Mathemaniac Courses

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

Matrix Transpose Isn't Just Swapping Rows and Columns

Visualize matrix transpose as a change of perspective that preserves measurements through covectors.

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

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

See why quintic equations lack a general formula through an intuitive tour of Galois groups, field extensions, and solvability.

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

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

An intuitive crash course on complex integration that builds from Pólya vector fields to Cauchy’s theorem, the Cauchy integral formula, and the residue theorem.

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

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

Visualize why defining 1/0 = ∞ becomes natural on the Riemann sphere through Möbius transformations and inversion.

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

What Do Complex Functions Look Like - Essence of Complex Analysis

Visualize complex functions through animated plots, branch cuts, roots, logarithms, and four-dimensional rotations of Riemann surfaces.

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

What Are Complex Numbers - Essence of Complex Analysis

A crash course in complex numbers, from Cartesian and polar representations through Euler’s formula, arithmetic operations, exponentiation, and de Moivre’s theorem.

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

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

Builds intuition for the Jacobian matrix and determinant by reframing derivatives as local linear maps and explaining their role in changing variables.

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

Exponentiating Vectors, Derivatives, and Vector Fields - Mathematical Concepts Explained

Explore the concept of exponentiation applied to vectors, derivatives, and vector fields, uncovering connections between seemingly different mathematical ideas and their practical applications.

• YouTube
• 30 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

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

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

The Action Principle Explained: Finding Satisfaction in Physics

Delve into the action principle in physics, exploring why this seemingly arbitrary quantity should be minimized and discovering a more intuitive understanding of this fundamental concept.

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