The Language of Mathematics

Abstract Algebra · Axiom Academy

INTRO The Language of Mathematics Discover how numbers, rotations, and matrices speak the same mathematical language through shared structural patterns. Let's start with something familiar: adding numbers. Click the properties below to see examples of how addition behaves. Now let's explore something completely different: rotating a square. Click the buttons to rotate the square and combine rotations. Let's look at one more example: multiplying 2×2 matrices. Select matrices to multiply and observe the patterns. Drag each property to match it with the structures where it appears. Some properties work for all structures! The Language of Abstract Algebra

This is the written version of the interactive lesson above. See the full Abstract Algebra course.