Undergraduate major and minor, M.S., and Ph.D. Master's study is according to the standard option or an industrial mathematics option. Doctoral study requires a primary specialty in algebra, analysis, topology, probability and statistics, or applied mathematics, as well as a secondary specialty in one of these, or an appropriate area in another department. Proficiency in a higher programming language is also required for doctoral students. A doctoral minor is also available.

Atmospheric Sciences, with strong emphasis on mathematical modeling, is now a program in the Mathematical Sciences Department; see the separate subject section in this manual.

Subspecialties include theoretical mechanics; linear and mathematical programming and optimization; differential equations; vector analysis; mathematical models; numerical analysis; computational linear algebra; vector geometry; advanced calculus; probability theory; symbolic logic; number theory; differential and projective geometry; chaotic dynamical systems; engineering mathematics; real, functional, numerical, and complex analysis; Fourier analysis; boundary problems; mathematical fluid dynamics; functions of a real variable; algebraic topology; stochastic processes; theory of sets, groups, rings and modules; iterated maps as dynamical systems; special functions; integral transforms; homology; nonlinear dynamics; biostatistics; analysis of variance; nonparametric statistics; regression analysis; time series analysis; multivariate statistical analysis; decision theory; and hypothesis testing.

Research.

        The following LC classification range descriptions represent areas of concentration for mathematics:

         GB (Physical Geography): Hydrometerology.

        QA (Mathematics): General; Mathematical logic; Algebra (Combinatorics; Group theory; Linear algebra. Matrices; Number theory. Algebraic fields; Set theory. Fuzzy sets; Machine theory; Coding theory. Cryptography. Switching theory; Game theory); Probabilities; Stochastic processes; Mathematical statistics; Numerical analysis; Analysis (Calculus; Functional analysis; Theory of functions; Differential equations; Continuous groups; Analytical methods; Difference, functional, integral equations); Geometry (Algebraic geometry; Topology. Knot theory; Differential geometry). Selectively collected categories: Applied mathematics (i.e., business and other fields); Interpolation. Sequences. Series; Analytic mechanics (Dynamics).

        QC (Physics): Meteorology. Climatology. Atmospheric conditions and pollutants.

        T (Technology (general)): The following category is selectively collected: Applied mathematics. Quantitative methods.

        TA (TA Engineering (general). Civil Engineering (general)): Engineering mathematics. Engineering Analysis (Mathematical models). Selectively collected categories: Engineering mathematics. Engineering Analysis (General works).

English; some German and other European languages.