Lectures related to Applied mathematics

Mathematics and Computer Science: Bonnie Berger at MIT

Features Bonnie Berger, a professor at MIT, discussing mathematics and computer science.

Delves into the historical challenge of duplicating the cube, exploring construction methods, misattributions, and geometric concepts.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Laplace Transform: Solving Differential Equations

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Diffusion Equations: Green's Function Approach

Covers the analysis and solution of diffusion equations using Green's function approach and discusses boundary conditions and dimensional analysis.

Nonlinear Bourgain's Projection Theorem

Explores a nonlinear version of Bourgain's Projection Theorem and its diverse applications in mathematics.

Optimal Transport: From Theory to Applications

Explores the history, theory, and applications of optimal transport in various fields, showcasing its importance in solving complex mathematical problems.

Nonlinear Equations: Methods and Applications

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Mathematics of Data: From Theory to Computation

Covers key concepts in data mathematics, including automatic differentiation, linear layers, and attention layers.

Introduction to Physics: Scientific Approach and Mathematics

Covers the scientific method, mathematical descriptions, and the role of mathematics in Physics.

Discriminant Analysis: Bayes Rule

Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.

Boundary Problems in 1D: Part 1

Covers the resolution of boundary problems in 1D, focusing on mathematical concepts and equations.

Nonlinear Systems: Equations and Solutions

Explores solving nonlinear systems of equations using Newton's method.

Calculus of Variations: Gradient Young Theorem

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Cauchy Problem: Solutions and Verification

Explores the Cauchy problem, emphasizing solution finding and verification processes.

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Canonical Correlation Analysis

Covers the mathematical development of canonical correlation analysis, including population and sample CCA.

Cauchy-Folgen: Induction

Covers Cauchy sequences, induction, recursive sequences, and convergence in mathematical analysis.