Welcome to Computational Mathematics
In the era of big data and ever-increasing computer power, Computational Mathematics methods are key drivers of progress and innovation in many areas of application that include:
- data science and machine learning,
- science and engineering,
- and numerous other areas of industry and government.
Solid skills in quantitative and computational modelling are now required for many of the most interesting and rewarding high-end jobs in banks, technology companies, industry and government. These skills are also crucial for progress in academic research in increasingly many fields.
Waterloo's Centre for Computational Mathematics offers undergraduate and masters degrees in Computational Mathematics that precisely teach those key quantitative and computational modelling skills. The following programs provide a world-class education in Computational Mathematics that gives students an edge for their professional or research careers:
- undergraduate major: Honours undergraduate plan in Computational Mathematics
- undergraduate minor: Computational Mathematics Minor
- Master of Mathematics (MMath) in Computational Mathematics
In addition, Waterloo's Computational Mathematics (CM) degrees provide students the unique opportunity of gaining co-op work experience in reputable global companies as part of their studies (during 4-month full-time work terms, well-paid).
Waterloo faculty members affiliated with the Centre for Computational Mathematics teach a large number of exciting CM classes, supervise CM masters students on their research projects, and carry out leading research in CM on the global stage. The Centre also promotes research interactions with industry and government, and holds monthly Colloquia where leading researchers highlight the newest advances in CM research.
What is Computational Mathematics?
Mathematical models and methods arise in a wide variety of fields, including business and finance, data science, engineering, science, machine learning, and medicine. The application of mathematics-inspired computational methods and models has revolutionized these fields and is one of the most significant achievements of the computer age and the data age.
Developing and analyzing such methods and models so that the numerical computations can be carried out efficiently, accurately and in a scalable manner involves more than classical mathematics and statistics and elementary computer science. They include issues such as:
- the efficiency, accuracy and stability of numerical computations,
- scalability of numerical algorithms to very large data,
- the implications of imprecision and round-off errors,
- the quantification of variability and uncertainties in results,
- the development and maintenance of mathematical software, and
- the effects of modern developments in computer architectures and networks
In the early days, these numerical methods and 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 methods and models and the exploding power of computers, there is now a great demand for specialists who thoroughly understand the theoretical and practical issues in computational mathematics. These specialists must be able to design new algorithms which cope with the computational demands, 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, statistics and computer science. Students in the program are exposed to a range of theme areas within the discipline and learn an area of application. Graduates of the program will be able to deploy effectively a wide range of mathematical, statistical and computational techniques to solve large problems in science, industry, big data and commerce; to develop, enhance and maintain the relevant software tools; and to communicate results of complex methods and models to end-users.
Some example applications of Computational Mathematics include: