Applied Mathematics, Ph.D.

Program Description

appliedmath.ucmerced.edu
Contact: Applied Mathematics Graduate Committee, online contact form

Applied Mathematics involves the use of analytical and computational mathematics to solve real-world problems. Its core is based on modeling, analysis and scientific computing. The Applied Mathematics graduate program offers opportunities for students interested in multidisciplinary mathematics projects at the interface with life sciences, physical sciences, engineering and social sciences. Master of Science (M.S.) and Doctor of Philosophy (Ph.D.) degrees are offered. The coursework provides training in the fundamental tools of applied mathematics, including ordinary and partial differential equations, asymptotic and perturbation methods, numerical analysis and scientific computing. An explicit goal of applied mathematical sciences is to contribute significantly to another discipline. Hence, the objective of applied mathematics is to foster multidisciplinary research and education.

During a student’s first year, he or she will take Applied Mathematics Core courses, take the preliminary exams, and become familiar with the various active research areas in the faculty graduate group. In the second year, a student will complete the Core courses, take Special Topics courses, and begin working on a M.S. or Ph.D. research project. M.S. students typically complete their degrees in two years. Ph.D. students take their qualifying exam in the second or third year of studies, and are expected to complete their degrees in four to six years total.

M.S. and Ph.D. graduates in Applied Mathematics will find a wide variety of careers and ongoing study opportunities. Employers value the analytical and computational skills acquired through the training provided in Applied Mathematics. Potential employers include government and industrial research labs in a broad array of fields including engineering, energy, telecommunications, transportation and pharmaceutical sciences, as well as consulting firms, financial institutions, schools, etc. The unique combination of solid mathematical background, computational expertise and advanced knowledge of an application area places our graduates ahead of the curve on a job market that increasingly values interdisciplinary research. Graduates seeking a career in academia as post-doctoral researchers or college professors will be in a distinctly favorable position through their teaching and research training, and through the breadth of their mathematical, computational, and scientific qualifications.

All Applied Mathematics graduate students are required to pass preliminary exams offered in the first year of studies, and to complete the five core courses covering partial-differential equations, asymptotic and perturbation methods, numerical methods and scientific computing. Details regarding specific degree requirements may be found at appliedmath.ucmerced.edu/academics/graduate-studies/degree-requirements.

Program Learning Outcomes

Upon graduating, we expect students completing the PhD degree in Applied Math to be able to:

1. Solve advanced mathematical problems using analytical methods.
2. Solve advanced mathematical problems using computational methods.
3. Give clear and organized written and verbal explanations of mathematical ideas to a variety of audiences including teaching undergraduate students.
4. Model real-world problems mathematically and analyze those models using their mastery of the core concepts.
5. Recognize ethical and responsible conduct and learn how to apply them to research.
6. Make an original and significant contribution to the knowledge in a chosen research subfield of Applied Mathematics.