Quaternion Courses and Certifications

3Blue1Brown

Visualizing Quaternions - 4D Numbers With Stereographic Projection

Explore 4D quaternions through stereographic projection, visualizing complex mathematical concepts in 3D space and understanding their geometric implications.

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

Institut des Hautes Etudes Scientifiques (IHES)

Quaternion Kähler Manifolds of Non-Negative Sectional Curvature

Explore quaternion Kähler manifolds with non-negative sectional curvature and their geometric properties, including the LeBrun-Salamon conjecture and connections to symmetric spaces.

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

TheIACR

Quantum Money from Quaternion Algebras

Explore quantum money concepts derived from quaternion algebras in this advanced cryptography session from MathCrypt 2022.

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

Navigation Technology and Application: Advanced Algorithm Implementation

Master inertial and integrated navigation algorithms through simulations, open-source code, and real cases covering UAVs, UUVs, vehicles, and airdrop systems.

• XuetangX
• Self-Paced
• Free Online Course

3Blue1Brown

Imaginary Interest Rates - Lockdown Live Math

Explore compound interest, e, and their relation to circles in this engaging mathematical journey, connecting complex concepts to real-world applications like springs and rotations.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems

Explore complex numbers and their connection to plane rotations, laying the groundwork for understanding quaternions and 3D rotations. Emphasizes a logical, algebraic approach without relying on transcendental functions.

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

Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Part 2 - Famous Math Problems 13b

Explore 3D rotations, their composition, and algebraic representation. Learn about Euler's theorem, vector operations, and the foundations for understanding quaternions in graphics and rocket science.

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

Michael Penn

The Only Real Cross Product is Three-Dimensional

Explore the unique properties of 3D cross products, their mathematical significance, and why they don't exist in other dimensions. Gain insights into vector algebra and spatial geometry.

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

Insights into Mathematics

The Geometry of the Dihedrons and Quaternions - Famous Math Problems

Explore the geometry of Dihedrons and Quaternions, comparing their properties and connections to relativity, linear algebra, and complex numbers. Gain insights into fundamental mathematical structures.

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

Insights into Mathematics

Hypercomplex Numbers - Math History - NJ Wildberger

Explore hypercomplex numbers, their historical development, and connections to geometry and number theory. Discover quaternions, octonians, and their surprising links to ancient mathematical formulas.

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

Freya Holmér

Math for Game Devs - Abstract Algebra, Procedural Animation & Splines

Explore advanced math concepts for game development, including abstract algebra, procedural animation, and splines. Learn about complex numbers, quaternions, and geometric algebra for enhanced game design and animation techniques.

• YouTube
• 3 hours 47 minutes
• Self-Paced
• Free Video

Paul McWhorter

Axis IMU- Visualizing 3D Rotations in Vpython Using Quaternions

Visualize 3D rotations using quaternions in Vpython. Learn to simulate rigid body movements, integrate Arduino with BNO055 IMU sensor, and convert quaternions to Euler angles for accurate representation.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Michael Penn

Representations of Finite Groups - A Few More Common Examples

Explore representations of finite groups including cyclic, dihedral, quaternions, and symmetric groups. Gain insights into advanced abstract algebra concepts and their applications.

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

HyperComplex Seminar

Quaternionic Foundations of Quantum Mechanics and Spin 1/2 Visualization

Explore quaternionic foundations of quantum mechanics and visualize spin 1/2 behavior. Gain insights into Dirac equation, spinors, and elastic continuum model using interactive simulations and quaternion representations.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Chromatic Algebra of 2x2 Matrices - Part 2

Explores chromatic algebra of 2x2 matrices, focusing on subalgebras, complexions, dot products, and the four-dimensional Dihedrons algebra. Compares to quaternions and highlights unique properties.

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