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Introduction to Algebra

Supercharge your thinking with the language of algebra.

This course explores the twin pillars of algebraic thinking—equations and graphs. With these two tools, we'll unpack algebra's big ideas and develop a powerful perspective to solve its essential problems.

By the end of this course, you'll understand graphs and their relationship to the equations they represent, enabling you to answer questions involving equations even when it's impossible to solve them by hand. Though a familiarity with solving equations is helpful, we'll start with a review of the basics and build on them throughout the course.



Concepts and

  1. 1


    Describe the world with the language of algebra.

    1. Writing Algebra

      Use algebra to trace the relationships between multiple unknown quantities.

    2. Calculation Shortcuts

      Sometimes asking a simpler question can produce the same answer for less.

    3. Graphical Reasoning

      Graphs can reveal surprising relationships and bypass calculation.

  2. 2


    Understand and solve equations.

    1. Included with
      Brilliant Premium

      Algebraic Relationships

      Use visual representations to analyze quantities.

    2. Included with
      Brilliant Premium

      Solving Equations

      Learn to solve equations by isolating variables.

    3. Included with
      Brilliant Premium

      Two Variable Equations

      Extend your thinking to equations with more variables.

  3. 3


    See the structure of algebraic relationships.

    1. Included with
      Brilliant Premium

      Creating Points

      Coordinates give us the tools to describe locations with precision.

    2. Included with
      Brilliant Premium

      Connect the Dots

      Reason about equations to uncover their properties and patterns.

    3. Included with
      Brilliant Premium

      Graph Menagerie

      Take a tour of the variety of shapes that equations can form.

    4. Included with
      Brilliant Premium

      Interpreting Graphs

      Use graphs to solve problems that resist algebraic unpacking.