Insights into Mathematics Courses

Arithmetic With Rectangles - Elementary Mathematics Explained

2 ratings

Learn arithmetic through row rectangles of unit squares, introducing natural numbers, counting, addition, multiplication, and comparing collection sizes.

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

Central Banks and National Currencies - Wild West Banking

1 rating

Explains how loan and credit creation—not simply “printing money”—makes modern banking inherently risky and unstable.

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

Boolean Algebra and Set Theory - Math Foundations - N J Wildberger

1 rating

Explore Boolean algebra through finite sets and Venn diagrams, proving De Morgan’s and distributive laws with truth tables and Boole’s algebra.

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

Classical Spherical Trigonometry - Universal Hyperbolic Geometry

1 rating

A concise summary of classical spherical trigonometry covering distances, angles, circular functions, and the principal laws for spherical triangles.

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

Numbers and Arithmetic - Math Terminology

1 rating

A quick review of arithmetic terminology—from number systems and Hindu-Arabic numerals to fractions, divisibility, and inequalities—for incoming university mathematics students.

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

Introduction to Topology in Mathematics History

1 rating

Explore topology's historical development, from Euler's polyhedron discoveries to Poincaré's insights. Learn about key concepts like Euler characteristic, Riemann surfaces, and surface classification in this mathematical journey.

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

The Central Object in Mathematics: Lattices and Their Connections

Explore the fundamental "lattice" structure in mathematics, its connections to various topics, and its significance in pure mathematics research.

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

The Cayley Transform: Rationalizing Physics Through Mathematical Economy

Explore how rational mathematics and the Cayley Transform can revolutionize modern physics by replacing infinite-based frameworks with finite computational approaches to quantum and particle physics.

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

The Mathematics of the Great Pyramid - Math History (Ancient to Modern) 35

Explore the fascinating mathematical secrets of the Great Pyramid, from ancient Egyptian "seked" measurements to connections with pi and the golden ratio through continued fractions.

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

A Proportionality Hypothesis for Modern Physics - Sociology and Pure Physics

Explore the relationship between dimensionless constants and proportional reasoning in physics, drawing parallels to ancient Greek geometry and Eudoxus' theory.

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

The Cross Law - #1 Formula in Geometry in Rational Trigonometry

Discover Rational Trigonometry, a modern alternative to traditional trigonometry, focusing on the Cross Law formula and its applications in various geometric contexts, including Euclidean and Relativistic geometry.

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

Solving Polynomial Equations and the Geode - Part I

Explore a novel approach to solving polynomial equations using hyper-Catalan number series, sidestepping traditional Galois theory methods and examining applications to the Bring radical and Wallis' cubic equation.

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

Subdigons and Solving Polynomial Equations and the Geode - Part II

Delve into the mathematical world of subdigons, hyper-Catalan numbers, and a novel series solution approach to polynomial equations that bypasses traditional Galois theory methods.

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

The Emperor's Functions Have No Clothes - Sociology and Pure Mathematics

Uncover the logical flaws in modern set-theoretic function definitions and explore alternative approaches to this fundamental mathematical concept.

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

The Definitional Weaknesses of Pure Mathematics Courses - Sociology and Pure Mathematics

Uncover critical logical flaws in pure mathematics education, examining definitional weaknesses in fundamental concepts like numbers, functions, and sequences.

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