Insights into Mathematics Courses

John Keil's Preface to Euclid - Sociology and Pure Mathematics

Exploration of John Keil's 1723 preface to Euclid's Elements, discussing its historical context and significance in geometry, including comparisons to Isaac Barrow's version.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Dual Complex Numbers and Leibniz's Differentiation Rules - Famous Math Problems

Explore algebraic infinitesimals, dual complex numbers, and Leibniz's differentiation rules in this advanced mathematics lecture, extending calculus to general and finite fields.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Greek Pure Mathematics and the Infinitude of Primes - Sociology and Pure Maths - N J Wildberger

Exploring Euclid's proof of prime number infinitude, challenging modern interpretations, and emphasizing the historical significance of Greek mathematics in shaping pure mathematical thinking.

• YouTube
• 33 minutes
• On-Demand
• Free Video

How to Develop a Proper Theory of Infinitesimals I - Famous Math Problems

Explore the history and development of infinitesimals in mathematics, from Archimedes to modern approaches, with a focus on the Dihedron algebra and dual complex numbers.

• YouTube
• 40 minutes
• On-Demand
• Free Video

The True Algebra of Complex Numbers - Via Dihedrons

Exploring complex numbers through Dihedron algebra, offering a fresh perspective on their structure and geometry. Highlights include quadratic inverse algebras and comparisons to Quaternions.

• YouTube
• 28 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Areas and Volumes for a Sphere - Universal Hyperbolic Geometry

Explore Archimedes' sphere formulas, rational turn angles, and Harriot's theorem. Learn key principles in spherical geometry and discover new ways to conceptualize angles and areas.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Spherical and Elliptic Geometries - Universal Hyperbolic Geometry

Explore spherical and elliptic geometries, from ancient Greek astronomy to modern concepts. Learn about longitude, latitude, measurement techniques, and key theorems in non-Euclidean spaces.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Spherical and Elliptic Geometries - An Introduction

Explore spherical geometry fundamentals: great circles, antipodal points, triangles, and circles. Learn key concepts and visualize ideas with physical models, connecting to 3D space and Euclidean geometry.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Trigonometric Dual Laws and the Parallax Formula - Universal Hyperbolic Geometry

Explore trigonometric dual laws and the Right parallax formula in Universal Hyperbolic Geometry. Learn about Pythagoras' theorem, Cross dual law, and zero quadrance/spread theorems.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Newton's Method for Approximating Cube Roots - Real Numbers and Limits Math Foundations

Newton's method for approximating cube roots: explore cubes, cube roots, and techniques to find approximate solutions. Learn about Taylor expansion, tangent lines, and advanced methods like the weighted Babylonian and quadratic Newton approaches.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

Explore interval arithmetic, its laws for natural numbers and integers, and the challenges with real number arithmetic. Gain insights into measurement, approximation, and foundational mathematical concepts.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Addition in Practice - Elementary Mathematics Explained

Explore addition laws, even/odd numbers, and their geometric representations. Learn associative and commutative properties, and discover practical applications in arithmetic and counting problems.

• YouTube
• 25 minutes
• On-Demand
• Free Video