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Applied Mathematics-Biology

The Applied Math - Biology concentration recognizes that mathematics is essential to address many modern biological problems in the post genomic era. Specifically, high throughput technologies have rendered vast new biological data sets that require novel analytical skills for the most basic analyses. These technologies are spawning a new "data-driven" paradigm in the biological sciences and the fields of bioinformatics and systems biology. The foundations of these new fields are inherently mathematical, with a focus on probability, statistical inference, and systems dynamics. These mathematical methods apply very broadly in many biological fields including some like population growth, spread of disease, that predate the genomics revolution. Nevertheless, the application of these methods in areas of biology from molecular genetics to evolutionary biology has grown very rapidly in with the availability of vast amounts of genomic sequence data. Required coursework in this program aims at ensuring expertise in mathematical and statistical sciences, and their application in biology. The students will focus in particular areas of biology. The program culminates in a senior capstone experience that pairs student and faculty in creative research collaborations. 


Standard program for the Sc.B. degree

Required coursework in this program aims at ensuring expertise in mathematical and statistical sciences, and their application in biology. The students will focus in particular areas of biology. The program culminates in a senior capstone experience that pairs student and faculty in creative research collaborations. Applied Math – Biology concentrators are prepared for careers in medicine, public health, industry and academic research.

Required Courses:

Students are required to take all of the following courses.

MATH 0090Single Variable Calculus, Part I1
MATH 0100Single Variable Calculus, Part II1
or MATH 0170 Single Variable Calculus, Part II (Accelerated)
MATH 0180Multivariable Calculus (or equivalent placement)1
MATH 0520Linear Algebra1
or MATH 0540 Linear Algebra With Theory
CHEM 0330Equilibrium, Rate, and Structure 11
PHYS 0030Basic Physics A1
or PHYS 0050 Foundations of Mechanics
Select one of the following sequences:2
Applied Ordinary Differential Equations
and Applied Partial Differential Equations I
Methods of Applied Mathematics I
and Methods of Applied Mathematics II
APMA 1650Statistical Inference I1
or APMA 1655 Honors Statistical Inference I
APMA 1070Quantitative Models of Biological Systems1
APMA 1080Inference in Genomics and Molecular Biology1
or NEUR 2110 Statistical Neuroscience
BIOL 0200The Foundation of Living Systems (or equivalent)1
Additional Courses
One additional course in Applied Math or Biology1
We strongly recommend that Applied Mathematics-Biology concentrators take one of the programming courses on or before their first semester as a concentrator. Those who do can use it to satisfy this requirement:
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
Accelerated Introduction to Computer Science
Introduction to programming
One research-related course in Applied Math or Biology. For example:1
A senior seminar course from the APMA 193X, 194X series
A directed research/independent study course from the APMA 1970, 1971, or BIOL 1950, 1960, or NEUR 1970 series
A directed research/independent study course in a related discipline (i.e. STEM disciplines, ENVS, PHP, etc.) if the project is relevant to the student's learning goals in the concentration and with approval from the concentration advisor.
A pre-approved course that satisfies the Biology AB capstone requirement: BIOL 1100, 1250, 1515, 1555, 1565, 1575, 1600, 1820, 1970.
A relevant CURE (Course-based Undergraduate Research Experience) course: BIOL 0190R, 0190S, 0285, 0440, 0600, 0940G, 1515, 1555; NEUR 1630, CLPS 1195.
A non-research course related to the concentration along with a research experience equivalent in scope and scale to work the student would pursue in an Applied Math or Biology independent study course. Examples include UTRAs, LINK awards, research programs at other institutions, etc. This requires approval from the concentration advisor and appropriate documentation.
Other equivalent opportunities not listed - with approval from the concentration advisor.
Four classes in the biological sciences agreed upon by the student and advisor. These four courses should form a cohesive grouping in a specific area of emphasis, at least two of which should be at the 1000-level. Some example groupings are below:4
Areas of Emphasis and Suggested Courses:
Some areas of possible emphasis for focusing of elective courses are listed below. Given the large number of course offerings in the biosciences and neuroscience, students are free to explore classes in these areas that are not listed below. However, all classes must be approved by the concentration advisor. APMA 1910 cannot be used as an elective.
Advanced Biochemistry
Organic Chemistry I
Chemical Biology
Biotechnology and Physiology
Principles of Physiology
Cell Physiology and Biophysics
and/or appropriate bioengineering courses, such as:
Polymer Science for Biomaterials
Tissue Engineering
Stem Cell Engineering
Synthetic Biological Systems
Ecology, Evolution, and Genetics
Invertebrate Zoology
and Evolutionary Biology
Principles of Ecology
and The Evolution of Plant Diversity
Experimental Design in Ecology
Foundations of Population Genetics
Human Population Genomics
Molecular Genetics
Mathematical Methods in the Brain Sciences
Neurosciences courses: See
Cell Physiology and Biophysics
Topics in Signal Transduction
Synaptic Transmission and Plasticity
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.


Requirements and Process: Honors in the Applied Math-Biology concentration is based primarily upon an in-depth, original research project carried out under the guidance of a Brown (and usually Applied Math or BioMed) affiliated faculty advisor.  Projects must be conducted for no less than two full semesters, and students must register for two semesters of credit for the project via APMA 1970 or BIOL 1950/BIOL 1960 or similar independent study courses.  One of these courses can be used to fulfill the research-related course requirement, but the other cannot be used elsewhere in the concentration.  The project culminates in the writing of a thesis which is reviewed by the thesis advisor and a second reader.  It is essential that the student have one advisor from the biological sciences and one in Applied Mathematics.  The thesis work must be presented in the form of an oral presentation (arranged with the primary thesis advisor) or posted at the annual Undergraduate Research Day in either Applied Mathematics or Biology.  For information on registering for BIOL 1950/BIOL 1960, please see

The concentrations in Applied Math (including joint concentrations) 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

The deadline for applying to graduate with honors in the concentration are the same as those of the biology concentrations.  However, students in the joint concentration must inform the undergraduate chair in Applied Mathematics of their intention to apply for honors by these dates.