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Applied Mathematics-Biology

Biology, the science of all life and living matter, is an incredibly diverse discipline offering students the opportunity to learn about topics ranging from the fundamental chemical reactions that fuel all living organisms to the population dynamics of entire ecosystems all the way to the question of how our brains give rise to the complexities of human cognition and experience. Applied mathematics is an increasingly important component of modern biological investigation. Modern technologies have enabled the creation of vast new biological data sets that often require sophisticated mathematical and statistical models for interpretation and analysis. Advances in computing have similarly enabled the simulation of biological phenomena at increasingly fine levels of detail. Entire subfields, such as bioinformatics and computational neuroscience, have developed around these new paradigms of biological investigation. The foundations of these new fields are inherently mathematical, with a focus on probability, statistical inference, and systems dynamics. 

The Applied Mathematics – Biology concentration allows students to develop complementary expertise in biology and applied mathematics. Students will focus their advanced biological coursework in an area of particular interest to them. The applied math requirements emphasize those areas of mathematics that have found widespread use throughout all of the biological sciences. The program culminates in a senior capstone experience that enables students to participate in creative research collaborations with faculty.

Standard program for the Sc.B. degree

Prerequisites – the equivalent of two semesters of single-variable calculus
Single-variable calculus is not an enforced requirement for our concentration, but it is a required prerequisite for many of our courses. At Brown, single-variable calculus consists of MATH 0090 followed by one of MATH 0100, MATH 0170, or MATH 0190.
Requirements – 16 courses 1
Mathematical Requirements – 7 courses
MATH 0180Multivariable Calculus1
or MATH 0200 Multivariable Calculus (Physics/Engineering)
or MATH 0350 Multivariable Calculus With Theory
MATH 0520Linear Algebra1
or MATH 0540 Linear Algebra With Theory
APMA 0350Applied Ordinary Differential Equations 21
APMA 0360Applied Partial Differential Equations I 31
APMA 1655Honors Statistical Inference I1
or APMA 1650 Statistical Inference I
APMA 1070Quantitative Models of Biological Systems1
APMA 1080Inference in Genomics and Molecular Biology1
or NEUR 2110 Statistical Neuroscience
Scientific Requirements – 7 courses
One approved course (or course grouping) covering Newtonian mechanics. 41
CHEM 0330Equilibrium, Rate, and Structure1
BIOL 0200The Foundation of Living Systems1
Two approved courses in the biological sciences. All four biological electives (two here and two in the next requirement) should form a cohesive grouping in a specific area of biological interest. 52
Two approved 1000-level or higher courses in the biological sciences. All four biological electives (two here and two in the previous requirement) should form a cohesive grouping in a specific area of biological interest. 52
Additional Requirements – 2 courses
One approved course in the mathematical, biological, or computational sciences. 61
One approved capstone, senior seminar, or research-related course in the mathematical or biological sciences. 71
Total Credits16

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, addressing these questions:

  • 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. Complete guidelines, requirements, and deadlines for honors are published on the APMA departmental website. The main requirements include:

  • Earning grades of A or S-with-distinction in at least 70% of the courses used for concentration credit, excluding calculus and linear algebra, by the end of the penultimate semester.
  • Completion of an in-depth, original research project in a STEM discipline carried out under the guidance of a Brown-affiliated faculty advisor and documented with the completion of two semesters of independent study courses under the advisor’s supervision.
  • Completion of an honors thesis describing this research project that also demonstrates both the use of mathematical methodology in the project and the relevance to the biological sciences.