Insights into Mathematics Courses

A Brief History of Logic - Stoics and Other Thinkers

Explore Stoic logic through its five indemonstrables, connectives, implication, excluded middle, and the temporal nature of truth.

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

The Group of Blue Planar Isometries - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore Euclidean isometries through rational trigonometry, deriving projection and reflection formulas and connecting line reflections to the Weierstrass substitution.

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

The Euclidean Rotation Group and Complex Number Multiplication - WildTrig

Explore a rational formulation of plane rotations connecting the Euclidean rotation group with complex number multiplication and half-slopes on the unit circle.

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

Isometry Groups in Planar Geometry - WildTrig: Intro to Rational Trigonometry - N J Wildberger

An algebraic treatment of isometry groups, reflections, and rotations across Euclidean and relativistic planar geometries without angles or transcendental functions.

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

Understanding Uniform Motion - Are Radians Really Necessary? - WildTrig

Examines why radian measure is used, tracing its dependence on calculus and challenging the usual high-school justification.

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

The True Role of the Circular Functions - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore the historical and conceptual role of circular functions, from uniform motion around a circle to the choice of natural and angular units.

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

Rheticus and 17th Century Trig Tables - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore how Rheticus’s 17th-century trigonometric tables shaped classical trigonometry through double-, half-, and triple-angle formulas.

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

The General Rational Laws of Trigonometry - WildTrig: Intro to Rational Trigonometry

Derive the general laws of rational trigonometry algebraically using quadrance, spread, and a bilinear form.

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

Geometry With a General Dot Product - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore rational trigonometry with an arbitrary symmetric-matrix dot product, extending quadrance, perpendicularity, and spread to a geometry whose unit circle may appear as an ellipse.

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

Back to Gauss and Modular Arithmetic - Data Structures in Mathematics Math Foundations

Learn how modular arithmetic and congruences simplify remainders, divisibility tests, and calculations involving powers of 10.

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

Astronomy and Trigonometry in India - Math History

A brief overview of ancient Indian contributions to astronomy and related trigonometry, including trigonometric sign tables and the work of Brahma Gupta.

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

Divisibility of Big Numbers - Data Structures in Mathematics Math Foundations

Explore divisibility of natural numbers using long division, repeated subtraction, and modular arguments for large-number problems.

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

Ancient Astronomy in Babylon and China - Math History - NJ Wildberger

Explore how Babylonian and other ancient observers understood the night sky through the celestial sphere, great circles, equatorial coordinates, and angular measurements.

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

Petrie Polygons of a Polyhedron - Universal Hyperbolic Geometry

Explores Petrie polygons of Platonic solids, regular tessellations, and their behavior under perspective and orthogonal projection.

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

The Remarkable Platonic Solids II- Symmetry - Universal Hyperbolic Geometry

Explore the rotational symmetries of Platonic solids through rigid motions, directed edges, and the duality of cubes and octahedra.

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