Lectures related to Mathematics and Computer Science: Bonnie Berger at MIT

Optimal Linear Response: Stochastic Dynamical Systems

Explores optimal linear response for stochastic dynamical systems, addressing perturbations and mixing rate optimization.

Optimization Methods: Convergence and Trade-offs

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

NumPy Arrays and Graphical Representations: Introduction

Covers NumPy arrays and their graphical representations using Matplotlib, focusing on array creation, manipulation, and visualization techniques.

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.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Primal-dual Optimization: Extra-Gradient Method

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

Discriminant Analysis: Bayes Rule

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

Principal Components: Properties & Applications

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

Multiple Integrals: Techniques and Properties

Explores multiple integrals, techniques, properties, and center of gravity calculation in various domains.

Duplication of the Cube

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

Copulas: Properties and Applications

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

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.

Nonlinear Systems: Equations and Solutions

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

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Volume Calculation: Two Cylinders Interaction

Explains the volume calculation by intersecting two cylinders using coordinates and integrals.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Cauchy-Folgen: Induction

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

The Fourth Pillar of Culture: Informatics

Explores informatics as the fourth pillar of culture, its evolution, integration into society, and applications in modern physics and mathematics.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.