Applied Mathematics

Applied mathematics is the branch of mathematics that is focused on developing mathematical tools and applying those tools to science, engineering, industry, and society. It includes mathematical topics such as partial and ordinary differential equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, and probability. Applied mathematicians use mathematical modeling techniques to solve the exciting and challenging real-world problems all around us.

Computational Science

Computational science is a multidisciplinary field focused on integrating applied mathematics, computer science, engineering, and the physical sciences. While theory and experimentation are common tools in the scientific community, computational science has become a third pillar to advance scientific knowledge and practice, allowing scientists and engineers to simulate real-world scenarios, propose solution methodologies, and test those solutions in a cost-effective fashion before attempting to deploy them in the real-world.

Data Science

Technology advances have allowed for the collection of vast amounts of data of all types. Data science is an interdisciplinary field that deals with all aspects of data management and analysis. Data scientists are involved in:

• data collection, including determining what data should be collected to answer a question
• data processing, including mining, classifying, summarizing
• analyzing, including qualitative and quantitative analysis, regression, and predictive analysis
• communicating the results, including using appropriate visualization tools, so they can be used to make strategic decisions

How Are They Used?

Applied mathematics, computational science, and data science are utilized in almost every discipline of science, engineering, industry, and technology. Industry relies on these tools for the design and manufacture of aircraft, automobiles, textiles, computers, communication systems, prescription drugs, and more. Work with applied mathematics often leads to the development of new mathematical models, theories, and applications that contribute to diverse areas of science.

Examples of the use of applied mathematics, computational science and data science:

• Simulation and prototype testing are used in manufacturing design and evaluation. For example, automotive companies are using computer-aided design to test for performance, safety, and ergonomics. In doing so, they dramatically lower the cost of constructing and testing prototypes.
• Computational simulations in aircraft design have been used to analyze the lift and drag of airfoil designs since the early days of computing. Advanced computation and simulation are now essential tools in the design and manufacture of an aircraft.
• A major advance in computing power will enable scientists to incorporate knowledge about interactions between the oceans, the atmosphere and living ecosystems, such as swamps, forests, grasslands, and the tundra, into the models used to predict long-term change. Climate modeling at the global, regional, and local levels can reduce uncertainties regarding long-term climate change, provide input for the formulation of energy and environmental policy, and abate the impact of violent storms.
• Accurate simulation of combustion systems offers the promise of developing the understanding needed to improve efficiency and reduce emissions as mandated by U.S. public policy. Achieving predictive simulation of combustion processes will require exascale computing and an unprecedented level of integration among disciplines including physics, chemistry, engineering, mathematics, and computer science.
• Meeting the needs of nuclear stockpile stewardship and management for the near future requires high-performance computing far beyond our current level of performance. The ability to estimate and manage uncertainty in models and computations is critical for this application and increasingly important for many others.
• Applied mathematics, computational science and data science are also useful in finance to design trading strategies, assist in asset allocation, and assess risk. Many large and successful hedge fund companies have successfully employed mathematics to do quantitative portfolio management and trading.

Where Could I Work?

Applied mathematicians, computational scientists and data scientists often hold jobs with titles such as actuary, statistician, scientific programmer, systems engineer, analyst, research associate, and technical consultant. They work for federal and state governments, financial services, and scientific research and development services, as well as management, scientific, and technical consulting services. Software publishers, insurance companies and aerospace, pharmaceutical, and other manufacturing companies also employ applied mathematicians, computational scientists and data scientists. Many work in academia, teaching the next generation and developing innovations through their own research.