Insights into Mathematics Courses

The Geometry of Euclidean Reflections and Rotations - Grounded Case

Explore Euclidean reflections and rotations using rational geometry. Learn about complex number multiplication, group structures, and a visual notation for describing transformations.

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

Old Babylonian Mathematics and Plimpton 322 - The World's First Exact Trigonometric Table

Explores a groundbreaking theory on Plimpton 322, an ancient Babylonian clay tablet, proposing it as the world's first and only exact trigonometric table based on ratios rather than angles.

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

Old Babylonian Mathematics and Plimpton 322 - The Remarkable Sexagesimal System

Explore the sophisticated Old Babylonian mathematical system, including sexagesimal numbers, reciprocal tables, and quadratic equations, with insights into their computational capabilities and historical significance.

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

Maths Education and Rational Trigonometry - Part 2

Exploring alternative approaches to teaching trigonometry and geometry, focusing on quadrance and spread within the Cartesian coordinate system for a more intuitive understanding.

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

Algebraic Calculus One - Introduction and Course Overview

Innovative approach to calculus, exploring its history and introducing a new perspective on this classical subject. Preview of an upcoming course that aims to revolutionize calculus education.

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

Colored Spreads and Generalizations in Rational Trigonometry - Lecture 2

Explore colored spreads in planar geometries, visualizing red and green spreads using cross products and determinants. Learn about generalized dot products and Pythagoras' theorem in different geometries.

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

Coloured Spreads and Generalizations in Rational Trigonometry - Lecture 1

Explore colored spreads theorem, planar dot products, and geometric interpretations of quadrances in blue, red, and green geometries. Gain insights into rational trigonometry and linear algebra concepts.

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

Infinities and Skepticism in Mathematics - Interview with N J Wildberger

Exploration of foundational issues in mathematics, including infinities, skepticism, and modern mathematical challenges. Discusses algorithms, paradoxes, and the future direction of mathematics.

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

Relations Between Multisets - Abstract Algebra Math Foundations - Lecture 225

Explore integral linear spans and relations between msets, drawing parallels to linear algebra's rank-nullity theorem. Learn to obtain relations using the Hermite normal form algorithm.

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

Integral Row Reduction and Hermite Normal Form - Math Foundations 223

Explores integral row reduction algorithm for finding a basis of integral linear space, paralleling Euclid's algorithm. Introduces Hermite normal form for msets of vexels in abstract algebra context.

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

Bases and Dimension for Integral Linear Spaces - Math Foundations 222

Explores algorithm for finding simplified bases of integral linear spaces, adapting Gaussian elimination to work with integral combinations. Introduces key concepts in abstract algebra through practical computation.

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

Lattice Relations and Hermite Normal Form - Abstract Algebra Math Foundations 224

Explore lattices and integral linear spans of vexels, including the Hermite normal form algorithm for understanding lattice structure and relations between elements in a spanning set.

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

Linear Spaces and Spans II - MathFoundations 220

Introduction to integral linear spaces as abstract algebraic objects, exploring their applications in mathematics, chemistry, and physics. Foundational concepts for linear algebra using vexel language for concrete examples.

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

Linear Spaces and Spans I - Abstract Algebra Math Foundations 219

Introduction to linear spaces and spans, generalizing natural numbers with addition to form spans of multisets. Explores fundamental concepts in abstract algebra and linear algebra.

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

Rethinking Roots of Unity in Complex Algebra - Math Foundations 218

Explores complex roots of unity, challenging traditional views and highlighting logical difficulties in their definition and existence, emphasizing rational parametrization and algebraic approaches over infinite processes.

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