Insights into Mathematics Courses

Sociology and Pure Mathematics - Pure Mathematics Relies on a Fake Arithmetic

Challenges modern pure mathematics' reliance on "fake arithmetic," proposing alternative approaches to calculus without infinite processes and calling for sociological analysis of mathematical practices.

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

The Geometry of the Dihedrons and Quaternions - Famous Math Problems

Explore the geometry of Dihedrons and Quaternions, comparing their properties and connections to relativity, linear algebra, and complex numbers. Gain insights into fundamental mathematical structures.

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

The Remarkable Dihedron Algebra - Famous Math Problems

Explore the Dihedron algebra, a key to constructing complex numbers. Learn its basis, properties, and connections to group theory in this comprehensive mathematical exploration.

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

How to Construct the True Complex Numbers I - Famous Math Problems

Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.

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

Computing Cyclotomic Polynumbers - Famous Math Problems

Explore cyclotomic polynomials, their factorization, and applications in algebra and number theory. Learn about Mersenne primes and the Schoenemann-Eisenstein criterion for irreducibility.

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

The Perspective Image of a Square III - The Solution

Explore the solution to projecting a square onto a quadrilateral, delving into geometry, perpendicularity, and perspective. Gain insights into mathematical problem-solving and related concepts.

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

Mirror Symmetry for Young Students - Elementary Mathematics Explained

Explore mirror symmetry through visual mathematics, focusing on regular tilings and their symmetry lines. Ideal for teachers and parents to introduce geometric concepts to young learners.

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

Regular Tilings of the Plane - Elementary Mathematics Explained

Explore the fascinating world of regular tilings, including square, equilateral, and hexagon patterns. Learn their properties, historical significance, and practical applications in various fields.

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

Adding Bigger Sums Using Open Numbers - Elementary Mathematics Explained

Learn a novel approach to adding larger sums using open numbers, focusing on a big end approach. Discover advantages and practice approximating sums by finding ranges for answers.

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

Polygonal Shapes - Elementary Mathematics Explained

Introduction to polygonal shapes in geometry, covering triangles, rectangles, parallelograms, and pentagons. Explores types of quadrilaterals and triangles, emphasizing the importance of geometry in early mathematics education.

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

The Holy Grail of Propositional Logic - MathFoundations - N J Wildberger

Explore mechanized reasoning in propositional logic through Boole's Algebra, featuring two solutions to a Sir Galahad puzzle: Boole Reduction and Boole-Mobius transform.

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

The Silver Crash and Long Depression of 1873 - Wild West Banking

Explores the global financial crash of 1873-1879, its causes, and long-lasting effects. Examines historical parallels to modern economic challenges and discusses the impact on banking practices.

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

Coin, Cash and Credit, and Fractional Reserve Banking - Wild West Banking - N J Wildberger

Explore the evolution of money, Wild West banking practices, and the intricacies of fractional reserve banking through historical examples and mathematical insights.

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

A Systematic Approach to Logical Deduction and the Boole-Mobius Transform II - N J Wildberger

Explore the Boole-Mobius transform as an alternative method for validating propositional logic implications, linking Boolean functions and Boole polynumbers through practical examples.

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

Mesopotamian Mathematics - MathHistory - N J Wildberger

Explore ancient Mesopotamian mathematics, including the remarkable sexagesimal system and advanced arithmetic techniques developed by Sumerians, Akkadians, and Babylonians from 3000-1600 BCE.

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