By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most ...

Differential Galois theory extends the classical study of algebraic symmetries into the realm of differential equations. This area investigates the relationship between a differential equation’s ...

Modern Algebra Group theory - basic properties, permutation groups, finite Abelian groups, cosets, normal subgroups, homomorphism theorems, representation. Ring theory - integral domains and fields, ...

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses. “I’m nearly at the end of the talk, and it’s ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? Representation theory transforms abstract algebra groups into things like simpler ...