Mathematical Fundamentals

Learn the essential tools for mastering algebra, logic, and number theory.


Rewrite, Rethink, Redraw

Thinking Forwards and Backwards

Reasoning from Results to Cause

Werewolves of London

Eliminating the Impossible

A Treasure Hunt

Mad Hatter Puzzles

Repairing Broken Puzzles

Strategic Arithmetic

Dissecting Numbers

Divisible by 3

Building Numbers to Spec

Numerical Logic

Compare the Pair

Understanding Fractions


Compound Interest

Magical Variables

Reverse Engineering Arithmetic

Sums and Symmetry

How Much Altogether?

Cryptogram Challenges

Pythagoras' Theorem

The Distributive Property

Difference of Squares

Difference of Squares Challenges

The Quadratic Formula

Course description

In this course, we'll introduce the foundational ideas of algebra, number theory, and logic that come up in nearly every topic across STEM. This course is ideal for anyone who's either starting or re-starting their math education. You'll learn many essential problem solving techniques and you'll need to think creatively and strategically to solve each challenge. Each exploration is designed to push your mathematical skills to the next level. Math isn't about memorizing formulas, it's about problem solving. It's about looking at patterns and predicting the future of those patterns, and it's about solving complex problems by using deductive reasoning to turn them into simple ones.

Topics covered

  • Algebraic Expressions
  • Arithmetic Operators
  • Cryptogram Puzzles
  • Discount Finance
  • Divisibility
  • Divisibility Rules
  • Logic Fundamentals
  • Rates and Ratios
  • Sequences
  • The Distributive Property
  • Variables

Prerequisites and next steps

This course is for anyone who remembers middle school math (basic algebra and fractions), and is ready for a refresher and new challenges on core mathematical concepts.

Next steps

  • Scientific Thinking
  • Computer Science Fundamentals