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

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.

Example Plan of Study

  • Astro 16
  • Astro 97hf
  • Astro 225
  • Formation of Stars and Planets
  • Astro 202b
  • Phys 15b

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") intermediate-level course in a life sciences concentration: 

  • MCB 60, 63, 64, 65, 68 for molecular and cellular biology or for chemical and physical biology; 
  • OEB 50-59 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: 

Introductory-level 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 full-year freshman course LS50 Integrated Science can be counted as two courses: once in the application area (where it counts both as an intermediate-level 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.

Example Plan of Study

  • Chem 20
  • Chem 60
  • Foundations of Physical Chemistry
  • Chem 160
  • Chem 165
  • Chem 242

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.

Example Plans of Study

  • AM 121
  • Introduction to Optimization: Models and Methods
  • ES 201
  • ES 202
  • ES 203
  • ES 209

  • Econ 1011a
  • AM 158
  • Feedback Control Systems: Analysis and Design
  • ES 201
  • Stat 171
  • AM 105

  • AM 121
  • AM 203
  • Introduction to Disordered Systems and Stochastic Processes
  • ES 201
  • ES 202
  • Stat 171

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.

Example Plan of Study

  • PS 12b
  • Electromagnetism and Statistical Physics from an Analytic, Numerical and Experimental Perspective

  • EPS 131
  • Introduction to Physical Oceanography and Climate
  • EPS 139
  • Paleoclimate as Prologue
  • EPS 132
  • Introduction to Meteorology and Climate
  • EPS 52
  • Global Geophysics: A Primer

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).

Example Plans of Study

  • Econ 1011a
  • CS 134
  • CS 181
  • CS 228
  • CS 286r

  • CS 121
  • CS 181
  • CS 136
  • Econ 1011a
  • Econ elective

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

Example Plans of Study

  • EPS 131
  • Introduction to Physical Oceanography and Climate
  • EPS 132
  • EPS 133
  • ES 123
  • EPS 232

Energy

Example Plans of Study

  • EPS 109
  • Chem 20
  • ESPP 90a
  • Econ 1661
  • Econ 1010a

Earth and Planetary Sciences/Energy

Example Plans of Study

  • ES 6
  • ES 103
  • ES 123
  • EPS 100
  • EPS 109

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

Example Plan of Study

  • Chem 160
  • EPS 107
  • Environmental Geochemistry
  • EPS 133
  • ES 123
  • ES 164

Atmospheric Science

Example Plan of Study

 

  • EPS 132
  • EPS 200
  • EPS 208
  • EPS 232
  • EPS 236

Sustainable Development

Example Plan of Study

  • Econ 1011b
  • Econ 1393
  • ES 162
  • ES 168
  • Aquatic Chemistry (not in course of instruction)
  • ES 261

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.

Example Plan of Study

  • Gov 2000
  • Introduction to Quantitative Methods I
  • Gov 2001
  • Advanced Quantitative Research Methodology
  • Gov 2005
  • Formal Theory 1
  • Gov 30
  • American Government: A New Perspective
  • Gov 97
  • Tutorial - sophomore year

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

Example Plan of Study

  • Astro 97hf
  • Astro 98hf
  • Astro 145
  • Astro 191
  • Phys 143a

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.

Example Plan of Study

  • Psych 15
  • Social Psychology
  • Psych 1578
  • The Invisible Hand: What Game Theory Reveals about Social Behavior
  • Stat 111
  • Ec 1030
  • Stat 140
  • Design of Experiments

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

Example Plan of Study

  • Stat 111
  • Stat 140
  • Design of Experiments
  • Stat 151
  • Multilevel and Longitudinal Models
  • Stat 160
  • Design and Analysis of Sample Survey
  • Stat 139

  • Stat 111
  • Stat 139
  • Stat 123
  • Introduction to Bayesian Inference and Applications
  • Stat 131
  • Time Series and Prediction
  • Stat 171

  • Stat 111
  • Stat 139
  • Stat 123
  • Applied Quantitative Analysis
  • Stat 170
  • Stat 171