Symmetries in Physics

This lecture introduces the concept of symmetries in physics, focusing on group theory as a mathematical framework. The instructor explains the properties of groups, including associativity, identity, and inverses, using examples like real numbers and permutations. The lecture highlights the importance of symmetries in describing physical systems and how different coordinate choices can be related through reparameterizations, forming a group of symmetries. The instructor emphasizes the role of symmetries in keeping the form of equations of motion unchanged, leading to the concept of subgroup and symmetries of a system.