Insights into Mathematics Courses

Arithmetic With Rectangles - Elementary Mathematics Explained

2 ratings

Explore arithmetic fundamentals using rectangles. Learn counting, addition, and multiplication with visual representations suitable for young learners. Develop a strong foundation in basic mathematical concepts.

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

Central Banks and National Currencies - Wild West Banking

1 rating

Explores central banking, fractional reserve banking, and loan creation, highlighting the risks and instability in modern banking systems through analogies and historical perspectives.

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

Boolean Algebra and Set Theory - Math Foundations - N J Wildberger

1 rating

Explore Boolean algebra, set theory, and Venn diagrams. Learn about De Morgan's laws, distributive properties, and their proofs using truth tables and Boole's algebra.

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

An Introduction to Abstract Algebra - Abstract Algebra Math Foundations

1 rating

Explore fundamental algebraic structures like groups, rings, fields, and vector spaces through intuitive examples, providing a bird's-eye view of abstract algebra's foundational concepts.

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

Logical Difficulties With the Modern Theory of Limits - Real Numbers + Limits Math Foundations

1 rating

Explores logical issues with the modern theory of limits in mathematics, examining the formal definition and its problems through examples and historical context.

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

Numbers and Arithmetic - Math Terminology

1 rating

A comprehensive review of fundamental mathematical concepts and terminology for university-level math, covering number systems, arithmetic operations, fractions, and basic number theory.

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

Classical Spherical Trigonometry - Universal Hyperbolic Geometry

1 rating

Comprehensive overview of classical spherical trigonometry, covering key concepts, laws, and theorems. Introduces a new algebraic approach to simplify and enhance the traditional framework.

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

Introduction to Topology in Mathematics History

1 rating

Explore topology's historical development, from Euler's polyhedron discoveries to Poincaré's insights. Learn about key concepts like Euler characteristic, Riemann surfaces, and surface classification in this mathematical journey.

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

Non-Euclidean Geometry - Math History - NJ Wildberger

1 rating

Explore the complex history and modern interpretations of non-Euclidean geometry, challenging traditional narratives and proposing new perspectives on this fundamental mathematical concept.

• YouTube
• 51 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

Rethinking Standard Model Numerology

Explore particle physics' Standard Model, focusing on quantum numbers, particle classifications, and novel representations of Baryon and Meson families. Gain insights into the eight-fold way and quark theory.

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