#### Mathematics Fundamentals

Demonstrate basic mathematical understanding and computational skills in calculus, linear algebra, and differential equations, and advanced calculus.

#### Effective Reasoning and Communication

Explain and criticize mathematical reasoning through speaking and writing in a precise and articulate manner.

#### Statistics

Demonstrate a knowledge of inference, estimation, regression, multivariable statistics, Bayesian statistics, time-series analysis, and state-space modeling.

#### Advanced Applied Mathematics

Demonstrate understanding of linear and nonlinear analysis, the analysis of algorithms, combinatorics, asymptotic methods, approximation theory, transform theory, optimization, dynamic programming, probability theory, stochastic processes, differential equations, dynamical systems and optimal control theory.

#### Computing

Demonstrate facility in computer programming, data processing, databases, numerical simulation, scientific visualization, and virtual experimentation. Write, compile and execute numerical algorithms in a low-level language, such as C/C++, as well as develop I/O wrappers for standard numerical libraries in a common scripting language, such as Python.

Demonstrate the ability to use the technologies for parallel and distributed computing.