Mathematical models arise in a wide variety of fields, including weather forecasting, engineering, business and finance, science, and medicine. The application of computer methods to simulate such models has revolutionized these fields and is one of the most significant achievements of the computer age.

Developing and analyzing such models so that the computer simulations can be carried out efficiently and accurately involves more than classical mathematics and elementary computer science. They include issues such as:

- the implications of imprecision and round-off errors, the efficiency
- accuracy and stability of numerical computations
- the development and maintenance of mathematical software, and
- the effects of modern developments in computer architectures and networks

Until recently, models and the corresponding software tools were primarily developed by practitioners in the application area (for example, by engineers, scientists, finance graduates). Because of the growing complexity of the models and the exploding power of computers, however, **there is now a significant demand for specialists who thoroughly understand the theoretical issues in computational mathematics**. These specialists must be able to design new algorithms which cope with the computational demands of the simulations, and to develop robust software to implement these algorithms.

Computational Mathematics at the University of Waterloo is an innovative, multidisciplinary program whose focus lies in the intersection of mathematics and computer science. Students in the program are exposed to a range of theme areas within the discipline - selecting two areas for further specialization - and learn one area of application. Graduates of the program will be able to deploy effectively a wide range of mathematical and computational techniques to solve large problems in science, industry and commerce; to develop, enhance and maintain the relevant software tools; and to communicate results of complex modeling and simulation to end-users.

These are a few examples of ongoing projects in Computational Mathematics: