of mathematical symmetry and its imperfections, focusing on modular forms and their variants. Discover how altering symmetries can reveal new insights and unexpected beauty.
Introduction to Frames and Riesz Bases - Part 1
Explore key concepts of frames and Riesz bases in functional analysis, including characterizations, properties, and applications like Sigma-Delta quantization.
Oriented Cayley Graphs
Explore oriented Cayley graphs, quantum walks, and association schemes. Discover applications in algebraic graph theory and quantum information, with insights on special eigenvalues and Galois groups.
Eigenvalue Gaps and Continuous Walks
Explore eigenvalue gaps, continuous walks, and perfect state transfer in algebraic graph theory, with applications to quantum information and oriented graphs.
Breakthroughs - A Refined Laser Method and Faster Matrix Multiplication
Explore advanced techniques in matrix multiplication, including the refined Laser method, to enhance computational efficiency and speed in mathematical operations.
Why Study Fluid Mechanics?
Explore the importance and applications of fluid mechanics in this engaging lecture by Rama Govindarajan, offering insights into this fundamental field of physics and engineering.
Homological Algebra for Persistence Modules
Introduction to persistence modules in algebraic topology, exploring tensor products, Hom operations, and their role in homological algebra. Insights into preserving exact sequences and advanced concepts.
Linear Obstacles in Linear Systems and Ways to Avoid Them
Explore topology in control theory, focusing on obstacle-avoiding paths and cohomology rings using homotopy limits. Gain insights into theoretical computer science applications.
Smoothed Analysis for Tensor Decompositions and Unsupervised Learning
Explore smoothed analysis for tensor decompositions and unsupervised learning, focusing on polynomial time guarantees and robust decompositions of symmetric overcomplete tensors.
Coassociative Fibrations in G2 Geometry
Explore G2 geometry in 7D spaces, focusing on coassociative submanifolds. Learn about their properties, deformation theory, and constructions forming fibrations with singular fibers in 7-manifolds.
Topological Recursion, Virasoro-W-Algebra Constraints, and Kontsevich-Soibelman
Explore Virasoro and W-algebra constraints in topological recursion, Kontsevich-Soibelman operators, and their connection to Conformal Field Theory in this advanced mathematics lecture.
Blow Up Formulae and Invariants II - Dimension Theory
Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.
Calculus 3 Lecture - The Cross Product
Explore vector cross products, determinants, orthogonal vectors, torque, and geometric applications. Master advanced calculus concepts with in-depth proofs and practical examples.
Calculus 3 - Using the Dot Product
Explore vector operations, angles, projections, and applications in physics using dot product. Master key concepts for advanced vector analysis and problem-solving in multivariable calculus.
Calculus 3 - An Introduction to Vectors
Discover vector operations, including addition, subtraction, position vectors, unit vectors, and magnitude. Gain a solid foundation in vector mathematics for advanced calculus applications.
Calculus 3 - Vectors in 3-D Coordinate System
Explore 3-D coordinate systems, position vectors, magnitude, and unit vectors. Master point relationships in three-dimensional space for advanced mathematical understanding.