The Sc.B. concentration in Applied MathComputer Science provides a foundation of basic concepts and methodology of mathematical analysis and computation and prepares students for advanced work in applied mathematics, computer science, and data science. Concentrators must complete courses in mathematics, applied math, computer science, and an approved English writing course. While the concentration in Applied MathComputer 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.
Standard Program for the Sc.B. degree.
Prerequisites – the equivalent of two semesters of singlevariable calculus  
Requirements – 17 courses ^{1,2}  
Completion of one CS pathway ^{3}  
Completion of one APMA pairing ^{4}  
Mathematical Requirements – 8 courses  
MATH 0180  Multivariable Calculus  1 
or MATH 0200  Multivariable Calculus (Physics/Engineering)  
or MATH 0350  Multivariable Calculus With Theory  
MATH 0520  Linear Algebra  1 
or MATH 0540  Linear Algebra With Theory  
or CSCI 0530  Coding the Matrix: An Introduction to Linear Algebra for Computer Science  
or APMA 1170  Introduction to Computational Linear Algebra  
APMA 0350  Applied Ordinary Differential Equations ^{5}  1 
APMA 0360  Applied Partial Differential Equations I ^{6}  1 
APMA 1160  An Introduction to Numerical Optimization  1 
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  
Two approved 1000level or higher APMA courses. The APMA pairing must be completed. ^{4,7}  2  
One 1000level or higher APMA or MATH course ^{7}  1  
Computer Science Requirements – 8 courses ^{2}  
Select one of the following introductory course sequences  2  
Introduction to ObjectOriented Programming and Computer Science and Program Design with Data Structures and Algorithms  
Computer Science: An Integrated Introduction and Program Design with Data Structures and Algorithms  
Computing Foundations: Data and Program Design with Data Structures and Algorithms ^{2}  
Select three of the following five intermediatelevel options, one of which must be mathoriented and one systemsoriented. The intermediate requirements of the chosen pathway must be completed. ^{3}  3  
Introduction to Discrete Structures and Probability (math)  
or MATH 1001  The Art of Writing Mathematics  
or MATH 1530  Abstract Algebra  
Theory of Computation (math)  
Honors Statistical Inference I (math ) ^{8}  
or APMA 1650  Statistical Inference I  
or CSCI 1450  Advanced Introduction to Probability for Computing and Data Science  
or MATH 1620  Mathematical Statistics  
Introduction to Software Engineering (systems)  
Introduction to Computer Systems (systems) ^{9}  
or CSCI 0300  Fundamentals of Computer Systems  
Three approved 1000level or higher CSCI courses. The advanced requirements of the chosen pathway must be completed. ^{3,10}  3  
Additional Requirements – 1 course  1  
One approved capstone in computer science or applied mathematics taken in the student’s senior year. ^{11}  
Total Credits  17 
^{1}  A required course may be replaced by a more advanced course with concentration advisor approval. No course may be used to satisfy more than one of the required 17 concentration credits. Transfer credits and courses receiving placement credit notation can satisfy concentration credit as long as they appear on the Brown internal transcript. At most 3 postmatriculation transfer credits (such as study abroad courses or summer courses at another institution) can be used for concentration credit. Pursuing honors will require 18 courses – these 17 along with two semesters of independent study courses for the honors research project, one of which can be used to satisfy the capstone concentration requirement. 
^{2}  Students who take the CSCI 0111, CSCI 0112, CSCI 0200 sequence will effectively need an additional course (CSCI 0112) to complete the concentration. Students wishing to go directly from CSCI 0111 to CSCI 0200 (without CSCI 0112) will need to successfully complete additional exercises to receive an instructor override code for CSCI 0200. 
^{3}  CS pathways are described in the bulletin for the CS concentration at this link and also on the CS website at this link. To complete a pathway students must complete one core CSCI course, one additional core, related, or graduate CSCI course, and all of the intermediate courses for that pathway. These courses can appear anywhere in the declaration. NonCSCI courses are not allowed, even if they are approved as part of a CS pathway or allowed as part of a pure CS concentration. 
^{4}  To complete an APMA pairing, students must complete two 1000level or higher APMA courses that adhere to a common theme. These courses can appear anywhere in the declaration. APMA 1910, APMA 1920 and research/independent study courses are not allowed. Themes can be broadly defined and are subject to concentration advisor approval. Examples include:

^{5}  APMA 0330 or MATH 1110 may be used in place of APMA 0350. If MATH 1110 is used, then the concentration must include at least four 1000level APMA courses (not including APMA 1910, APMA 1920 or research/independent study courses). 
^{6}  APMA 0340 or MATH 1120 may be used in place of APMA 0360. If MATH 1120 is used, then the concentration must include at least four 1000level APMA courses (not including APMA 1910, APMA 1920 or research/independent study courses). 
^{7}  APMA 1910, APMA 1920 and research/independent study courses are not allowed. 
^{8}  APMA 1655 is recommended. At most one of APMA 1650, APMA 1655, CSCI 1450, MATH 1610, MATH 1620 can be used for concentration credit. Note that MATH 1610 is a prerequisite for MATH 1620, so if MATH 1620 is used, the presumption is that MATH 1610 or the equivalent has also been taken (but only one can be used for concentration credit). 
^{9}  At most one of CSCI 0300 and CSCI 0330 can be used for concentration credit. 
^{10}  At most one arts, humanities, or social science CS course can be used for concentration credit (currently CSCI 1250, CSCI 1280, CSCI 1360, CSCI 1370, CSCI 1800, CSCI 1805, CSCI 1870, CSCI 1952B, CSCI 1952X, CSCI 2002, CSCI 2952S). NonCSCI courses are not allowed, even if they are approved as part of a CS pathway or allowed as part of a pure CS concentration. 
^{11}  The capstone does not have to be part of the chosen CS pathway (unlike the pure CS concentration), but it can be used as one of the courses that completes a pathway or one of the courses that completes the APMA pairing. Completing a capstone prior to the senior year requires prior approval from the concentration advisor and the Director of Undergraduate Studies in CS. The following options can be used to satisfy this requirement:

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:
 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
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 nonAPMA or CS advisor should contact the Directors of Undergraduate Studies in APMA and CS to discuss options.