3Blue1Brown Courses

Why π Is in the Normal Distribution - Beyond Integral Tricks

Explore the mathematical origins of π in the normal distribution through geometric insights, classic proofs, and the Herschel-Maxwell derivation, offering a deeper understanding beyond integral tricks.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

But What Is the Central Limit Theorem?

Visual exploration of the Central Limit Theorem, explaining its significance in probability and statistics through animations, simulations, and real-world examples.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

But What Is a Convolution?

Explore the concept of convolution in mathematics, from probability to image processing and FFTs, with clear explanations and engaging animations.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Group Theory, Abstraction, and the 196,883-Dimensional Monster

Explore group theory, abstraction, and the fascinating 196,883-dimensional monster group in this engaging introduction to mathematical symmetry and classification.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Why Do Prime Numbers Make These Spirals? - Dirichlet’s Theorem, Pi Approximations, and More

Explore the fascinating patterns of prime numbers in spirals, delving into Dirichlet's theorem, pi approximations, and prime distributions through engaging animations and mathematical insights.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

But What Is a Fourier Series? From Heat Flow to Drawing With Circles

Explore Fourier series through heat flow and circular drawings, understanding complex mathematical concepts with engaging animations and clear explanations.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Differential Equations, a Tourist's Guide

Explore ordinary differential equations through intuitive visualizations, covering concepts like vector fields, phase spaces, and real-world applications in physics and social dynamics.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Winding Numbers and Domain Coloring

Explore winding numbers and domain coloring to solve 2D equations numerically. Learn about graphing techniques, color mapping, and applications in complex analysis.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Gradient Descent, How Neural Networks Learn

Explore gradient descent and neural network learning through animations, examples, and expert insights. Gain a deeper understanding of cost functions, network analysis, and cutting-edge research in machine learning.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Taylor Series

Explore the power of Taylor polynomials for approximations and analysis, covering cos(x), e^x, geometric interpretations, and convergence issues in this animated math lesson.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Integration and the Fundamental Theorem of Calculus

Explore intuitive explanations of integrals and their relationship to derivatives, using animated visuals to demystify the fundamental theorem of calculus and its real-world applications.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Euler's Formula with Introductory Group Theory

Intuitive exploration of Euler's formula using group theory concepts, providing a fresh perspective on the relationship between exponentials, complex numbers, and rotations.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Fractals Are Typically Not Self-Similar

Explore fractal dimension, self-similarity, and scaling in this engaging explanation that challenges common misconceptions about fractals and their properties.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Visualizing the Riemann Zeta Function and Analytic Continuation

Explore the Riemann zeta function's visualization, analytic continuation, and its connection to the famous Riemann hypothesis through engaging animations and clear explanations.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

The Medical Test Paradox and Redesigning Bayes' Rule

Explore the medical test paradox and a redesigned Bayes' rule, focusing on likelihood ratios and Bayes factors to enhance understanding of conditional probability in diagnostic testing.

• YouTube
• 21 minutes
• Self-Paced
• Free Video