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 field of biological sciences can be broken into several sub-areas, and it is possible for specialization in any of these areas.  The focus should be on attaining competence and basic knowledge in the field of biology and learning how mathematics can be substantively applied to this field.  The categories include:

  • Ecology and Evolutionary Biology
  • Biomechanics and Bioengineering
  • Systems and Molecular Biology, including mathematical genomics
  • Neuroscience

Example Plans of Study

This plan of study is a solid program in mathematical genomics, giving both a basic introduction to the molecular biology of the genome (and applications to immunology); learning the mathematical foundations of population genetics and how this information can be used to analyze genomic information.

  • MCB 52
  • MCB 169
  • Math 153
  • OEB 152
  • Stat 115

  • MCB 199
  • OEB 152
  • OEB 261r
  • Stat 115
  • Stat 160
  • Design and Analysis of Sample Surveys

  • Math 153
  • OEB 152
  • Stat 115
  • HEB 1330
  • HEB 1331

  • Math 153
  • MCB 195
  • MCB 52
  • OEB 53
  • Sys Bio 200
  • MCB 52
  • MCB 54
  • MCB 195
  • OEB 125
  • Stat 120
  • Intermediate Biostatistical Methods

Neurobiology

Example Plan of Study

  • MCB 80
  • Math 153
  • Neuro 130
  • ES 148
  • (?)
  • BME 130 (ES 149)

  • MCB 80
  • Math 153
  • MCB 105
  • MBB S-94
  • OEB 57

Theoretical Neuroscience

Example Plan of Study

  • MCB 80
  • CS 121
  • ES 125
  • ES 149
  • ES 159

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.

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

  • Math 116
  • ES 201
  • ES 202
  • ES 203
  • ES 209

  • Stat 139
  • Stat 171
  • AM 111
  • Econ 1723
  • MIT 6.872

  • Econ 1011a
  • Econ 1052
  • ES 201
  • Stat 171
  • AM 105

  • AM 121
  • Econ 1052
  • ES 201
  • ES 202
  • Stat 171

Earth and Planetary Sciences

Example Plan of Study

  • EPS 7
  • EPS 100
  • EPS 121
  • Terrestrial Planets
  • EPS 161
  • EPS 166

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 that CS121 is sometimes a prerequisite to both CS 181 and CS 182.  It can count in the application or as a discrete mathematics breadth course.

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

Example Plan of Study

  • Gov 2000
  • Introduction to Quantitative Methods I
  • Gov 2001
  • Advanced Quantitative Research Methodology
  • CS 109a
  • Data Science I: Introduction to Data Science
  • Gov 30
  • American Government: A New Perspective
  • Gov 1360
  • American Public Opinion

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 quantative 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, and Engineering Sciences.  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