Lectures related to Computational Thinking Test: Evaluation and Design

Textual Data Analysis: Classification & Dimensionality Reduction

Explores textual data classification, focusing on methods like Naive Bayes and dimensionality reduction techniques like Principal Component Analysis.

Nearest Neighbor Classifier: Curse of Dimensionality

Explores the nearest neighbor classifier method, discussing its limitations in high-dimensional spaces and the importance of spatial correlation for effective predictions.

Decomposition into Line Metrics: Example and Outlook

Covers the decomposition into line metrics, providing examples and discussing its implications.

Threshold Functions in Neural Networks

Explores threshold functions in neural networks for classifying data points based on positive and negative values.

Tori: Character Forms and Monomials

Explores Tori in algebraic geometry, emphasizing character forms and monomials.

Curse of Dimensionality in Deep Learning

Delves into the challenges of deep learning, exploring dimensionality, performance, and overfitting phenomena in neural networks.

Kernel Regression: Basics and Applications

Explores kernel regression, the curse of dimensionality, and random features in neural networks.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.

Scalar, Vector or Tensor? Gravity

Discusses defining tensors, space-time dimensionality, and challenges in formulating a relativistic theory of gravity.

Chaos Theory: Fractals and Dimensionality

Explores chaotic systems, fractals, and dimensions in Chaos Theory.

Kernel Methods: Efficient Dot Product Computation

Demonstrates efficient dot product computation and introduces nonlinear boundaries in the original space.

Visualizing the Fourth Dimension: A Mathematical Journey

Explores visualizing the Fourth Dimension through points, lines, circles, spheres, and punching through, covering vector space properties, dimensionality, bases, and theorems.

Unsupervised Learning: Clustering Methods

Covers unsupervised learning focusing on clustering methods and the challenges faced in clustering algorithms like K-means and DBSCAN.

Deep Learning: Dimensionality and Data Representation

Delves into deep learning's dimensionality, data representation, and performance in classifying large-dimensional data, exploring the curse of dimensionality and the neural tangent kernel.

Unsupervised Learning: Principal Component Analysis

Covers unsupervised learning with a focus on Principal Component Analysis and the Singular Value Decomposition.

Tangent spaces to submanifolds

Introduces tangent spaces to submanifolds and their properties in optimization on manifolds.

Convolutional Neural Networks: Filters and Channels

Explores weight sharing, filters, channels, and data augmentation in convolutional neural networks.

Tensor Spaces and Unitary Representations

Explores tensor spaces, unitary representations, and prime factorization in mathematical presentations.

Linear Classification: Logistic Regression

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

The Coordinate Ring of a Linearly Reductive Group

Covers the properties of the coordinate ring of a linearly reductive group.