Insights into Mathematics Courses

Polynumbers and De Casteljau Bezier Curves - Algebraic Calculus and DCB Curves - N J Wildberger

Explore polynumbers and de Casteljau Bezier curves in algebraic calculus. Learn new formulas for planar integration and use GeoGebra to visualize these remarkable curves, with applications in design and animation.

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

Emile Borel - Real Number Enthusiast or Skeptic? - Sociology and Pure Mathematics

Explore Emile Borel's contributions to measure theory and his skepticism about real numbers, including normal numbers and the intriguing concept of a "know-it-all" number.

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

A Brief History of Geometry - Sociology and Pure Mathematics

Explore geometry's evolution from ancient times to 1400 AD, covering key theorems, Platonic solids, and applications in astronomy, surveying, and construction. Highlights include Islamic contributions to spherical geometry.

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

How to Set Up Fractions IV - The Relation Between Fractions and Other Number Systems

Explore number systems, focusing on rational numbers and their relationships. Challenges traditional views on real numbers, emphasizing the distinction between counting and measuring in mathematics.

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

Euclid Book 1 Props VI-VIII - A Foundation for Geometry - Sociology and Pure Maths - N J Wildberger

Examines Euclid's Elements Book 1 Propositions VI-VIII, discussing proofs, logical issues, and questioning its suitability as a foundation for modern geometry. Explores alternatives and implications for mathematics.

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

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

Explore computational challenges of fractions, including mixed fractions and Euclid's division lemma. Learn strategies to simplify fraction arithmetic and understand its importance in mathematics education.

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

Exceptional Structures in Mathematics and Physics From Dynamics on Graphs

Explore exceptional structures in math and physics through graph dynamics, connecting to Coxeter diagrams, root systems, and Lie algebras. Discover new combinatorial structures and their role in representation theory and modern physics.

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

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

Critical review of Euclid's Book 1 Propositions I-V, examining logical foundations and constructions. Explores historical significance and questions modern interpretations of Euclidean geometry.

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

Infinitesimal Calculus with Finite Fields - Famous Math Problems

Explore infinitesimal calculus in finite fields through the semi-cubical parabola over F_7, challenging traditional real number analysis and emphasizing polynumbers and de Casteljau Bezier curves.

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

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

Algebraic approach to calculus using dual complex numbers and bi-polynumbers, introducing the Derivative theorem and deriving Product and Chain Rules without limits or real numbers.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video