Applied mathematical science involves the use of analytical and
computational mathematics to solve real-world problems. Its core
is comprised of modeling, analysis and scientific
computing. Using that core, applied mathematical scientists
study a broad spectrum of problems across several
disciplines. In fact, applied mathematicians are connected more
closely through their shared approach and attitude toward
interdisciplinary research rather than a shared interest in any
particular set of problems. Moreover, an explicit goal of
applied mathematical science is to contribute significantly to
another discipline. Hence, the objective of applied mathematics
is to foster interdisciplinary research and education.
Research and education in applied mathematical science involves
four stages. The first stage is finding an interesting problem
that may benefit from mathematical analysis. The second stage is
developing an abstract model (i.e., a "mathematical model") that
describes salient features of the problem. The third stage is
applying existing analytical and computational methods or
developing new methods to solve the mathematical model. The
fourth stage is to determine what insight the mathematical model
has provided to the original problem.
Applied mathematicians are inherently interdisciplinary. As
mentioned above, applied mathematicians are connected closely
through their shared approach toward interdisciplinary
research. They are individuals who are well trained in the
development of mathematical models for real-world problems,
and the modern analytical and computational tools to solve
them. A strong group of applied mathematicians can be a great
asset to any number of scientific and engineering programs
within the university where they can provide the
theoretical/quantitative support or foundation.
Applied mathematics research requires a deep understanding of
mathematics and broad knowledge of other disciplines. Applied
mathematicians must be well-trained in fundamentals of
mathematics to model, analyze and compute solutions to
real-world problems. Real-world mathematics problems usually
are not amenable to complete abstraction. Therefore, they
often do not fall within the admissible set of problems for
"pure" mathematics research. Instead, applied mathematicians
must work through these issues to respect the connections that
any mathematical analysis will have to the
application. Because mathematics serves as the framework for
so many different areas in science and engineering, applied
mathematicians are continually increasing their breadth of
knowledge in other fields. In fact, applied mathematics
research is usually assessed through two criteria: (1) the
sophistication of the mathematics used and (2) the novelty of
the application.
Please visit the links below to explore more the applied
mathematics research going on at UC Merced.