Insights into Mathematics Courses

The Chaotic Complexity of Natural Numbers - Data Structures in Mathematics

Exploring the complex nature of arithmetic with large numbers, focusing on exponential and triangular complexity, and examining the role of powers in mathematical computations.

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

Singletons, Vexels, and the Rank of a Maxel II - Data Structures Math Foundations

Explore vexels, maxels, and their multiplication. Learn about row and column ranks of maxels, and discover the Rank theorem. Gain insights into linear algebra concepts through a generalized framework.

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

Singletons, Vexels, and the Rank of a Maxel - Data Structures in Mathematics

Explores vexels as multisets of singletons, analogous to maxels, to structure vector space theory. Introduces concepts like singleton multiplication, friezes, and maxel rank, offering a broader perspective on linear spaces.

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

Maxel Algebra I - Data Structures in Mathematics Math Foundations

Explore maxel algebra, a new matrix theory focusing on idempotent diagonal maxels and sets of natural numbers. Learn about multiplication, identity maxels, and key propositions in this mathematical foundation.

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

Maxel Theory - New Thinking About Matrices II - Data Structures Math Foundations

Exploring maxel theory as an extension of matrix theory, focusing on multiset views, distributive and associative laws, 1-maxels, and frames. Introduces new terminology and notation for a data structure-oriented approach.

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

Arrays and Matrices II - Data Structures in Mathematics Math Foundations

Explore matrices from traditional linear algebra to a novel data structure approach. Learn matrix multiplication, algebra, and a new perspective using pixels and maxels.

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

Arrays and Matrices - Data Structures in Mathematics Math Foundations | NJ Wildberger

Introduction to arrays and matrices as 2D data structures, exploring definitions, examples, and extending to 3D arrays. Distinguishes between arrays and matrices, offering a novel approach to linear algebra.

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

Higher Data Structures - Data Structures in Mathematics Math Foundations

Explore advanced mathematical data structures, including nested combinations of lists, ordered sets, multisets, and sets. Learn their applications in combinatorics, graph theory, and other mathematical fields.

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

Inclusion-Exclusion via Multisets - Data Structures in Mathematics Math Foundations

Explore inclusion/exclusion via multisets, expanding to integral multisets with negative multiplicities. Learn a conceptual approach to this fundamental Set Theory theorem and its applications.

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

An Introduction to the Tropical Calculus - Data Structures in Mathematics

Explore Tropical calculus, a novel approach to set algebra using unique addition and multiplication concepts derived from union and addition operations.

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

The Classification of Platonic Solids I - Universal Hyperbolic Geometry

Exploring the classification of Platonic solids using modern notation and turn angles. Examines planar, spherical, and higher-dimensional cases, highlighting mathematical constructions and challenges in Euclid's proof.

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

Petrie Polygons of a Polyhedron - Universal Hyperbolic Geometry

Explore Petrie polygons on polyhedra, focusing on Platonic solids. Learn about tesselations, Schlafli symbols, and orthogonal projections in this geometric journey.

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

Canonical Structures Inside the Platonic Solids III - Universal Hyperbolic Geometry

Explore the rich symmetries of the dodecahedron through internal structures like handle sets, inscribed cubes, tetrahedra, and face diameters. Discover five-fold and six-fold symmetries in this fascinating Platonic solid.

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

Canonical Structures Inside Platonic Solids II - Universal Hyperbolic Geometry

Explore symmetries and canonical structures within the cube, including 2-fold, 3-fold, and 4-fold symmetries. Gain insights into rigid motions and even/odd symmetries using graph theory concepts.

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

The Remarkable Platonic Solids II- Symmetry - Universal Hyperbolic Geometry

Explore the symmetries of Platonic solids through rigid motions and rotations, examining tetrahedron, cube, and dodecahedron symmetries while connecting rotations to directed edges and discussing duality.

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