Insights into Mathematics Courses

How to Set Up Fractions II - The Computational Challenge - Famous Math Problems

Explores the computational challenges of fractions, including mixed fractions, alternate arithmetic, least common multiples, and primary-school fraction addition.

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

Exceptional Structures in Mathematics and Physics From Dynamics on Graphs

Explore how graph games generate exceptional structures such as the E8 root system and its symmetries.

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

Euclid Book 1 Props I - V - A Critical Review - Sociology and Pure Mathematics - N J Wildberger

A critical examination of Euclid’s first five propositions, from compass-and-straightedge constructions to the logical foundations of geometry.

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

Infinitesimal Calculus with Finite Fields - Famous Math Problems

Explore how derivatives and infinitesimal analysis can be formulated over the finite field F₇ using polynumbers and a semi-cubical parabola.

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

An Algebraic Infinitesimal Approach to Product and Chain Rules - N J Wildberger

An algebraic infinitesimal framework for derivatives over a general field, using dual complex numbers and bi-polynumbers to derive the product and chain rules.

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

The Geometry of the Dihedrons and Quaternions - Famous Math Problems

Explore Dihedrons, sister algebras to Quaternions, through their rich relativistic geometry, determinant quadratic form, and connections to complex numbers.

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

Mesopotamian Mathematics - MathHistory - N J Wildberger

Explore Mesopotamian arithmetic, including the sexagesimal system, Babylonian algorithms, quadratic equations, multiplication, and reciprocal tables.

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

Propositional Logic and the Algebra of Boole - N J Wildberger

An introduction to propositional logic using truth values, truth tables, equivalences, and Boole’s algebra to analyze and simplify formulas.

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

Puzzles Using Arithmetic - Elementary Mathematics Explained

Explore arithmetic puzzles through geometric solutions, powers of two, triangular numbers, and step-by-step problem-solving strategies.

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

Measuring Weight - Elementary Mathematics Explained

Introduces weighing everyday objects through scales, metric and imperial units, and approximate quantities, connecting measurement to arithmetic for young learners.

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

Affine and Projective Geometry, and the Problem of Lines

An introductory geometric treatment of affine and projective points uses projective coordinates to solve 2D problems and represent curves.

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

Boole Polynumbers and Equivalent Circuits - Math Foundations - N J Wildberger

Learn how Boole polynumbers represent Boolean functions and identify equivalent logic circuits through algebraic invariants.

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

Boolean Algebra and Shannon's Circuit Analysis - Math Foundations - N J Wildberger

Explore Boolean algebra through Huntington’s axioms and Shannon’s 1938 connection between logical reduction rules and simplifying series and parallel circuits.

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

Implication and Logical Operations - Math Foundations - N J Wildberger

Explore the 16 logical connectives, implication, and Modus Ponens through truth tables and Boole’s algebra.

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

A Brief History of Logic - Medieval and Arabic Logic - Math Foundations

A brief history of how Aristotle’s logic shaped medieval European and Arabic thought through Boethius, al-Kindi, Avicenna, and later medieval logicians.

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