# Graduate Study in Mathematics

While a career in mathematics can be very attractive, it takes time to acquire the necessary skills, particularly for basic research at the Ph.D. level. Graduate study is essential for most fields. The undergraduate course sequence provides a foundation upon which more advanced mathematics will be built. In graduate study, one or two further years of coursework completes this basic training. Thereafter, more specialized courses, often at the frontiers of research, are taken. Applied mathematics students will take courses in various application areas to acquire experience in modeling the real world, and to learn how mathematics can help with problems from the physical and biological sciences, and in finance.

The breadth and depth of work will depend on the degree level. With an M.S. degree, the student is prepared for many jobs in government, business, and industry; with the Ph.D. degree the choices are wider. Many Ph.D. mathematicians join the faculty of a university or four-year college, where they not only teach but also conduct research and publish their results in scholarly journals and books. Others take post-doctoral positions at various laboratories around the world, where work of interest to them is being done. Still others pursue careers in corporate research and management. With either an M.S. or a Ph.D., starting salaries are significantly higher than those of graduates with bachelor's degrees.

At both the M.S. and Ph.D. levels, graduate study in mathematics develops a number of important skills for solving problems suggested either by mathematics or by real world questions. Foremost is the ability to break complex issues into smaller, more manageable problems, until a model is reached which can be thoroughly studied and understood. Applied mathematics develops the art of extracting quantitative models from problems of physics, biology, engineering and economics. This ability comes from experience, such as that acquired gradually from examples studied in graduate courses.