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Concept

Dimension

Related lectures (31)

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Bernoulli convolutions: The dimension of Bernoulli convolutions

Explores the dimension of Bernoulli convolutions, discussing fair tosses and polynomial roots.

Dimensional Analysis: Fundamentals and Applications

Covers dimensional analysis fundamentals and applications in scientific and engineering problems, including estimating atom size using Schrödinger's equation.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Chaos Theory: Fractals and Dimensionality

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

Descent methods and line search: Inexact line search MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Explores descent methods, line search, and the importance of small steps.

Computational Thinking Test: Evaluation and Design

Presents a test to evaluate computational thinking skills, discussing its design, analysis of previous tools, sample question, and study results.

Introduction to Structures: Part 2

Introduces subsystems, forces calculation, materials, and dimensioning in structures, emphasizing interactive learning.

Lagrange Method: 2 Constraints

Explains the Lagrange method with 2 constraints and composite functions' derivatives.

Tangent spaces to submanifolds MOOC: Introduction to optimization on smooth manifolds: first order methods

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

Nonlinear Integrate-and-Fire Model MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Explores the Nonlinear Integrate-and-Fire Model, reduction to one dimension, stimulus impact, and sparse activity in vivo.

AutoCAD: Text and Annotations

Explores creating text and annotations in AutoCAD, including managing properties and working with layers.

Finite Dimensional Spaces

Explores finite dimensional spaces, covering extraction process, bases generation, and space completion.

Cosmological Puzzles: Dark Matter and Energy

Explores fundamental cosmological puzzles related to dark matter and energy.

Area: Axioms and Rectangles

Covers the concept of area, axioms, and the area of rectangles.

Dimensional Analysis & Scaling Laws Log in to Mediaspace to watch this video

Explores dimensional analysis, scaling laws, physical similarity, and the interdependency of variables in physical systems.

Dimensional Analysis: Scaling and Theorems Log in to Mediaspace to watch this video

Explores dimensional analysis, scaling, and the Buckingham theorem in analyzing physical systems.

Fractals: Dimensions and Applications Log in to Mediaspace to watch this video

Explores fractals, dimensions, and applications, including mountain formation simulation and landscape authoring through erosion and vegetation interplay.

Projective Varieties: Invariants and Dimensions Log in to Mediaspace to watch this video

Covers invariants and dimensions of projective varieties, emphasizing their importance.

AutoCAD: Orthophotos and Orthoplans Calibration Log in to Mediaspace to watch this video

Covers the calibration of orthophotos and orthoplans in AutoCAD, emphasizing precise modifications and accurate measurements.