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

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

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

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 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

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 Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems

Explore complex numbers and their connection to plane rotations, laying the groundwork for understanding quaternions and 3D rotations. Emphasizes a logical, algebraic approach without relying on transcendental functions.

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

Rational Trigonometry, Generalized Triangle Geometry and Four-Fold Incenter Symmetry

Explores rational trigonometry and generalized triangle geometry, introducing quadrances, spreads, and chromogeometry. Discusses Euler lines, incenters, and various triangle centers, culminating in a novel result on colored incenters.

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

Euclid's Construction Problems I - Famous Math Problems

Explore Euclid's fundamental geometric constructions using straight-edge and compass, enhancing understanding of mathematical logic and the importance of constructing objects before theorizing about them.

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

Steiner's Regions of Space Problem - Famous Math Problems

Exploration of Steiner's space division problem, analyzing how many regions n planes can create in space, with insights into the analogous 2D problem and mathematical reasoning.

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