Insights into Mathematics Courses

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

Rational Trigonometry in Action - Applications to Surveying and Real-World Problems

Explore rational trigonometry's practical applications in surveying using quadrance and spread concepts, plus visual measurement methods for solving real-world geometric problems.

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

The Underlying Arithmetic of Physics - Matrices or Maxels?

Explore how matrices and maxels could serve as the fundamental computational engine of physics, moving beyond standard arithmetic to non-commutative realms for deeper insights.

• YouTube
• 18 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

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

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

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

Geometric Linear Algebra

Discover a visual approach to linear algebra emphasizing geometry, logic, and exact arithmetic through vectors, matrices, transformations, and applications to physics and geometry.

• YouTube
• 1 day 9 hours 34 minutes
• Self-Paced
• Free Video

Algebraic Topology

Explore topological spaces, surfaces, knots, and fundamental groups through geometric intuition and algebraic methods in this comprehensive mathematical journey.

• YouTube
• 1 day 5 hours 1 minute
• Self-Paced
• Free Video

Universal Hyperbolic Geometry - A Projective and Algebraic Approach

Explore hyperbolic geometry through a projective, algebraic approach using rational trigonometry—no calculus required, connecting to relativity and Minkowski geometry.

• YouTube
• 1 day 7 hours 7 minutes
• Self-Paced
• Free Video

Real Numbers and Limits

Explore fundamental concepts of real numbers, limits, and mathematical foundations through critical examination of infinity, sequences, and numerical approximation methods.

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