Quantum mechanics is a branch of science that studies how tiny particles such as atoms, electrons, and photons act. It tries to explain how these particles behave in different situations. Mathematical formulations of quantum mechanics are mathematical equations (like algebra) that are used to describe the behavior of these particles. These equations tell us how the particles move, what positions they take, and how they interact with other particles. By using these equations, scientists can better understand quantum particles and use this knowledge to create new technologies.