You can add, subtract, and multiply, but you can’t always divide (e.g., 1 divided by 2 is not an integer). Polynomials: Expressions like
There is a "neutral" element (like 0 in addition) that leaves others unchanged. Algebra: Groups, rings, and fields
If you'd like to dive deeper into one of these structures, let me know if you want: You can add, subtract, and multiply, but you
💡 These structures are nested. Every field is a ring, and every ring is a group. By stripping away specific numbers and focusing on these structures, mathematicians can solve massive classes of problems all at once. Every field is a ring, and every ring is a group
Groups are the mathematical tool for studying symmetry. Whether it is rotating a square or shuffling a deck of cards, groups help us classify how objects can be transformed without losing their essential form. Adding Complexity: Rings
The order of grouping doesn't change the result.
Every element has an opposite that brings it back to the identity.