Lectures related to Foundations of mathematics

Wiener Filtering: Theory and Applications

Covers the theory and applications of Wiener filtering in signal processing.

Philosophy of Mathematics: Ontology and Structures

Explores the existence of mathematical objects, truth of propositions, and knowledge about them, covering Platonism, Intuitionism, Structuralism, Nominalism, Logicism, and Formalism.

Mathematical Rigor and Course Organization

Emphasizes mathematical rigor, clear communication, and exercise organization in teaching methods.

Sets and Operations: Introduction to Mathematics

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

Continuous-Time Stochastic Processes: Linear System

Covers the analysis of continuous-time stochastic processes in the context of linear systems.

Optimization Methods: Convergence and Trade-offs

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

Generalization in Deep Learning

Explores generalization in deep learning, covering model complexity, implicit bias, and the double descent phenomenon.

Stochastic Gradient Descent: Theory and Applications

Covers the theory and applications of Stochastic Gradient Descent in machine learning models.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Set Theory: Introduction and Operations

Covers the foundation of mathematics through set theory concepts like membership and unions.

Discriminant Analysis: Bayes Rule

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

Wiener Filter for Discrete-Time Stochastic Processes

Covers the theory and application of the Wiener filter for discrete-time stochastic processes.

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.

Lagrange Theorem: Applications and Proofs

Covers the application and proof of the Lagrange theorem in group theory.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Conformal Blocks: Understanding Young Diagrams and Weight States

Covers conformal blocks, Young diagrams, and their significance in weight states.

Advanced Counting: Quiz

Covers advanced counting techniques and includes a quiz session.