Applied mathematics and statistics are branches of mathematics that are devoted to the use of mathematical methods and reasoning to solve real-world problems of a scientific or decision-making nature in a wide variety of subjects, principally (but not exclusively) in engineering, medicine, the physical and biological sciences, and the social sciences. Applied mathematical modeling often involves the use of systems of (partial) differential equations to describe and predict the behavior of complex real-world systems that unfold dynamically in time. Statistics, construed broadly, is the study of uncertainty: how to measure it (using ideas and methods in probability theory), and what to do about it (using concepts from statistical inference and decision theory).
Applied mathematics and statistics faculty offer courses under the sponsorship of the School of Engineering. Applied mathematics and statistics faculty also teach courses in collaboration with Mathematics, Economics, and other departments.
Graduate programs leading to M.S. and Ph.D. degrees in applied mathematics and statistics are currently under development and review. At present, students wishing to pursue graduate study in these subjects should apply for admission through the existing graduate programs in Computer Science, Physics, stating clearly in the application process that they are interested in graduate study in Applied Mathematics and Statistics.
Undergraduate Programs
Requirements for an Undergraduate Minor in Statistics
The statistics minor is available for students who wish to gain a quantitative understanding of how to (a) measure uncertainty and (b) make good decisions on the basis of incomplete or imperfect information, and to apply these skills to their interests in another field. This minor could also be combined with a major in mathematics as a preparation for a graduate degree in statistics or biostatistics.
Students are required to take a two-quarter basic calculus sequence:
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Basic calculus sequence: Applied Mathematics and Statistics 11A-B or Economics 11A-B or Mathematics 11A-B or Mathematics 19A-B or Mathematics 20A-B
Plus one course from each of the following nine categories:
- Statistical Concepts: Applied Mathematics and Statistics 5 or 7/L
- Computer Programming: Bioinformatics 60 or Computer Science 12A/L or 5C or 5J or 5P or Computer Engineering 13/L
- Engineering Mathematics or Linear Algebra: Applied Mathematics and Statistics 27/L or Applied Mathematics and Statistics 10 or Mathematics 21
- Multivariate Calculus: Mathematics 22 or 23A
- Probability: Applied Mathematics and Statistics 131 or Computer Engineering 107
- Statistical Inference: Applied Mathematics and Statistics 132 or Applied Mathematics and Statistics 162
- Computational Methods: Applied Mathematics and Statistics 147
- Bayesian Statistics: Applied Mathematics and Statistics 206
- Statistical Elective: Applied Mathematics and Statistics 198, or Applied Mathematics and Statistics 205A, or Biomolecular Engineering 205, or Computer Engineering 108, or Economics 114, or Electrical Engineering 151, or Mathematics 114, or Psychology 181, or Sociology 103A
Students planning graduate work in statistics are recommended to choose Mathematics 23A and Applied Mathematics and Statistics 205A, and also to take Mathematics 23B and Mathematics 105A-B.
Requirements for an Undergraduate Minor in Applied Mathematics
The applied mathematics minor is available for students who wish to develop (1)proficiency in modeling real-life problems using mathematics and (2) knowledge of standard, practical analytical and numerical methods for the solution of these models. This minor could be combined with a major in any of the physical, biological, mathematical, or engineering sciences as preparation for a graduate degree in that field or in applied mathematics.
Students are required to take the four-quarter calculus sequence:
- Calculus Sequence: Mathematics 19A-B and Mathematics 23A-B
Plus one of the following sequences:
- Applied Mathematics and Statistics 10 and 20
- Mathematics 21, Mathematics 24, and Applied Mathematics and Statistics 27L
- Physics 116A, Physics 116B, and Applied Mathematics and Statistics 27L
Plus one course from each of the following categories:
- Probability Theory: Applied Mathematics and Statistics 131 or Computer Engineering 107
- Dynamical Systems: Applied Mathematics and Statistics 114 or Applied Mathematics and Statistics 214
- Introduction to Numerical methods: Applied Mathematics and Statistics 147, Physics 115, or Earth Sciences 119
- Partial Differential Equations: Applied Mathematics and Statistics 212A, Physics 116C, or Mathematics 106B
Plus one applied-mathematics elective from the following list:
- Applied Mathematics and Statistics 107/217, 115/215, 132, 198, 212B, 213, 216, 231, 290B
Students may also propose other electives which use applied mathematical methods, subject to approval by the department.
