Areas of Application
The area of application is an integral part of the concentration. Students are encouraged to select an area of application that corresponds to an area of intellectual interest. Current concentrators have chosen application areas ranging from government, psychology, astronomy or astrophysics, and chemistry, to theoretical neuroscience.
Note: your transcript and diploma will not explicitly state your area of application.
 Astronomy
 Biological Sciences
 Chemistry
 Computer Science
 Data Science
 Decision and Control
 Earth and Planetary Sciences
 Economics
 Economics and Computer Science
 Engineering
 Government
 Physics
 Psychology
 Scientific Computing
 Statistics
Astronomy
Combining applied mathematics with astronomy or another similar physical science allows delving deeper into mathematical foundations, while maintaining a strong overview of the major concepts and methods.
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Biological Sciences
The biological sciences application area combines the foundation of a life sciences concentration with a focus on biological data analysis and/or modeling using computation, statistics, and mathematics.
At least one course should be a broad ("gateway", "portal", or "foundation") intermediatelevel course in a life sciences concentration:
 MCB 60, 63, 64, 65, 68 for molecular and cellular biology or for chemical and physical biology;
 OEB 5059 for integrative biology;
 MCB 80, 81,105,115,125 for neuroscience;
 SCRB 10 for human developmental & regenerative biology;
 HEB 1280, 1328, 1330, 1420 for human evolutionary biology.
At least three of the five application area courses should be "quantitative", meaning that they have substantial mathematical or computational content. The quantitative application area courses can be drawn from any area relevant to quantitative biology, not just life sciences courses but also including computer science, statistics, and applied math courses, provided they form a coherent plan. Some examples of life sciences courses that currently count as quantitative include:
LS50 Integrated science
MCB105 Systems neuroscience
MCB111 Mathematics in biology
MCB112 Biological data analysis
MCB131 Computational neuroscience
MCB195 Foundations of systems biology
MCB198 Advanced mathematical techniques for modern biology
MCB199 Statistical thermodynamics and quantitative biology
Neuro140 Biological and artificial intelligence
Neuro141 Physics of sensory systems in biology
Neuro1401 Computational cognitive neuroscience
OEB242 Population genetics
OEB252 Coalescent theory
Some examples of other courses suitable as quantitative AM/bio
application area courses include:
CS181 Machine learning
CS182 Artificial intelligence
Math153 Evolutionary dynamics
Stat 111 Introduction to statistical inference
Stat115 Computational biology and bioinformatics
Stat117 Data analysis in modern biostatistics
Stat 139 Linear models
AM 120 Applied linear algebra and big data
AM 121 Introduction to optimization: models and methods
ES 201 Decision theory
Notes:
Introductorylevel life sciences courses including LS1a/b and OEB10 do not count toward AM/bio concentration requirements, although they may be prerequisites for other courses.
The special fullyear freshman course LS50 Integrated Science can be counted as two courses: once in the application area (where it counts both as an intermediatelevel foundational course and as quantitative), and also toward the modeling category in the breadth requirement.
Chemistry
Theoretical chemistry provides an opportunity for several potential areas of application, in physical, inorganic, and organic chemistry.
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Computer Science
Applied Mathematics concentrators specializing in computer science will build a broader base of applicable mathematics and focus on those aspects of the subject which depend most directly on such mathematics.
For an application in computer science, students will take at least one course in the 120 series, as well as at least two more courses drawn from the 120s, 130s, 150s, 161, 175, or the 180s.
Note:
CS 51 is recommended preparation for CS 136, CS 181, CS 182, so students with one of those courses on their plan of study will be asked to have CS 51 on the plan as well. (CS 51 can be removed from the plan of study once it has been completed).
Data Science
Applied Mathematics concentrators specializing in data science will take AM 120, Stat 111, CS 181 or CS 182 (and applicable prerequisite courses), and two electives.
Recommended electives include MCB 112, Astro 100 and 193, additional statistics coursework beyond Stat 110/111, ES 201 and 202, further CS coursework, and econometrics.
