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Mathematical Fundamentals

The essential tools for mastering algebra, logic, and number theory!

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.

Interactive
quizzes

28

Concepts and
exercises

225+
  1. 1

    Introduction

    Explore the foundations of algebra and logic without any rote memorization.

    1. Generalize

      Algebra was never meant to be memorized. Learn a new way to see.

    2. Rewrite, Rethink, Redraw

      Explore fractal patterns and compound interest in the mathematics of fractions.

    3. Thinking Forwards and Backwards

      To solve new problems, you need to be able to think in several directions.

  2. 2

    Logical Reasoning

    Logic shows you how to win!

    1. Included with
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      Reasoning from Results to Cause

      You can't trust everything you hear, but you'll always have logic.

    2. Included with
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      Werewolves of London

      Werewolves are predictably treacherous creatures. But they make for great puzzles.

    3. Included with
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      Eliminating the Impossible

      Once you eliminate the impossible, whatever remains must be the truth.

    4. Included with
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      A Treasure Hunt

      The real treasures are the truths we find along the way.

  3. 3

    Numerical Reasoning

    Use the basics of arithmetic and algebra to uncover properties of numbers.

    1. Included with
      Brilliant Premium

      Strategic Arithmetic

      Learn to sum 100 numbers at a glance with this one simple trick.

    2. Included with
      Brilliant Premium

      Dissecting Numbers

      See the composition of numbers in a brand new light.

    3. Included with
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      Divisible by 3

      Dividing numbers in clever ways is the first step towards number theory.

    4. Included with
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      Building Numbers to Spec

      Bring your divisibility rules, because not just any numbers will do.

  4. 4

    Contextual Reasoning

    Mathematical reasoning about the real world.

    1. Included with
      Brilliant Premium

      Compare the Pair

      Find the best deals in town by breaking down these problems.

    2. Included with
      Brilliant Premium

      Understanding Fractions

      A high-stakes Segway race puts you on the fast lane to comparing rates and ratios.

    3. Included with
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      Probability

      The Lumps has hit Flatland. Can you use probabilities to separate fact from fiction?

    4. Included with
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      Compound Interest

      Questionable business practices and multiplying fractions greater than one are quick ways to get exponential growth.

  5. 5

    Algebraic Reasoning

    Build and practice problem solving strategies with these algebra puzzles.

    1. Included with
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      Magical Variables

      Writing down equations is often the easiest way to organize information and solve problems.

    2. Included with
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      Reverse Engineering Arithmetic

      Find the patterns and you'll be able to solve these problems.

    3. Included with
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      Sums and Symmetry

      Algebra is all about maintaining symmetry and balance.

    4. Included with
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      How Much Altogether?

      Mix, match, and compare unknown values – then put them to work.

  6. 6

    Geometric Reasoning

    A new way of learning the algebra and identities that you thought you knew.

    1. Included with
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      Pythagoras' Theorem

      A visual proof of the most famous theorem in all of mathematics.

    2. Included with
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      The Distributive Property

      If you replace algebra with geometry, you'll never need to factor again.

    3. Included with
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      Difference of Squares

      This isn't how you learned this identity at school.

    4. Included with
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      Difference of Squares Challenges

      Put all your learnings to the test.