Mathemaniac Courses

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

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

The Gauss-Bonnet Theorem in Differential Geometry - From Intuition to Generalization

Delve into the fundamental Gauss-Bonnet theorem through visual explanations, exploring Gaussian curvature, parallel transport, and geodesics while uncovering its deep connections to differential geometry.

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

The More General Euler Characteristic Formula - Understanding Surface Topology

Explore the deeper implications of Euler's characteristic formula as an inequality, examining its relationship with genus, Morse functions, and topological surfaces through intuitive explanations.

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

Why the 4-Color Theorem is Easier to Prove on a Torus - A Mathematical Analysis

Explore the fascinating proof of why maps on a torus require 7 colors while planar maps need only 4, using clear mathematical reasoning and step-by-step demonstrations of key inequalities.

• YouTube
• 17 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

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

Lie Groups, Algebras, and Brackets - Visual Introduction to Lie Theory

Discover Lie theory through visual intuition, exploring groups, algebras, rotations in higher dimensions, exponentials, matrix operations, and the geometric meaning behind abstract concepts.

• YouTube
• 2 hours 17 minutes
• Self-Paced
• Free Video

Essence of Group Theory

Discover the fundamental concepts of abstract algebra through symmetries, group actions, and key theorems like Lagrange's and orbit-stabilizer in this comprehensive series.

• YouTube
• 1 hour 44 minutes
• Self-Paced
• Free Video

Deep Dive into Combinatorics

Explore advanced combinatorics beyond school curriculum, covering Catalan numbers, their generalizations, and mathematical research thinking processes.

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

Every Power-Law Force Has a Conformal Dual

Explore conformal transformations between power-law forces and discover how any force can be mapped to another (except inverse cube law) through mathematical duality.

• YouTube
• 23 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 Story of "dx" - Essence of Differential Forms #1

Discover the fascinating history behind "dx" and how differential forms revolutionized mathematics and physics through algebraic computations and geometric insights.

• YouTube
• 16 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