3Blue1Brown Courses

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

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 How Does Bitcoin Actually Work?

Explore the mathematical foundations of cryptocurrencies, including digital signatures, decentralization, cryptographic hash functions, and blockchain technology in this informative video.

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

Olympiad Level Counting - How Many Subsets of {1,…,2000} Have a Sum Divisible by 5?

Explore advanced counting techniques using generating functions and complex numbers to solve a challenging subset sum problem, with applications to Olympiad-level mathematics.

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

Solving Wordle Using Information Theory

Explore information theory and entropy through the lens of solving Wordle, learning strategies to optimize guesses and improve game performance.

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

Alice, Bob, and the Average Shadow of a Cube

Explore problem-solving approaches to calculate a cube's average shadow area, comparing two methods and their implications for understanding geometric principles.

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

Beyond the Mandelbrot Set - An Intro to Holomorphic Dynamics

Explore holomorphic dynamics, iterative complex functions, and fractals. Delve into Mandelbrot sets, fixed points, cycles, and Julia sets for a fascinating journey through mathematical visualization.

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

Newton's Method Produces This Fractal, Why Don't We Teach It in Calculus Classes?

Explore the fascinating fractal produced by Newton's method for finding roots of polynomials, revealing unexpected complexity in a seemingly simple mathematical technique.

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

How -and Why- to Raise e to the Power of a Matrix

Explore matrix exponentiation through engaging examples, from love dynamics to quantum mechanics, with clear animations and intuitive explanations of complex mathematical concepts.

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