Insights into Mathematics Courses

The Remarkable Platonic Solids I - Universal Hyperbolic Geometry

Explore the five Platonic solids through symmetry, Euclid’s formulas, Euler’s polyhedral relation, and regular tilings of the sphere.

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

Applications of Rational Spherical Trigonometry II - Universal Hyperbolic Geometry

Compare classical and rational spherical trigonometry to calculate the distance and bearing between Sydney and New Delhi from latitude and longitude.

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

The Realm of Natural Numbers - Data Structures in Mathematics

Explore natural numbers through multiset-inspired addition, union, and intersection, proving their laws and a surprising distributive relation linked to tropical calculus.

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

Sets and Other Data Structures - Data Structures in Mathematics

Introduces lists, ordered sets, multisets, and sets by distinguishing whether structures are ordered and whether repetitions are allowed.

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

Combinatorics - Math History - NJ Wildberger

A historical tour of combinatorics through counting problems, graph theory, generating functions, Fibonacci and Catalan sequences, and Ramsey theory.

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

Problems With the Calculus - Math History - NJ Wildberger

A historical examination of the unresolved conceptual problems behind calculus, from Newton and Leibniz’s infinitesimals to limits, complex numbers, and probability.

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

Absolute Versus Relative Measurements in Geometry - Rational Geometry Math Foundations

Explore why geometry favors relative proportions over absolute measurements, from Euclid’s theory of proportions to affine points, vectors, and planes.

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

Number Systems and Stevin's Decimals - Math History

Trace the development of number systems from Greek, Indian, and Arabic traditions to Stevin’s decimal arithmetic and related work in music and physics.

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

Oriented Circles and Relativistic Geometry II - Wild Linear Algebra

Signed circles connect homothetic centers, Monge’s theorem, tangency, and Apollonius’s problem with relativistic geometry.

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

How to Write Mathematics at the College Level - Math Terminology

Learn to write clear, logically structured mathematics solutions using defined terms, complete explanations, and careful diagrams.

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

The Language of Calculus - Math Terminology

Explore the language of calculus through motion, function notation, differentials, and the relationship between position, velocity, and acceleration.

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

Sets, Logic and Graphs - Math Terminology - NJ Wildberger

Review the language and notation of sets, logic, statements, graphs, and circuits used across higher mathematics.

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

The Language of Algebra - Math Terminology

A terminology-focused algebra review for incoming university students, covering polynomials, the binomial theorem, sequences and series, rational functions, and polynomial calculus.

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

The Language of Geometry - Math Terminology

A concise review of elementary geometry terminology, from Euclidean shapes and triangles to transformations, Platonic solids, and Cartesian coordinates.

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

The Relativistic Dot Product - Wild Linear Algebra B

Introduces a planar relativistic dot product and shows how quadrance, Pythagoras, lines, projections, and circles change beyond Euclidean geometry.

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