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01. Linear algebra and matrix theory.
02. Real and complex analysis including approximation theory, integral transforms (including Fourier series and wavelets), integral equations, asymptotic methods, and special functions.
03. Ordinary differential equations including dynamical systems.
04. Partial differential equations including inverse problems.
05. Discrete mathematics and graph theory including combinatorics, combinatorial optimization, and networks.
06. Numerical analysis (theory).
07. Computational mathematics including scientific computing, parallel computing, and algorithm development.
08. Computer science including computer architecture, computer hardware, computational complexity, applied logic, database, symbolic computation.
09. Applied probability including stochastic processes, queueing theory, and signal processing.
10. Statistics including data analysis and time series analysis.
11. Control and systems theory including optimal control.
12. Optimization theory and mathematical programming including discrete and numerical optimization and linear and nonlinear programming.
13. Communication theory including information theory and coding theory.
14. Applied geometry including computer-aided design and related robotics.
15. Image processing including computer graphics, computer vision, related robotics, and tomography.
16. Classical mechanics of solids including elasticity, structures and vibrations, and constitutive models.
17. Fluid mechanics including turbulence, aeronautics, and multiphase flow.
18. Quantum physics, statistical mechanics, and relativity
19. Geophysical sciences including reservoir modeling, seismic exploration, and petroleum engineering.
20. Atmospheric and oceanographic sciences.
21. Chemical kinetics, combustion theory, thermodynamics, and heat transfer.
22. Biological sciences including biophysics, biomedical engineering, and biomathematics.
23. Environmental sciences.
24. Economics.
25. Social sciences.
26. Functional analysis and operator equations, and integral and functional equations.
27. Management sciences including operations research.
28. Applied mathematics education (K-12, undergraduate curriculum, graduate study and modeling courses).
29. Astronomy, planetary sciences, and optics.
30. Simulation and modeling.
31. Materials science, polymer physics, and structure of matter.
32. Electromagnetic theory, semiconductors, and circuit analysis.
40. Applications of Mathematics and Computation in Industry
43. Dynamical Systems
44. Nonlinear Waves and Coherent Structures
48. Data Mining
99. General Interest