Mathematics · Beginner

Mathematical Foundations

Rebuild mathematics from the ground up. Every rule you were once told to memorise is rediscovered here — visually, logically, step by step — until it feels inevitable.

10 modules ~40 hours Beginner
Outcomes

What you'll be able to do

  • See why arithmetic rules work, not just how
  • Reason fluently with fractions, ratios and percentages
  • Translate word problems into clean algebra
  • Write your first rigorous arguments and proofs
Syllabus

Module by module

10 modules · about 40 hours of guided learning

01What a number really is

Place value, magnitude and estimation as a way of seeing quantity.

02Operations, visually

Area models for multiplication, number lines for subtraction, grouping for division.

03Fractions without fear

Parts, wholes and equivalence built from pictures, then made symbolic.

04Ratio, rate and proportion

The single idea behind speed, scale, recipes and percentages.

05Patterns and sequences

Spotting structure, describing it, then generalising it.

06The language of algebra

Variables as placeholders for 'any number' — and what that unlocks.

07Equations as balance

Solving by keeping both sides true, never by memorised moves.

08Geometry and measurement

Angles, area and the Pythagorean theorem through dissection proofs.

09Logic of proof

If–then reasoning, counterexamples and why 'it worked three times' isn't proof.

10Capstone: explain it back

Teach a concept of your choice from first principles.

How you'll learn

The WyPy way

See it first

Every idea starts as a picture or interactive model, then becomes notation.

Reason it through

Guided problems ask you to think and explain, not to copy a method.

Step by step

Short lessons with checkpoints, so each idea is solid before the next.

Is it for you?

Who this course is for

Designed for

Students who were taught maths as rules to memorise, adults returning to maths, and anyone heading into science or computing.

Before you start

None. This is the place to start.

Keep going

More foundations.

All courses
ThinkingPQ
Beginner

Logic & Structured Problem Solving

A toolkit for thinking clearly: decompose, model, test and verify — on puzzles first, then on real problems.

8 modules ~24 hrs
Mathematics
Intermediate

Algebra & Functions, Visually

Graphs that move, functions you can feel. Linear, quadratic and exponential thinking made intuitive.

9 modules ~32 hrs
Math × CS
Intermediate

Discrete Mathematics for Computer Science

Sets, logic, counting, induction and graphs — the mathematics that computers actually run on.

9 modules ~36 hrs