## Frequently asked questions

Many questions about our concentrations and courses are answered in our Undergraduate Handbook.

### Why study Applied Mathematics?

**What is Applied Mathematics?**

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. 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. Our courses cover modelling, differential equations, probability, scientific computing, and statistics, which are areas of mathematics that are used most often in applications in science, society and industry.

**What jobs do Applied Mathematicians work in?**

Many of our students find employment in the banking and investment sector, but our graduates also work for consulting, insurance, pharmaceutical, software, and service companies and for non-profit organizations; many of our students go on to graduate school, typically to the best schools in the US: job placements of our recent graduates can be found on Focal Point (links to job placements are listed separately for each of our four concentrations). 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, or go to the career pages of AMS, MAA and SIAM.

### Questions about courses

**Do I need to take Calculus and Linear Algebra before taking Applied Mathematics courses?**

APMA 0160, 0650, and 1650 do not require multi-variable calculus and linear algebra. Most of our other courses require multi-variate calculus and linear algebra: the prerequisites for specific courses can be checked on Banner.

*I’m interested in taking courses in Applied Mathematics, where should I start?*

The majority of students begin by finishing the multi-variable calculus and linear algebra sequence offered by the Mathematics department. These courses are prerequisites to the majority of Applied Mathematics courses. The most common choice for the first Applied Mathematics courses that students take is APMA 0330 or 0350 (differential equations), APMA 1650 (statistics), or a computing course.

*What is the difference between APMA 0330/0340 and APMA 0350/0360? Is it possible to take APMA 0330 and APMA 0340 in place of APMA 0350 and APMA 0360 to fulfill concentration requirements?*

While both classes cover similar material, the APMA 0330-0340 and APMA 0350-0360 sequences satisfy separate needs. The first sequence stresses methods and is more appropriate for students in engineering and the sciences, while the second stresses conceptual foundations and meets the needs of applied math concentrators and most students in economics better. In the event that you would like to substitute one sequence for the other, please discuss it with a concentration advisor first.

*What computing courses are recommended for students interested in Applied Mathematics and which fulfill the concentration requirement?*

The following courses will fulfill the computing course requirement for Applied Mathematics concentrators: APMA 0160, CSCI 0040, 0150, 0170. Higher level courses may be accepted with the approval of a concentration advisor. APMA 0160 and CSCI 0040 are Matlab-based programming courses. APMA 0160 focuses primarily on algorithms within mathematics (calculation of integrals, curve fitting, etc.) while CSCI 0040 focuses on more general applications in engineering, the sciences and the humanities. CSCI 0150 is a Java-based programming course that also includes an introduction to data structures and user interface design. CSCI 0170 is a more general introduction to computation principles including recursion and algorithm analysis using Racket, ML and Java.

*It appears that similar courses are offered in both the Mathematics and Applied Mathematics departments. How do I choose between them?*

There are topics such as probability and statistics and differential equations that are studied by students and faculty in both departments although the approach and specific topics may differ. In general, courses in the Mathematics department will take a more theoretical/proof-based approach whereas Applied Mathematics courses will develop the necessary theory while focusing on applications, computations, or problems from which the mathematics was developed. It is suggested that students shop or take courses in both departments to determine which approach best fits their interests and goals.

### Questions about our concentrations

Please check Focal Point or contact one of our concentration advisors with any questions you may have. Some commonly asked questions are answered below.

*What should I consider in choosing between the AB and ScB concentrations in Applied Mathematics?*

Neither of these options is inherently better, whether you consider attending graduate school or wish to pursue a career in industry right after your undergraduate studies. The program you pursue should above all reflect your interests, abilities, time constraints, career goals, and other interests. AB programs permit more time for you to pursue other courses outside mathematics, an advantage if you wish to explore other academic areas. Also, AB programs may be embellished, for example, by adding courses beyond the minimum number required or by including a research project, independent study or honors thesis. ScB programs include most of the required courses for students aiming at graduate schools in Applied Mathematics. However, graduate and professional schools are more concerned with these factors: challenging thoughtful courses; well-rounded skills; focus; and research experience. These factors are much more important than whether you completed an AB or an ScB. Another issue to consider is that cross-departmental degrees give students a larger range of courses to fulfill their upper-level concentration requirements. However, the increase in breadth may mean that a student is not required to have as much depth in either area.

*What should I do if I am interested in applying to Graduate School?*

If you are considering applying to graduate school, we encourage you to discuss your plans early on (ideally before your senior year) with a concentration advisor or other faculty mentors in the Division.

### Research Opportunities for Undergraduates

*What summer research opportunities are available for undergraduate in Applied Mathematics?*

Summer research projects provide a fantastic opportunity to see how new mathematics is developed and applied. These activities also allow you to draw from materials from many courses to work on and solve a concrete longer-term project. Many faculty members are willing to supervise summer research projects. For instance, 12 undergraduate students worked in the Division during summer 2013 on projects ranging from mathematical biology and pattern formation to black holes and other topics. Undergraduate Teaching and Research Awards (UTRAs) provide funds on a competitive basis to undergraduate students who wish to pursue collaborative projects with Brown faculty. The deadline is in early February for summer funding. If you are interested in participating in a summer research project, please contact a concentration advisor or speak directly with Applied Mathematics professors in whose research you are interested, ideally before December or early January. Another option is to apply for one of the many Research Experience for Undergraduates Summer Programs that are offered at universities and colleges throughout the US. The American Mathematical Society keeps an up-to-date list of such activities posted on their website entitled, Research for Undergraduates Summer Programs.

** Are Independent Study opportunities available?**If you are interested in learning about a specific topic, and there are no courses offered in the Division that cover this topic, you are encouraged to approach a concentration advisor or other faculty members in the Division to discuss the feasibility of an Independent Study.

*Are there any student groups for undergraduates in Applied Mathematics?*

The AMDUG (Applied Mathematics Departmental Undergraduate Group) organizes activities for students within the Department. Past activities include seminars, a panel discussion on career choices/graduate school, a brain teaser competition and more. Please see the AMDUG website (for more information or to sign up for the AMDUG email list.