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1 | P a g e BROWN UNIVERSITY Division of Applied Mathematics Guide to Undergrad

1 | P a g e BROWN UNIVERSITY Division of Applied Mathematics Guide to Undergraduate Programs Revised February 6, 2014 2 | P a g e Table of Contents INTRODUCTION 3 WHAT IS APPLIED MATHEMATICS? 3 CAREER PATHS 4 APPLIED MATHEMATICS AT BROWN 4 FREQUENTLY ASKED QUESTIONS 5 CHOOSING COURSES 6 INTRODUCTION 6 ROADMAP 6 SAMPLE COURSE PROGRAMS 9 INDEPENDENT STUDY 11 SENIOR SEMINARS 11 THE WRITING REQUIREMENT 12 STANDARD CONCENTRATIONS 13 APPLIED MATHEMATICS PROGRAM — A.B. DEGREE 13 APPLIED MATHEMATICS PROGRAM — SC.B. DEGREE 13 APPLIED MATHEMATICS–BIOLOGY — SC.B. DEGREE 14 APPLIED MATHEMATICS–COMPUTER SCIENCE — SC.B. DEGREE 15 APPLIED MATHEMATICS–ECONOMICS CONCENTRATION 16 CONCENTRATION ADVISORS 19 UNDERGRADUATE RESEARCH 21 HONORS PROGRAM 21 PRIZES 23 THE ROHN TRUELL PREMIUM PRIZE 23 SIGMA XI 23 APPLIED MATHEMATICS COURSES TO BE OFFERED IN 2011-2012 24 COURSES 25 COURSES IN APPLIED MATHEMATICS 25 COURSES IN OTHER DEPARTMENTS 38 3 | P a g e Introduction This short guide is intended to give students and faculty an overview of the undergraduate program in Applied Mathematics at Brown University, and to answer some of the commonly raised questions. Applied Mathematics is an interdisciplinary subject involving both mathematics and many areas of application. More so than in many other areas it is important to have an overview of the subject and how it relates to other programs at Brown. What is Applied Mathematics? Applied Mathematics has a profound impact on our daily lives. Whether it is weather forecasts, search engines, climate research, secure online shopping, or movie recommendations, none of these would work the way they do without algorithms and tools from the mathematical sciences. More generally, Applied Mathematics is an inherently interdisciplinary subject, which covers a wide spectrum of scientific activities. It is the mathematics of problems arising in the physical, life and social sciences as well as in engineering, and provides a broad qualitative and quantitative background for use in these fields. Owing to its nature, Applied Mathematics appeals to people with a variety of different interests, ranging from those with a desire to obtain a good quantitative background for use in some future career, to those who wish to have a better understanding of the basic mathematical aspects of other fields, or to those who are interested in the fundamental mathematical techniques and approaches in themselves. Many students begin taking courses in the Division of Applied Mathematics and discover their favorite areas of study as they go along. The program stresses but is not limited to computing, differential equations, and applied probability which are areas of mathematics that are used most often in applications in science, society and industry. The curriculum of the Division is flexible enough to meet the goals and interests of a very wide range of students. The basic mathematical skills of Applied Mathematics come from a variety of sources, which depend on problems from areas of interest: the theory of ordinary and partial differential equations, matrix theory, statistical sciences, probability and decision theory, risk and insurance analysis, the classical methods for formulating and solving problems in the sciences, operational analysis, optimization theory, the mechanics of solid materials and of fluids flows, numerical analysis, scientific computation and the science of modern computer based modeling. Students take courses in applied mathematics for many reasons, not necessarily with an applied mathematics concentration in mind. The value of learning about applied mathematics goes beyond a career opportunity. It provides an education in the use of quantitative methods in thinking about and solving problems: knowledge that is valuable in all walks of life. 4 | P a g e Career Paths The various concentrations in Applied Mathematics do prepare students for a great variety of career opportunities. In recent years, students who have followed one of the undergraduate concentrations in Applied Mathematics have gone into many different areas including: banking, finance, and investment sector; actuarial and insurance sector; computer and software industry; consulting companies; teaching; graduate study in applied mathematics, business, economics, engineering, physical or earth sciences; scientific careers in industry or government service; medical school; operations research or statistical analysis in industry or government agencies. In particular, courses offered in applied mathematics provide the preparation needed for several of the actuarial professional examinations. Business schools often seek graduate applicants with a good background in applied mathematics and economics. If you would like to find out more about what Applied Mathematics is useful for and which types of careers people pursue with a degree in Applied Mathematics, please have a look at SIAM's career brochure at http://www.siam.org/careers/thinking/pdf/brochure.pdf or go to the career pages of the following professional societies: American Mathematical Society (AMS) http://www.ams.org/profession/ca reer-info/career-index Society for Industrial and Applied Mathematics (SIAM) http://www.siam.org/careers/ Mathematical Association of America (MAA) http://www.maa.org/careers/ American Statistical Society (ASA) http://www.amstat.org/ Association for Women in Mathematics (AWM) http://www.awm-math.org/ Institute for Operations Research and the Management Sciences (INFORMS) http://www.informs.org National Academy of Sciences http://www.nap.edu Casualty Actuarial Society http://www.casact.org Society of Actuaries http://www.soa.org Each fall, the American Mathematical Society publishes an informative online guide entitled Assistantships and Graduate Fellowships in the Mathematical Sciences, which may be useful for undergraduates interested in pursuing a graduate degree in the mathematical sciences. Applied Mathematics at Brown Brown University is unusual in having a separate department devoted to Applied Mathematics. The Division of Applied Mathematics was created in 1941 in response to the awareness of the contributions that such a program could make to the dramatically increasing national scientific and engineering needs of that period. Since then the scope and interests of the Division have developed as the subject areas have evolved. 