
Comprehensive exploration of scalars and vectors in physics, covering definitions, types, operations, and properties, with practical examples and numerical problem-solving.

Explore Hopf-Galois theory, its applications in field extensions, and arithmetic properties derived from algebraic curves. Gain insights into this generalization of classical Galois theory.

Explore convex integration and mixing flows in hydrodynamics, focusing on the Muskat problem and alternative approaches to understanding fluid behavior in unstable regimes.

Explore non-semisimple TQFTs and modified traces in topology, focusing on construction methods, invariants, and mapping class group representations derived from modular categories.