Decision and Control
The Decision and Control area is concerned with topics that are sometimes called operations research and/or systems engineering. The common theme is optimization, in various forms and contexts, both to understand natural systems and to design man made systems.
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Earth and Planetary Sciences
AM students planning to pursue an application to the earth sciences should take the Physical Sciences 12 or Physics 15 sequence as important background knowledge. Courses in EPS that have both physics and 21a/21b prerequisites are appropriate for the application.
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Economics
Mathematical modeling is used extensively in economics, and it is generally agreed that the foundation of economic theory is formed on a mathematical basis. The requirements for applied mathematics and economics are made and continuously updated in cooperation with the Economics Department.
See full list of courses and details
Economics and Computer Science
The birth of internet technology has strengthened the argument for combining computer science and economics into a single track. The core part of such a program should include Ec 1011a; one CS 134, and/or CS 136; and CS 181 and/or CS 182.
Note:
CS 51 is recommended preparation for CS 136, CS 181, CS 182, so students with one of those courses on their plan of study will be asked to have CS 51 on the plan as well. (CS 51 can be removed from the plan of study once it has been completed).
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Engineering
Three important general paths of study involve circuit design, signal processing/communications, and the mathematics of intelligent machines.
Environmental Science and Engineering
At Harvard, atmospheric, hydrological, and oceanographic phenomena are the primary locus of study, and one can adopt a dynamical, chemical, or biological point of view. Descriptive models of phenomena such as the movement of pollutants through liquid, gaseous, and porous media are useful for predicting environmental quality and the consequences of control or abatement programs.
Environmental Science
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Energy
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Earth and Planetary Sciences/Energy
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Geophysical Sciences
Four themes within the geophysical sciences include planetary physics and seismology, oceanography, meteorology, and atmospheric chemistry. The geophysical fluid mechanics courses are central to the study of environmental sciences.
Atmospheric Chemistry and Engineering
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Atmospheric Science
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Sustainable Development
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Government
Applied Math concentrators on a Government Track are required to take at least 2 substantive (i.e., primarily about politics) Government classes and 3 Government courses that are more mathematically oriented.
Substantive courses (two Gov courses): Gov 97 Sophomore Tutorial (recommended)
Core statistics course (one course): Gov 1000/2000 Introduction to quantitative methods (recommended) or one of Stat 111 or 139 (accepted). The Gov 2000 courses are open to AM/Gov students
Core formal theory course (one course): Gov 2005 Formal Theory 1(recommended) or one of Gov 1729 Models of Conflict in International Relations, 1780 International Political Economy, 94HL Political Economy of Development
One additional mathematical course: Gov 1002/2001 Advanced quantitative research methodology, Gov 2002 Causal Inference, Gov 2003 Advanced Topics in Political Methodology, Gov 1430 Data Science to Save the World (by petition), Gov 2006 Formal Theory 2. Other courses may be able to count by petition.
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Mechanical Engineering
Three interwoven strands characterize applied mechanics: fluid mechanics, solid mechanics, and materials science. Ramifications in biomechanics and geophysical fluid dynamics are included under other headings.
Physics
There are two main options in this area: macroscopic (or classical) physics and microscopic (or quantum) physics. While no specific course sequences are outlined here, programs involving astrophysics, biophysics, and the like are also possible.
Astrophysics
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Psychology
Applied Mathematics concentrators specializing in psychology will build a psychology foundation while developing an understanding of complementary mathematics.
For an application in psychology, students will take one foundational psychology course, one advanced psychology course from within the Psychology Department, and three quantitative courses. One of the three quantitative courses must be a statistical inference course (either Stat 111 or Stat 139). The other two can be drawn from Statistics, Computer Science, Economics, Engineering Sciences, or Mathematical Biology. Psych 1401 also counts as a quantitative course for the psychology application area. As with all applications, the five courses should form a coherent plan.
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Scientific Computing
This area is concerned with the design, implementation and study of algorithms for the approximate solution of continuous mathematical problems on digital computers: problems posed in the language of calculus and linear algebra, including differential and integral equations, root finding, and optimization.
Statistics
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