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Applied Mathematics-Computer Science

The Sc.B. concentration in Applied Math-Computer Science provides a foundation of basic concepts and methodology of mathematical analysis and computation and prepares students for advanced work in computer science, applied mathematics, and scientific computation. Concentrators must complete courses in mathematics, applied math, computer science, and an approved English writing course. While the concentration in Applied Math-Computer Science allows students to develop the use of quantitative methods in thinking about and solving problems, knowledge that is valuable in all walks of life, students who have completed the concentration have pursued graduate study, computer consulting and information industries, and scientific and statistical analysis careers in industry or government. This degree offers a standard track and a professional track.

Requirements for the Standard Track of the Sc.B. degree.

Prerequisites - two semesters of Calculus, for example
Single Variable Calculus, Part I
and Single Variable Calculus, Part II
Single Variable Calculus, Part II (Accelerated)
Concentration Requirements (17 courses)
MATH 0180Multivariable Calculus1
or MATH 0350 Multivariable Calculus With Theory
MATH 0520Linear Algebra1
or MATH 0540 Linear Algebra With Theory
or CSCI 0530 Coding the Matrix: An Introduction to Linear Algebra for Computer Science
Core-Applied Mathematics:
APMA 0350Applied Ordinary Differential Equations1
APMA 0360Applied Partial Differential Equations I1
APMA 1160An Introduction to Numerical Optimization1
or APMA 1170 Introduction to Computational Linear Algebra
or APMA 1180 Introduction to Numerical Solution of Differential Equations
or APMA 1690 Computational Probability and Statistics
or APMA 1740 Recent Applications of Probability and Statistics
Core-Computer Science:
Select one of the following Series:2
Series A
Introduction to Object-Oriented Programming and Computer Science
and Introduction to Algorithms and Data Structures
Series B
Computer Science: An Integrated Introduction
and Computer Science: An Integrated Introduction
Series C
Accelerated Introduction to Computer Science (and an additional CS course not otherwise used to satisfy a concentration requirement; (this course may be CSCI 0180, an intermediate-level CS course, or a 1000-level course)
Series D 1
Computing Foundations: Data
and Computing Foundations: Program Organization
and Computer Science: An Integrated Introduction
Select three of the following intermediate-level courses, one of which must be math-oriented and one systems-oriented. The intermediate courses must cover the requirements of the pathway chosen under additional requirements for CS.3
Introduction to Discrete Structures and Probability
Introduction to Software Engineering
Introduction to Computer Systems
Fundamentals of Computer Systems
Theory of Computation
Advanced Introduction to Probability for Computing and Data Science 2
Statistical Inference I
Three 1000-level Computer Science courses. Two of these courses and the intermediate courses must satisfy one of the CS pathways. Non-CSCI courses are not allowed, even if they are approved as part of a CS pathway or allowed as part of a pure CS concentration. At most one of the three courses can be a designated arts, humanities, or social science oriented CS course (which includes CSCI 1250, 1280, 1370, 1800, 1805, 1870, but see here [] for the current list) 33
Three 1000-level Applied Mathematics courses approved by the concentration advisor, of which two should constitute a standard sequence or address a common theme. Typical sequences include: APMA 1200/1210 and APMA 1650 or 1655/1660. APMA 1910 cannot be used as an elective.3
A capstone course: a one-semester course, taken in the student's last undergraduate year, in which the student (or group of students) use a significant portion of their undergraduate education, broadly interpreted, in studying some current topic in depth, to produce a culminating artifact such as a paper or software project. The title and abstract of the artifact, along with the student's and faculty-sponsor's names, will be placed in the CS website. The inclusion of a relevant image or system diagram is strongly encouraged. The complete text of the best artifacts of each class will be featured on the CS website. A senior thesis, which involves two semesters of work, may count as a capstone 41
Note: CSCI 1010 and 1450 may be used either as a math-oriented intermediate courses or as advanced courses. CSCI 1010 was formerly known as CSCI 510: they are the same course and hence only one may be taken for credit. CSCI 1450 was formerly known as CSCI 450: they are the same course and hence only one may be taken for credit. Applied Math 1650 or 1655 may be used in place of CSCI 1450. However, concentration credit will be given for only one of Applied Math 1650, 1655, and CSCI 1450.
Total Credits17

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:

  • 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.


Concentrators that demonstrate excellence in grades and in undergraduate research can be awarded departmental honors. Honors students with primary advisors in Applied Math should follow the guidelines, requirements, and deadlines for honors as described in the bulletin for Applied Math concentrators and as published on the APMA departmental website. Honors students with primary advisors in Computer Science should follow the guidelines, requirements, and deadlines for honors as described in the bulletin for Computer Science concentrators and as published on the CS departmental website. Students wishing to do honors research with a non-APMA or CS advisor should contact the Directors of Undergraduate Studies in APMA and CS to discuss options.