Insights into Mathematics Courses

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

Curvature for the General Paraboloid - Differential Geometry - NJ Wildberger

Novel approach to surface curvature using projective geometry and linear algebra. Explores paraboloid curvature through characteristic polynomials, offering insights for higher-dimensional generalizations.

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

Stevin Numbers, Infinitesimals and Complex Numbers - Famous Math Problems

Explore the evolution of decimal numbers, infinitesimals, and complex numbers in mathematics. Delve into Stevin's contributions, calculus challenges, and modern perspectives on real and complex numbers.

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

Classification of 2-Manifolds and Euler Characteristic - Differential Geometry

Explore the classification of compact, oriented 2-manifolds and their Euler characteristics through combinatorial methods, cut-and-paste operations, and topological invariants in differential geometry.

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

The Area of a Triangle and Archimedes' Formula - Famous Math Problems

Novel approach to calculating triangle area using rational trigonometry, avoiding unnecessary irrationalities in Heron's formula. Presents a clearer solution based on Pythagoras' theorem and Triple quad formula, with practical applications.

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

Paraboloids and Associated Quadratic Forms - Differential Geometry

Explore paraboloids and quadratic forms in differential geometry, covering diagonalization, eigenvalues, and Dupin's indicatrix. Learn key concepts for understanding surface curvature.

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

Manifolds, Classification of Surfaces and Euler Characteristic - Differential Geometry

Informal introduction to manifolds, focusing on 2D surfaces. Explores charts, orientation, and classification using Euler characteristic. Highlights key concepts in differential geometry.

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

Geometric and Algebraic Aspects of Space Curves - Differential Geometry

Explore geometric and algebraic aspects of space curves, including tangent vectors, normal planes, curvature, torsion, and associated surfaces. Learn about Monge's contributions and invariant properties.

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

The Normal Distribution - Probability and Statistics

Explore the normal distribution, its importance in statistics, and the Central Limit Theorem. Learn about probability density, standard and general normal distributions, and cumulative distribution functions.

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

The Frenet Serret Equations - Differential Geometry

Explore the Frenet-Serret equations, describing space curves' behavior using vector-valued derivatives. Learn about tangent, normal, and bi-normal vectors, curvature, and torsion in 3D space.

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

Trigonometry in Elliptic Geometry II - Universal Hyperbolic Geometry - NJ Wildberger

Explore elliptic trigonometry laws, including Spread, Cross, and Dual cross, using linear algebra. Learn proofs for Thales', Pythagoras', and Triple Quad formulas in elliptic geometry.

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

Curvature, Turning Numbers and Winding Numbers - Differential Geometry

Explores advanced concepts in planar curvature, including turning numbers, winding numbers, and parametric curves. Connects to complex analysis and circular motion, offering insights into differential geometry.

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

Trigonometry in Elliptic Geometry - Universal Hyperbolic Geometry

Explore elliptic geometry's trigonometry, including projective points, quadrances, and spreads. Learn key laws connecting triangles and their polar counterparts in this fundamental mathematical realm.

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

Binomial and Geometric Distributions - Probability and Statistics

Explore binomial and geometric distributions, probability generating functions, and calculating means and variances in this comprehensive overview of key probability concepts.

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

Curvature, Turning Numbers and Winding Numbers - Differential Geometry

Explore curvature, turning numbers, and winding numbers in planar curves. Learn about irrational numbers and transcendental functions from an applied perspective using rational turn angles.

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