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





 Formation of Stars and Planets





Biological Sciences
The field of biological sciences can be broken into several subareas, 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.









 Design and Analysis of Sample Surveys










 Intermediate Biostatistical Methods

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



 Foundations of Physical Chemistry







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
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 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
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

 Introduction to Physical Oceanography and Climate









Energy
Example Plans of Study
Earth and Planetary Sciences/Energy
Example Plans of Study
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



 Environmental Geochemistry







Atmospheric Science
Example Plan of Study
Sustainable Development
Example Plan of Study







 Aquatic Chemistry (not in course of instruction)



Government
Example Plan of Study

 Introduction to Quantitative Methods I


 Advanced Quantitative Research Methodology


 Data Science I: Introduction to Data Science


 American Government: A New Perspective



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
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



 The Invisible Hand: What Game Theory Reveals about Social Behavior







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





 Multilevel and Longitudinal Models


 Design and Analysis of Sample Survey








 Introduction to Bayesian Inference and Applications


 Time Series and Prediction








 Applied Quantitative Analysis




