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Applied Mathematics

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 0180Intermediate Calculus1
MATH 0520Linear Algebra 21
APMA 0350
APMA 0360
Applied Ordinary Differential Equations
and Applied Partial Differential Equations I 3
2
Select one course on programming from the following: 41
Introduction to Mathematical Modeling
Introduction to Scientific Computing
Introduction to Scientific Computing and Problem Solving
Computing Foundations: Data
Introduction to Object-Oriented Programming and Computer Science
Computer Science: An Integrated Introduction
Five additional courses, of which four should be chosen from the 1000-level courses taught by the Division of Applied Mathematics. APMA 1910 cannot be used as an elective.5
Total Credits10

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 0180Intermediate Calculus1
MATH 0520Linear Algebra 21
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: 41
Introduction to Mathematical Modeling
Introduction to Scientific Computing
Introduction to Scientific Computing and Problem Solving
Computing Foundations: Data
Introduction to Object-Oriented Programming and Computer Science
Computer Science: An Integrated Introduction
Ten additional courses, of which six should be chosed from the 1000-level or higher level courses taught by the Division of Applied Mathematics. APMA 1910 cannot be used as an elective.10
Total Credits18

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 full-time professional experiences doing work that is related to their concentration programs, totaling 2-6 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 S-with-distinction 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 S-with-distinction 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.