| Application | Key Mathematics Areas |
| Acoustic and electromagnetic propagation models for use in matched filters to compare with sensor data | stochastic processes, harmonic analysis, differential equations, statistics, numerical methods |
| Models of acoustic and electro-magnetic sensors; predict power requirements and performance | differential equations, numerical methods, physics |
| Predicting performance of proposed sonar, radar, or communication systems | stochastic processes, harmonic analysis, differential equations, statistics, numerical methods |
| Models and algorithms that allow sensors and other systems to process and assess information automatically and autonomously | stochastic processes, stochastic filtering, harmonic analysis, statistics, numerical methods |
In all these applications computer software plays an important role, both in the implementation of algorithms and for simulation when models are too difficult to get in "closed form". Some sort of quantitative analysis is often needed to make decisions about what sort of technology to pursue in future years (third use listed above); engineers and managers are often looking to quantitatively compare two or more different possible systems, and some quick/simple model has to be proposed and its mathematical properties assessed.
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