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Concept

Foundations of mathematics

Related lectures (28)

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.

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.

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.

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.

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.

Primal-dual Optimization: Extra-Gradient Method

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

Real Numbers: Sets and Operations

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Programming Thymio with Aseba Studio MOOC: The Thymio robot as a tool for discovering digital science

Demonstrates students using Aseba Studio to learn programming basics and computational thinking through math-related activities.

Mathematics of Data: Optimization Basics

Covers optimization basics, including metrics, norms, convexity, gradients, and logistic regression, with a focus on strong convexity and convergence rates.

Copulas: Properties and Applications

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