The concentration in Applied Mathematics allows students to investigate the mathematics of problems arising in the physical, life and social sciences as well as in engineering. The basic mathematical skills of Applied Mathematics come from a variety of sources, which depend on the problems of interest: the theory of ordinary and partial differential equations, matrix theory, statistical sciences, probability and decision theory, risk and insurance analysis, among others. 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 are interested in the basic techniques and approaches in themselves. The standard concentration leads to either the A.B. or Sc.B. degree. Students may also choose to pursue a joint program with biology, computer science or economics. The undergraduate concentration guide is available here.
Both the A.B. and Sc.B. concentrations in Applied Mathematics require certain basic courses to be taken, but beyond this there is a great deal of flexibility as to which areas of application are pursued. Students are encouraged to take courses in applied mathematics, mathematics and one or more of the application areas in the natural sciences, social sciences or engineering. Whichever areas are chosen should be studied in some depth.
Standard program for the A.B. degree.
Prerequisites  
Introductory Calculus, Part I and Introductory Calculus, Part II  
Or their equivalent  
Program  
Ten additional semester courses approved by the Division of Applied Mathematics. These classes must include: ^{1}  
MATH 0180  Intermediate Calculus  1 
MATH 0520  Linear Algebra ^{2}  1 
APMA 0350 & APMA 0360  Applied Ordinary Differential Equations and Applied Partial Differential Equations I ^{3}  2 
Select one course on programming from the following: ^{4}  1  
Introduction to Mathematical Modeling  
Introduction to Scientific Computing  
Introduction to Scientific Computing and Problem Solving  
Computing Foundations: Data  
Introduction to ObjectOriented Programming and Computer Science  
Computer Science: An Integrated Introduction  
Five additional courses, of which four should be chosen from the 1000level courses taught by the Division of Applied Mathematics. APMA 1910 cannot be used as an elective.  5  
Total Credits  10 
^{1}  Substitution of alternate courses for the specific requirements is subject to approval by the division. 
^{2}  Concentrators are urged to consider MATH 0540 as an alternative to MATH 0520. 
^{3}  APMA 0330, APMA 0340 will sometimes be accepted as substitutes for APMA 0350, APMA 0360. APMA 1910 cannot be used as an elective. 
^{4}  Concentrators are urged to complete their introductory programming course before the end of their sophomore year. 
Standard program for the Sc.B. degree.
Program  
Eighteen approved semester courses in mathematics, applied mathematics, engineering, the natural or social sciences. These classes must include: ^{1}  
MATH 0090 & MATH 0100  Introductory Calculus, Part I and Introductory Calculus, Part II  2 
MATH 0180  Intermediate Calculus  1 
MATH 0520  Linear Algebra ^{2}  1 
APMA 0350 & APMA 0360  Applied Ordinary Differential Equations and Applied Partial Differential Equations I ^{3}  2 
Select one senior seminar from the APMA 1930 or APMA 1940 series, or an approved equivalent.  1  
Select one course on programming from the following: ^{4}  1  
Introduction to Mathematical Modeling  
Introduction to Scientific Computing  
Introduction to Scientific Computing and Problem Solving  
Computing Foundations: Data  
Introduction to ObjectOriented Programming and Computer Science  
Computer Science: An Integrated Introduction  
Ten additional courses, of which six should be chosed from the 1000level or higher level courses taught by the Division of Applied Mathematics. APMA 1910 cannot be used as an elective.  10  
Total Credits  18 
^{1}  Substitution of alternate courses for the specific requirements is subject to approval by the division. 
^{2}  Concentrators are urged to consider MATH 0540 as an alternative to MATH 0520. 
^{3}  APMA 0330, APMA 0340 will sometimes be accepted as substitutes for APMA 0350, APMA 0360. 
^{4}  Concentrators are urged to complete their introductory programming course before the end of their sophomore year. 
Professional Tracks
The requirements for the professional tracks include all those of each of the standard tracks, as well as the following:
Students must complete fulltime professional experiences doing work that is related to their concentration programs, totaling 26 months, whereby each internship must be at least one month in duration in cases where students choose to do more than one internship experience. Such work is normally done at a company, but may also be at a university under the supervision of a faculty member. Internships that take place between the end of the fall and the start of the spring semesters cannot be used to fulfill this requirement. On completion of each professional experience, the student must write and upload to ASK a reflective essay about the experience, to be approved by the student's concentration advisor.
On completion of each professional experience, the student must write and upload to ASK a reflective essay about the experience, to be approved by the student's concentration advisor:

Which courses were put to use in your summer's work? Which topics, in particular, were important?

In retrospect, which courses should you have taken before embarking on your summer experience? What are the topics from these courses that would have helped you over the summer if you had been more familiar with them?

Are there topics you should have been familiar with in preparation for your summer experience, but are not taught at Brown? What are these topics?

What did you learn from the experience that probably could not have been picked up from course work?

Is the sort of work you did over the summer something you would like to continue doing once you graduate? Explain.

Would you recommend your summer experience to other Brown students? Explain.
Honors
The concentrations in Applied Math require that honors students demonstrate excellence in grades for courses in the concentration. Students must have earned grades of A or Swithdistinction in at least 70% of the courses used for concentration credit, excluding calculus and linear algebra, or be in the upper 20% of the student's cohort (as measured by the fraction of grades of A or Swithdistinction among courses used for concentration credit, excluding calculus and linear algebra). Since S with distinctions do not appear on the internal academic record or the official transcript, the department will consult directly with the Registrar’s Office to confirm a student’s grades in concentration courses. Additional guidelines and requirements for honors are published on the department website.