5 | P a g e The Division of Applied Mathematics provides a special environment for the interaction of people with varied scientific interests. The Division draws together faculty who elsewhere might be dispersed in quite different departments, depending on their primary interests. The standard Applied Mathematics concentrations lead to either the A.B. or Sc.B. degrees. The program is very flexible. Numerous joint programs with other departments are described below, and individual concentrations suited to particular needs can be arranged. The range of offerings, either within Applied Mathematics alone or in combination with offerings of other departments, provides almost endless opportunities. Frequently Asked Questions A list of frequently asked questions (and answers) about our undergraduate program can be found on the Division’s website at http://www.dam.brown.edu/undergraduate/. 6 | P a g e Choosing Courses Introduction The courses in Applied Mathematics are designed for students with a wide range of goals and are not limited to the needs of students following an applied mathematics concentration. There are many opportunities for students to explore different subject areas and see which they find most interesting. At the end of this undergraduate guide, we list and explain the courses offered by the Division and a selection of courses from other departments that are relevant to applied mathematics by either giving further applications or providing additional mathematical background. In the present section, we discuss a few general guidelines and recommendations for choosing courses. When choosing courses consider what your goals are. Do you wish to pursue applied mathematics at a graduate level? Do you wish to gain a good basis in applied mathematics at an undergraduate level, but intend later to pursue some other related area? Are you simply taking courses for general understanding and knowledge? A general recommendation for students planning to follow graduate study in any subject relating to applied mathematics (engineering, economics, physics, chemistry, computer science, etc.) is to complete the three semester calculus sequence MATH 0090, 0100 and 0180 or the equivalent; and in addition to complete the linear algebra course MATH 0520 or MATH 0540. This recommendation is also sound advice for all students. Students taking courses in applied mathematics start either with one of the lower level courses (APMA 0090 or APMA 0160) or with the Mathematical Methods courses APMA 0350/0360 (or 0330/0340), which provide many of the basic approaches used in applied mathematics. The Statistical Inference course APMA 1650 provides the introduction to the other courses in statistics and operations research, while APMA 1170 gives a good overview of numerical methods. Beyond these comments, students should select courses so that they pursue specific topic areas in a coherent manner. Students following the applied mathematics concentration and intending to go on to graduate study in this subject should take some additional mathematics courses, such as those mentioned later in this section. Faculty concentration advisors will be glad to give advice on course selections to all students. Roadmap The following two pages contain a roadmap for choosing courses and explain in particular some of the prerequisites that determine the order in which courses should be taken. Beginning in Fall 2014, Applied Math will offer a new class APMA 0090 to freshman exploring applied math. Roadmap'to'Choosing'Courses'(Explanation'of'Prerequisites)' Courses'Intended'for'Non<Majors:' APMA$0180,$0410,$0650$ $ Courses'to'Fulfill'the'Programming'Concentration'Requirement' APMA$0090,$0160,$CSCI$0040,$0150,$0170$ $ Prerequisites:' Most$courses$in$the$Division$of$Applied$Mathematics$require$MATH$0090$and$0100.$$It$will$be$expected'that$most$students$ taking$APMA$0330,$0340,$and$ALL'students$taking$APMA$0350,$0360$will$have$taken$MATH$0180$or$MATH$0350$(or$ equivalent).$$Although$some$students$will$be$taking$this$course$at$the$same$time,$it$is$not$recommended.$$Students$are$ strongly$encouraged$to$take$MATH$0520$or$0540$(Linear$Algebra).$$The$majority$of$students$in$APMA$0350,$0360$have$taken$a$ linear$algebra$course.$$Linear$Algebra$may$be$taken$concurrently$with$APMA$0350,$0360$but$some$material$may$not$be$ covered$before$it$is$needed$and$the$student$will$be$expected$to$cover$this$material$independently.$ Prerequisites'Summary:'MATH$0090,$0100,$0180/0350,$and$0520/0540$ $ Introductory'Courses:' 1st'year:' ' ' Finish$calculus$sequence$and$linear$algebra$in$the$Math$department$ 2nd''year:' ' ' ' ' ' Differential'Equations'(Note$recommended$prerequisites$above)' $ APMA$0330,$0340$$$ $ $ $ $ OR$$ $ $ $ $ APMA$0350,$0360$ (intended$for$majors$in$the$physical$sciences/engineering)$$ $ $ $ uploads/Science et Technologie/ apma-guide.pdf