The core of the concentration is the area of application. Students
are encouraged to define areas of applications that correspond to their
area of greatest intellectual interest. Historically, most students in
the concentration have chosen Economics as their application area. This
is the most rigid option in the applied math concentration--as
described below.
Students are encouraged to explore other areas of potential
interest. Current concentrators have chosen application areas ranging
from government,
psychology, linguistics, sustainable development, astronomy or
astrophysics, urban planning, chemistry,energy, theoretical
neuroscience, and architecture. The rule of thumb in non-traditional
cases is that of the five classes required for the Application section, in general three to five must have significant mathematical content, while the other two can
provide needed background for the field.
If you are thinking of doing something unusual, you should prepare a
draft of the courses you want to take, and also think through an
intellectual justification for why this set of courses is intellectually
coherent. You should then meet with the Director or Assistant Director of Undergraduate
Studies to discuss your plans. Details are worked out on a case by case
basis: in all cases the overarching principal is that the program should
be intellectually coherent and prepare you for applying mathematical
ideas in a substantive way to the area of application. In some cases it
is easier to do this given Harvard's course offerings than others, and
the availability of proper courses provides the fundamental constraint
for what is possible.
To give you a general guide to the programs that students follow, we list here some of the areas of study that current or recent students have followed, including with them examples of approved plans of study. We are giving you this information NOT because you should copy the plans of study verbatim, but to give you ideas about the types of plans of study you can put together under this concentration.
Architecture/Urban Planning
Architecture
The idea here is to combine an understanding of architectural practice with the scientific and engineering principles underlying architecture. The plan of study below combines two basic architecture classes with two classes in the engineering design of structures, and the fundamental mechanics of solids and fluids. Other possibilities include combining an interest in architectural acoustics with a study of acoustics and sound propagation.
Example Plan of Study
Urban Planning
Here the notion is to combine study of decision theory and optimization with an interest in using these ideas for urban planning. In the case below, the focus is on water resource design and transportation policy.
Example Plan of Study
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
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- Formation of Stars and Planets
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Biology
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.
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- Design and Analysis of Sample Surveys
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- Intermediate Biostatistical Methods
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Neurobiology
Example Plan of Study
Theoretical Neuroscience
Example Plan of Study
Chemistry
Theoretical chemistry provides an
opportunity for several potential
areas of application, in physical,
inorganic, and organic chemistry.
Example Plan of Study
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- Foundations of Physical 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.
Example Plans of Study
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- Artificial Intelligence: Reasoning and Planning Systems
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- Cryptography: Trust and Adversity
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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
Earth and Planetary Sciences
Example Plan of Study
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 strenthened the argument for
combining computer science and economics into a single track. The core
part of such a program should include Ec 1011a and/or 1011b; Ec 1052
(advanced game theory); CS 181 and CS182. For those seeking more of a
theoretical basis into computer science, CS121 could help round out the
program.
Example Plans of Study
Electrical 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.
Example Plans of Study
Environmental Science
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- Introduction
to Physical Oceanography and Climate
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Energy
Earth and Planetary Sciences/Energy
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
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- Environmental Geochemistry
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Atmospheric Science
Example Plan of Study
Sustainable Development
Example Plan of Study
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- Aquatic Chemistry (not in course of instruction)
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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.
Music
Example Plan of Study
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- Analysis of 20th-Century Music II (?)
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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
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.
Social and Behavioral Sciences
The social and behavioral sciences
use mathematical techniques
beyond the level of undergraduate
calculus and statistics only in isolated
instances. The few available
mathematically oriented courses
usually are at the graduate level but
are accessible to suitably prepared
undergraduates. The Mind, Brain,
and Behavior Initiative, administered
by the Psychology Department,
approaches this broad subject from
different perspectives through several
concentrations.
Government
Example Plan of Study
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- Introduction to Agent-Based Modeling
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- Strategic Models of Political Economy
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International Studies
Example Plan of Study
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- Strategic Models of Political Economy
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Linguistics
Example Plan of Study
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- Artificial Intelligence: Reasoning and Planning Systems
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- Natural Language Processing
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Psychology
Example Plan of Study
Statistics
Example Plan of Study
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