Insights into Mathematics Courses

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

Computer Science is More Rigorous than Pure Maths - The Case for Certificates

Explore why Computer Science's certificate-based validation makes it more rigorous than Pure Mathematics, examining the P=NP problem and flaws in mathematical definitions.

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

Quadrea, Area and Archimedes' Formula - Rational Trigonometry

Discover the elegant algebraic relationship between triangle area and quadrances/spreads through Archimedes' formula, replacing Heron's with beautiful rational trigonometry.

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

Five Main Laws of Rational Trigonometry

Discover the five main laws of Rational Trigonometry, a rational and algebraic approach that replaces traditional transcendental trigonometric laws and extends to various fields and geometries.

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

The History behind Hyper-Catalan Series Solutions to Polynomial Equations

Explore the historical journey of Catalan numbers and their hyper-Catalan generalizations with Dr. Dean Rubine, examining primary sources to uncover new mathematical insights beyond conventional wisdom.

• YouTube
• 1 hour 10 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

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

The Complicated Nature of Mathematical Space - From Euclid to Rational Trigonometry

Explore the evolution of mathematical space concepts, from Euclidean geometry to rational trigonometry, examining how modern computational limitations reshape our understanding of infinite mathematical objects.

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

Towards a New Mathematics and Types versus Sets - Sociology and Pure Maths

Explore Box Arithmetic, a revolutionary approach to mathematics foundations using nested empty boxes instead of infinite sets, distinguishing types from sets.

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

Math Terminology for Incoming University Students

Master essential mathematical vocabulary and notation needed for university-level studies across algebra, geometry, calculus, and logic in this comprehensive preparation guide.

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

Elementary Mathematics Explained - K-6

Discover fundamental math concepts through visual geometry, arithmetic patterns, and practical applications designed for elementary education and teacher development.

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

Arithmetic and Geometry Math Foundations

Explore fundamental mathematical concepts from arithmetic and geometry to abstract algebra, challenging conventional approaches with rational number systems and innovative geometric frameworks.

• YouTube
• 4 days 1 hour 49 minutes
• Self-Paced
• Free Video

Arithmetic and Geometry - Math Foundations

Explore fundamental mathematical concepts from basic arithmetic through advanced geometry, covering number systems, fractions, Euclidean geometry, algebra, polynomials, and calculus foundations.

• YouTube
• 18 hours 52 minutes
• Self-Paced
• Free Video

Wild Trig - An Introduction to Rational Trigonometry

Discover a revolutionary algebraic approach to trigonometry using quadrance and spread instead of angles and irrational numbers for more efficient geometric calculations.

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