A career in this field might include the application of a wide range of mathematical and computational methods. For example, mapping and understanding the human genome relies on the use of sophisticated mathematical and computational tools. Newer and better tools make research quicker and cheaper, resulting in the creation of new career opportunities in technology, medicine, and drug development and design.
Data Mining and Data Privacy
Data mining allows the discovery of patterns and previously unknown information in large data sets. Emerging career opportunities can be found in applications of data mining in fields such as security, forensics, e-commerce, bioinformatics and genomics, astrophysics, medicine, and chemical and electrical engineering.
Materials science is the study of the properties, processing, and production of a broad range of existing and new materials, including metallic alloys, composites, liquid crystals, biological materials, and thin films. The rational design and analysis of materials depends on mathematical models and computational tools. Career opportunities abound in science, manufacturing, and materials design for applications in fields such as aerospace, engineering, electronics, biology, and nanotechnology.
Computer Animation and Digital Imaging
The Fields Institute in Toronto describes computer animation as “an eclectic science that uniquely combines mathematics, computer science, fine art, classical animation, physics, biomechanics, and anatomy, to name but a few fields. Algorithms for computer animation rely heavily on techniques from scientific computation, statistics, signal processing, linear algebra, control theory, and computational geometry.” With a diverse and exciting set of applications to such areas as medical diagnostics, entertainment (film, television, and video games), and fine arts (dancing, sculpture, painting), there are many avenues and career opportunities to explore.
Finance and Economics
Financial mathematics is the development of quantitative techniques and computational models used in the financial industry. Banks, insurance companies, investment and securities firms, energy companies and utilities, multinationals, corporations, government regulatory institutions, and other industries have come to rely on applied mathematics and computational science. Sophisticated math models and the computational methods and skills needed to implement them are used to support investment decisions, to develop and price new securities, to manage risk, and for portfolio selection, management, and optimization.
Professionals in these fields might look at populations and their interactions and model them as systems of differential equations that can be used to model diseases in human populations (i.e. the spread of infection under various immunization protocols). Other applications in these fields include the management of ocean fisheries and the study of insect population growth, spread, and reaction to insecticides.
Climatology depends on simulating the component forces that drive the climate, for example, ocean circulation and heat exchange between land, air, and ocean. It requires very sophisticated models based on physical principles, expressed as complex partial differential equations. These are implemented in very large-scale numerical codes on high-performance computers, and use data from observations of satellites, ocean buoys, and other monitoring equipment to drive the solutions.