Mathemaniac Courses

Why All Maps Are Wrong - Theorema Egregium

Explore Theorema Egregium's geometric proof, revealing why no world map can preserve both area and angles. Understand curvature, spherical areas, and the Gauss map in this mathematical journey.

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

Matrix Transpose Isn't Just Swapping Rows and Columns

Explore a unique visualization of matrix transpose, focusing on changing perspective rather than swapping rows and columns. Gain insights into covectors, metric tensors, and adjoints in various fields.

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

Demystifying Spin 1/2 - Math of Quantum Mechanics

Explore the mathematics behind spin 1/2 particles, debunking common misconceptions and providing a clear, visual explanation using the Bloch sphere representation of quantum states.

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

Why You Can't Solve Quintic Equations - Galois Theory Approach

Explore the fascinating world of Galois theory and discover why quintic equations can't be solved using a formula, with insights accessible to math enthusiasts of all levels.

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

Complex Integration, Cauchy and Residue Theorems - Essence of Complex Analysis

Explore complex integration, Cauchy's theorem, and the residue theorem in this intuitive explanation using Pólya vector field. Gain insights into key concepts of complex analysis.

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

What if We Define 1-0 = Infinity - Möbius Transformations Visualized

Explore Möbius transformations and their connection to defining 1/0 = ∞, with insights on circular inversion, Riemann sphere, and applications in geometry and complex analysis.

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

What Do Complex Functions Look Like - Essence of Complex Analysis

Explore complex functions through vivid visualizations, covering addition, multiplication, exponentiation, power functions, and logarithms. Delve into branch cuts, Riemann surfaces, and 4D rotations with engaging animations.

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

What Are Complex Numbers - Essence of Complex Analysis

Comprehensive guide to complex numbers, covering representations, operations, Euler's formula, and de Moivre's theorem. Ideal for beginners and as a refresher for advanced learners.

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

What Is Jacobian - The Right Way of Thinking Derivatives and Integrals

Explore the Jacobian matrix and determinant in multivariable calculus, rethinking derivatives and integrals for a deeper understanding of changing variables in higher dimensions.

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

Dream Cheating Scandal - Explaining All the Math Simply

Comprehensive breakdown of the math behind the Dream cheating scandal, explaining binomial distribution, biases, and statistical analysis for both novices and math enthusiasts.

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

Queuing Theory and Poisson Process

Introduction to M/M/1 queue model and Poisson process, covering fundamental concepts of queuing theory. Explores key principles and applications in simple queuing systems.

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

How Physics Solves Plateau's Problem - Applications in Math and 3D Graphics

Explore how physics and mean curvature flow solve Plateau's problem, with applications in mathematics, soap films, and 3D graphics. Discover connections between minimal surfaces and active research areas.

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

The Clever Way Curvature is Described in Math - Gaussian and Mean Curvatures

Explore Gaussian and mean curvatures in differential geometry, focusing on the shape operator to understand surface curvature and its applications in minimal surfaces.

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

Different Forces, Same Elliptical Orbits - Coincidence? - Hidden Gems #2

Explore the surprising mathematical connection between Newtonian gravity and Hooke's law through their shared elliptical orbits, uncovering Newton's geometric insights.

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

The Hidden Conservation Law of Gravity - Deriving the LRL Vector Using Complex Numbers and Bohlin Transformation

Uncover the mysterious LRL vector in gravity through Bohlin transformation and complex numbers, revealing hidden conservation laws via Arnold-Vasiliev duality and harmonic oscillator analogies.

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