Lectures related to Linear Classification: Variants and Stochastic Gradient Descent

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Neural Networks: Multilayer Learning

Covers the fundamentals of multilayer neural networks and deep learning, including back-propagation and network architectures like LeNet, AlexNet, and VGG-16.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Multiclass Classification

Covers the concept of multiclass classification and the challenges of linearly separating data with multiple classes.

Differential Functions: Definitions and Notations

Covers the definition of differentiable functions and introduces the concept of differential functions.

Vertical Metronome: Equilibrium and Stability

Explores equilibrium and stability of a vertical metronome system with springs.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Linear Classification: Logistic Regression

Covers linear classification using logistic regression, regularization, and multiclass classification.

Logistic Regression: Fundamentals and Applications

Explores logistic regression fundamentals, including cost functions, regularization, and classification boundaries, with practical examples using scikit-learn.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Multilayer Neural Networks: Deep Learning

Covers the fundamentals of multilayer neural networks and deep learning.

Machine Learning Fundamentals

Introduces fundamental machine learning concepts, covering regression, classification, dimensionality reduction, and deep generative models.

Linear Binary Classification: Perceptron, SGD, Fisher's LDA

Covers the Perceptron model, SGD, and Fisher's Linear Discriminant in binary classification.

Classification Algorithms: Generative and Discriminative Approaches

Explores generative and discriminative classification algorithms, emphasizing their applications and differences in machine learning tasks.

Fluid Friction Forces

Explores fluid friction forces, including laminar and turbulent flow, viscosity, and terminal velocity calculation.

Mathematical Complements: df or δf, Consequences

Explores the consequences of exact differential forms and necessary conditions for total exact differentials, using examples from mountain hiking.