Mathematics is studied both as a tool and for its own sake. Its usefulness in the sciences - physical, biological, social, behavioral, and environmental - and in decision-making processes is so established as to make it an indispensable part of many curricula.Mathematics is chosen as a major area of study by individuals who find it challenging, fascinating, and beautiful. It is also appreciated by many who seek primarily to use mathematics as a tool.A career in mathematics, except for teaching at the secondary level, generally requires a graduate degree as preparation. Careers include teaching, research, and the application of mathematics to diverse problems in institutions of higher learning, business, industry, and government.<br><br>Applied mathematics refers to those topics in mathematics that are most useful for analyzing real world applications in engineering, physics, chemistry, earth sciences and biological sciences. The emphasis is often on constructing a (sometimes nonlinear) model of the real world application, and then applying analytic and numerical/computational solution techniques to the differential, difference or integral equations that result. Job opportunities for applied mathematicians exist in most industries, as well as in the National Laboratories (e.g. Sandia, Los Alamos and Lawrence Livermore). Academic opportunities are also available for applied mathematicians with an advanced degree.<br><br>At UM, the applied mathematics group works in the areas of numerical analysis, perturbation methods and dynamical systems, with applications in astronomy, chemistry, biology, forestry, medical imaging, and pharmaceutical science, to name a few. Model development for problems in these studies is central, followed by the analysis of these models using numerical and analytical techniques, with the goal of a better understanding of the mechanisms at work in the phenomena. We offer courses in solution techniques (Ordinary Differential Equations, Partial Differential Equations, Numerical Methods, Linear Algebra) and modeling and qualitative analysis (Deterministic Models and Statistical, Dynamical and Computational Modeling).<br><br>The applied mathematics concentration also requires the ability to do rigorous analysis, so this option can be chosen by students planning to do graduate work in an applied science or in mathematics. Students in this concentration are urged to learn a computer language such as Matlab or Python, as these are often valuable in the analysis of applied problems.