What does mean Mathematical Physics? The Journal of Mathematical Physics defines the field as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories"Journal of Mathematical Physics

Classical Physics Mechanics, Electrodynamics, Acoustics, Hydrodynamics, Thermodynamics, Aerodynamics,  Partial Differential Equation  Variational Methods  Fourier Analysis  Potential Theory  Vector and Matrix Analysis  Symplectic Geometry

Quantum Mechanics and Quantum Field Theory Functional Analysis Operator Theory Hilbert Spaces Partial Differential Equation Lie Groups and Lie Algebras Probability Special Function and Polynomials Complex Analysis Representation Theory

Relativity and Cosmology Special and General Relativity Tensor Analysis Differential Geometry Topology

Statistical Mechanics Probability Ergodic Theory Operator Algebra

Mathematical Physics and Theoretical Physics Theoretical physics emphasizes the links to observations and Experimental Physics which often requires theoretical physicists (and mathematical physicists in the more general sense) to use heuristic, intuitive, and approximate arguments. Such arguments are not considered rigorous by mathematicians. Arguably, rigorous mathematical physics is closer to mathematics, and theoretical physics is closer to physics. This is reflected institutionally: mathematical physicists are often members of the mathematics department.

A Mathematical Physics Program Mathematics Courses Differential Geometry Differential Topology Geometric Analysis Topology Lie Theory Homological Algebra Complex Geometry Modular Forms Algebra Infinite Dimensional Lie Groups Integrable Models Global Riemannian Geometry Kaehler Geometry Algebraic Geometry

Physics Courses Quantum Field Theory String Theory Conformal Field Theory Supersymmetry and Unification General Relativity Phenomenology of Physics Beyond Standard Model

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