Model catalog · 01 / 05

Mathematics

An algebraic expression and a geometric picture can describe the same relationship. The courses put calculations beside their drawings, so you can check the working and see how changing a number affects the picture.

28models08learning tracks

SetsIntervals

Introduction to sets

A set records which elements belong to it, regardless of order or repetition. Intervals and Venn diagrams show what union, intersection, difference and complement mean.

Reference age · UK/US 12+ · East Asia 12+Open model

First functionsCoordinates

Introduction to function

A rule turns an input into an output. Calculations, tables and graphs give us different ways to describe that relationship.

Reference age · UK/US 14+ · East Asia 13+Open model

Calculus

The definition of derivative

A curve can become steeper or flatter. We need a slope at each point, and a way to draw those slopes on another graph.

Reference age · UK/US 17+ · East Asia 17+Open model

First matricesBasis vectorsLinear maps

Matrix and linear transformation

The two columns of a matrix record where two basic directions go, determining what happens to the whole picture.

Reference age · UK/US 18+ · East Asia 18+Open model

Matrix multiplicationRows and columnsDot product

Matrix multiplication

One row and one column produce one entry. The individual multiplications and additions explain Ax, xA and AB.

Reference age · UK/US 18+ · East Asia 18+Open model

Linear algebraSubspacesLinear systems

Four fundamental subspaces

Some outputs of a matrix cannot be reached; others come from more than one input. These differences determine whether Ax = b has a solution, and whether it is unique.

Reference age · UK/US 19+ · East Asia 19+Open model

Number theoryCongruencesCompetition proofs

Congruences

Finding a large number’s last digit need not mean calculating the whole number. Congruences keep track of remainders, showing which arithmetic operations are valid, when factors can be cancelled and whether an equation has integer solutions.

Reference age · UK/US 16+ · East Asia 16+Open model

First groupsSymmetryCombining moves

A first look at groups

A labelled square can keep its outline after a turn or reflection while its letters move. Recording these operations lets us compare their order, combine instructions and find ways to undo them.

Reference age · UK/US 19+ · East Asia 19+Open model

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MathematicsMathematics

Mathematics