Explore the mathematical concept of tensors in this 27-minute video lecture. Gain a deeper understanding of tensors from a mathematician's perspective, learning their definition, properties, and applications in various fields of mathematics and physics. Discover how tensors generalize the notion of scalars, vectors, and matrices, and how they are used to represent multilinear maps between vector spaces. Delve into the abstract algebraic structure of tensors and their importance in differential geometry, relativity theory, and other advanced mathematical topics.