Insights into Mathematics Courses

Arithmetic With Rectangles - Elementary Mathematics Explained

2 reviews

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
• On-Demand
• Free Video

Central Banks and National Currencies - Wild West Banking

1 review

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
• On-Demand
• Free Video

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

1 review

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
• On-Demand
• Free Video

An Introduction to Abstract Algebra - Abstract Algebra Math Foundations

1 review

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
• On-Demand
• Free Video

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

1 review

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
• On-Demand
• Free Video

Numbers and Arithmetic - Math Terminology

1 review

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
• On-Demand
• Free Video

Classical Spherical Trigonometry - Universal Hyperbolic Geometry

1 review

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
• On-Demand
• Free Video

Non-Euclidean Geometry - Math History - NJ Wildberger

1 review

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
• On-Demand
• Free Video

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

1 review

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

• YouTube
• 14 minutes
• On-Demand
• Free Video

Logical Difficulties with Cyclotomic Fields - Famous Math Problems 20

Explores logical issues in cyclotomic fields, focusing on the challenges of embedding roots of unity into complex numbers and the limitations of purely algebraic approaches.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Irreducibility and the Schoenemann-Eisenstein Criterion - Famous Math Problems 20

Explores irreducibility in cyclotomic polynomials, Gauss's lemma, and Schoenemann's criterion. Applies concepts to prime-indexed cyclotomic polynomials and establishes Eisenstein's criterion.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Regular Colourings of Regular Tilings - Elementary Mathematics K-6 Explained - Lecture 39

Explore symmetry and patterns through regular colourings of plane tilings. Learn about reflection, translation, and rotation while creating visually pleasing designs. Ideal for developing spatial awareness and creativity in young learners.

• YouTube
• 26 minutes
• On-Demand
• Free Video

The Perspective Image of a Square - Number Theoretic Approach - Lecture 18d

Explores the number theoretic aspects of perspective images of squares, including algebraic solutions, quadratic equations, and harmonic ranges, with applications to spheres and algebraic theorems.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Perspective Image of a Square - More Projective Geometry - Lecture 18b

Explore advanced projective geometry concepts, including perspective images, vanishing points, and Desargues' theorem, with applications in 2D and 3D space.

• YouTube
• 29 minutes
• On-Demand
• Free Video

The Perspective Image of a Square - Famous Math Problems 18a

Explore projective geometry concepts like quadrilaterals, quadrangles, duality, and cross ratios in relation to perspective images of squares. Novel approach using planar vector cross products.

• YouTube
• 33 minutes
• On-Demand
• Free Video