Mathematical Physics

Advanced mathematical methods and structures in physics

Mathematical Physics#

Mathematical physics explores the advanced mathematical structures and methods that underlie physical theories.

Topics#

  • Differential Geometry
  • Topology in Physics
  • Lie Groups and Algebras
  • Fiber Bundles
  • Manifold Theory
  • Category Theory
  • Algebraic Topology
  • Symplectic Geometry
  • Complex Analysis
  • Functional Analysis
  • Group Theory
  • Representation Theory
  • Quantum Groups
  • Homological Algebra
  • Algebraic Geometry
  • Operator Theory
  • Noncommutative Geometry
  • Index Theory
  • K-Theory
  • Morse Theory

Resources#

Books#

  • Geometry, Topology, and Physics by Mikio Nakahara
  • The Geometry of Physics by Theodore Frankel
  • Mathematical Physics by Robert Geroch
  • Methods of Mathematical Physics by Richard Courant and David Hilbert

Online Resources#

Practice Problems#