Insights into Mathematics Courses

Sets and Other Data Structures - Data Structures in Mathematics

Explore four fundamental data structures in mathematics: lists, ordered sets, multisets, and sets. Learn their characteristics, applications, and a new notation system for easier recognition and distinction.

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

What Exactly Is a Set - Data Structures in Mathematics Math Foundations

Explores the concept of sets in mathematics, discussing definitions, challenges, and criticisms of modern set theory. Examines everyday usage, examples, and foundational issues in mathematical logic.

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

The Circumquadrance of a Cyclic Quadrilateral - Rational Geometry Math Foundations - NJ Wildberger

Explore a rational approach to cyclic quadrilateral geometry, avoiding transcendental quantities and extending to other fields and geometries. Learn Parameshvara's formula and its non-convex counterpart.

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

The Projective Quadruple Quad Formula - Rational Geometry Math Foundations

Explore the projective Quadruple quad formula and its connection to cyclic quadrilateral geometry, advancing beyond classical trigonometry to a more powerful approach applicable to general fields.

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

The Curvature of a Parabola, Without Calculus - Rational Geometry Math Foundations

Algebraic approach to calculate parabola curvature without calculus, using circle circumquadrance and triangle properties. Demonstrates wider applicability to various algebraic curves.

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

The Triple Spread Formula, Circumcircles and Curvature - Rational Geometry Math Foundations

Explores the Triple spread formula in Rational Trigonometry, relating it to circumcircles and curvature. Connects projective geometry with one and two-dimensional geometries through core circles and quadratic curvature.

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

Relativistic Velocity, Core Circles and Paul Miller's Protractor - Rational Geometry

Exploring Paul Miller's protractor for efficient spread measurement in projective geometry, linking projective and affine measurements through core circles and the Triple quad formula.

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

Seminar - Some Fundamental Formulas from Metrical Algebraic Geometry

Explore fundamental formulas in metrical algebraic geometry, connecting classical theorems to modern discoveries. Gain insights into affine and projective variants applicable across various fields.

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

Relativistic Velocity, Core Circles, and Paul Miller's Protractor - Rational Geometry

Explores core circles in rational geometry, connecting projective and Euclidean geometry. Covers parametrization, quadrances, and theorems, bridging abstract concepts with practical applications.

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

Combinatorics - Math History - NJ Wildberger

Explore combinatorics through historical examples, counting problems, graph theory, and generating functions. Delve into partitions, Fibonacci numbers, Catalan sequence, and famous theorems in this engaging mathematical journey.

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

Relativistic Velocity, Core Circles and Paul Miller's Protractor - Rational Geometry

Explore core circles in rational geometry, connecting projective and Euclidean concepts. Learn about relativistic velocity addition and its implications for Einstein's special theory of relativity.

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

The Three-Fold Symmetry of Chromogeometry - Rational Geometry Math Foundations

Explore chromogeometry's three-fold symmetry, combining Euclidean and relativistic geometries. Discover new patterns and relations beyond traditional approaches, opening doors to 21st century geometric insights.

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

Isometry Groups of the Projective Line III - Rational Geometry Math Foundations

Exploring relativistic geometry in one dimension, extending projective geometry to incorporate Einstein's special theory of relativity and its impact on physics and mathematics.

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

Sets, Logic and Computability - Math History - NJ Wildberger

Overview of set theory, logic, and computability in late 19th/early 20th century math, covering Cantor's work, Dedekind's constructions, paradoxes, and philosophical schools addressing foundational issues.

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

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

Exploring finite field geometry: isometries, rotations, and reflections on the projective line, revealing connections to relativistic geometry and offering a new perspective on Euclidean concepts.

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