Insights into Mathematics Courses

Geometric Linear Algebra

Discover a visual approach to linear algebra emphasizing geometry, logic, and exact arithmetic through vectors, matrices, transformations, and applications to physics and geometry.

• YouTube
• 1 day 9 hours 34 minutes
• Self-Paced
• Free Video

Algebraic Topology

Explore topological spaces, surfaces, knots, and fundamental groups through geometric intuition and algebraic methods in this comprehensive mathematical journey.

• YouTube
• 1 day 5 hours 1 minute
• Self-Paced
• Free Video

Universal Hyperbolic Geometry - A Projective and Algebraic Approach

Explore hyperbolic geometry through a projective, algebraic approach using rational trigonometry—no calculus required, connecting to relativity and Minkowski geometry.

• YouTube
• 1 day 7 hours 7 minutes
• Self-Paced
• Free Video

Real Numbers and Limits

Explore fundamental concepts of real numbers, limits, and mathematical foundations through critical examination of infinity, sequences, and numerical approximation methods.

• YouTube
• 17 hours 19 minutes
• Self-Paced
• Free Video

Differential Geometry - Complete Course with Classical Curves, Surfaces, and Curvature Theory

Explore curves, surfaces, and curvature through classical and modern approaches, including projective geometry, algebraic methods, and computational visualization with GeoGebra.

• YouTube
• 1 day 1 hour 10 minutes
• Self-Paced
• Free Video

Elementary Probability and Statistics

Discover fundamental concepts in probability theory and statistics, from basic counting to normal distributions, with clear explanations of random variables and statistical measures.

• YouTube
• 7 hours 35 minutes
• Self-Paced
• Free Video

Year 9 Mathematics - Complete Course

Master fundamental arithmetic operations, index laws, and scientific notation through comprehensive Year 9 mathematics instruction by NJ Wildberger.

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

The Algebra of Boole - Logic and Circuit Analysis - MF250-280

Explore Boole's algebra for logic and circuit analysis, covering historical foundations, logical operations, transistors, and systematic deduction methods.

• YouTube
• 14 hours 24 minutes
• Self-Paced
• Free Video

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

Rational Trigonometry, Generalized Triangle Geometry and Four-Fold Incenter Symmetry

Explores rational trigonometry and generalized triangle geometry, introducing quadrances, spreads, and chromogeometry. Discusses Euler lines, incenters, and various triangle centers, culminating in a novel result on colored incenters.

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

Euclid's Construction Problems I - Famous Math Problems

Explore Euclid's fundamental geometric constructions using straight-edge and compass, enhancing understanding of mathematical logic and the importance of constructing objects before theorizing about them.

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

Steiner's Regions of Space Problem - Famous Math Problems

Exploration of Steiner's space division problem, analyzing how many regions n planes can create in space, with insights into the analogous 2D problem and mathematical reasoning.

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

The Integral of X^n - Famous Math Problems

Algebraic approach to polynomial integration using Binomial theorem and five basic properties, avoiding real numbers and limits. Compares with classical integration theories and their limitations.

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

The Integral of X^n - Famous Math Problems

Explores the integral of x^n, its historical development, and challenges in modern analysis. Proposes a new 'Algebraic Calculus' approach, addressing issues with continuum, infinite processes, and area theory.

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

Distances to the Sun and Moon - Famous Math Problems

Explore ancient Greek methods for calculating celestial distances, from Thales to Aristarchus. Learn how early astronomers determined Earth's size and the distances to the sun and moon.

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