The Structures of Mathematical Physics: An Introduction

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups —— mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics —— such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equ...