Insights into Mathematics Courses

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

Differential Geometry - Complete Course with Classical Curves, Surfaces, and Curvature Theory

Explore curves, surfaces, and curvature through classical and modern approaches, including projective geometry, algebraic methods, and computational visualization with GeoGebra.

• YouTube
• 1 day 1 hour 10 minutes
• Self-Paced
• Free Video

Elementary Probability and Statistics

Discover fundamental concepts in probability theory and statistics, from basic counting to normal distributions, with clear explanations of random variables and statistical measures.

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

Year 9 Mathematics - Complete Course

Master fundamental arithmetic operations, index laws, and scientific notation through comprehensive Year 9 mathematics instruction by NJ Wildberger.

• YouTube
• 6 hours 32 minutes
• Self-Paced
• Free Video

The Algebra of Boole - Logic and Circuit Analysis - MF250-280

Explore Boole's algebra for logic and circuit analysis, covering historical foundations, logical operations, transistors, and systematic deduction methods.

• YouTube
• 14 hours 24 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 Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths

Explores the divide between exact and approximate theories in pure mathematics, challenging conventional views on arithmetic, algebra, topology, and number theory, including the Riemann Hypothesis.

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

The Mathematics of Scales and Modes - Maths and Music

Explore mathematical framework for scales and modes using 12-tone chromatic scale. Learn interval sequences, scale types, and connections to clock arithmetic and discrete calculus.

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

The Operation of Caret - Exponentiation via Multisets - Math Foundations

Explore a new arithmetic operation called "caret" (exponentiation) for multisets, extending the ladder of operations beyond addition and multiplication with concrete examples and recursive counting functions.

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

The Big Step from Polynumbers to Multinumbers - Math Foundations - N J Wildberger

Explore the transition from polynumbers to multinumbers, expanding arithmetic concepts using multisets. Learn new notations and operations for a more flexible algebraic framework.

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

A Multiset Approach to Arithmetic - Math Foundations

Explore a new framework for arithmetic using multisets, introducing natural numbers, polynumbers, and multinumbers. Learn innovative definitions and operations that offer profound insights into mathematical structures.

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