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Course Library
Explore the Textbook of the Future

GeometryNumbers and AlgebraProbability and Applications

Middle School

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More Constructions
Under construction
Angles and Proofs
Under construction
Origami and Paper Folding

Transformations and Symmetry

IntroductionRigid Transformations
Congruence
Under construction
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
Similarity
Under construction

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and Similarity
Under construction
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral Triangles
Under construction
TrigonometrySine and Cosine Rules

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross Sections
Under construction
Platonic Solids

High School

Circles and Pi

IntroductionDegrees and RadiansTangents, Chords and Arcs
The Circle Theorems
Under construction
Cyclic Polygons
Under construction
Spheres, Cones and CylindersConic Sections

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher Dimensions
Under construction

Fractals

IntroductionThe Sierpinski TriangleThe Mandelbrot Set
Space Filling Curves
Under construction

Middle School

Divisibility and Primes

Factors and MultiplesDivisibility RulesPrime NumbersThe Distribution of PrimesLowest Common MultiplesGreatest Common Factors

Sequences and Patterns

IntroductionArithmetic and Geometric SequencesFigurate Numbers
Sequences as Functions
Under construction
Fibonacci NumbersSpecial SequencesPascal’s Triangle
Limits and Convergence
Under construction

Quadratic Equations

Introduction
Binomial Expressions
Under construction
Solving Quadratic Equations
Under construction
The Quadratic Formula
Under construction
Graphing Quadratics
Under construction
Projectile Motion
Under construction
More Applications
Under construction

High School

Exponential Functions

Carbon Dating
Exponential Growth and Decay
Under construction
Comparing Models
Under construction
Compound Interest
Under construction
Population Dynamics
Under construction

Logic, Sets and Proof

Logic and ParadoxesAxioms and ProofProof by InductionInfinity and Hilbert’s Hotel

Middle School

Probability

Introduction
Probability Trees and Venn Diagrams
Under construction
Conditional Probability
Under construction
The Monty Hall Problem
The Birthday Problem
Under construction
True Randomness

Statistics and Data

Casino Mathematics
Data Visualisation
Under construction
Center and Spread of Data
Under construction
Sampling and Estimation
Under construction
The Wisdom of Crowds
Under construction
Linear Models
Under construction

Combinatorics

FactorialsPermutationsCombinations

High School

Graphs and Networks

IntroductionThe Bridges of KönigsbergHandshakes and DatingPlanar GraphsMap ColouringThe Travelling Salesman Problem
Scheduling Problems
Under construction
Graphs in Everyday Life

Codes and Ciphers

Introduction
Binary Numbers
Under construction
Error Detection
Under construction
Secret Codes
Under construction
The Enigma
Under construction
Public Key Cryptography
Under construction

Game Theory

The Prisoners’ Dilemma
Cards, Coins and Dice
Under construction
The Winning Move
Random Walks
Under construction

Chaos Theory

Introduction
Mathematical Billiard
Under construction
The Three Body Problem
Under construction
Phase Space and Strange Attractors
Under construction
The Logistic Map
Under construction
Popular Courses
Intermediate – Circles and Pi
Spheres, Cones and Cylinders
Intermediate – Sequences and Patterns
Fibonacci Numbers
Intermediate – Graphs and Networks
The Bridges of Königsberg
Advanced – Fractals
The Mandelbrot Set