What is Applied Mathematics?

There are many ways to view applied mathematics. One definition concentrates on the advances in mathematical methods that have had an impact on applications (e.g., the analysis of the nonlinear partial differential equations that underlie fluid mechanics).

We like to think of applied mathematics in the context of an application, and hence, we define applied mathematics to be the use of mathematics to make a substantial contribution to some field of human inquiry.

This explains why we require students to complete courses in both mathematics and an area of application. Applied Math 50 has been designed to introduce students to the breadth of options available through papers and talks by Harvard University faculty.

Here at Harvard, applied mathematics is the lifeblood of researchers in the sciences from biology to psychology as well as engineering, allowing them to …

• uncover the mysteries of the natural world by understanding how paper crumples, ice cracks, and the Venus flytrap snaps
• manipulate how water and other liquids flow from taps, making way for novel printing and even drug delivery techniques
• better understand how the human brain is wired and figure out how neuronal pulses control our thoughts and actions
• reveal the mechanics and physics behind earthquakes and other geological events
• model the behavior of financial markets or online auctions.

Moreover, the technologies behind companies like Google, Yahoo!, and MapQuest are built on algorithms. Investment banking and insurance firms rely on good prediction models (of both behavior and the markets) to increase their bottom lines. As important, for those who love a good puzzle, dream of Sudoku in their sleep, and/or can recite Pi to the nth digit, applied mathematics may be the best game in town.

The field’s fun, challenging, and infinitely adaptable—over four years and over a lifetime.

Why study Applied Mathematics at Harvard?

Applied mathematics moves beyond theory, blending the study of mathematics with a wide array of applications in many fields: biology, genomics, chemistry, computer science, decision and control, economics, electrical engineering, geophysical sciences, mechanical engineering, scientific computing, physics, social and behavioral sciences, and statistics.

Harvard in particular provides an ideal environment for pursuing such a diverse and interdisciplinary field.

• Small classes in engineering and applied sciences courses, with an average 5:1 student/faculty ratio, give students direct access to professors.
• Being at Harvard provides unmatched opportunities to use the latest tools and technologies—from fabricating and testing transistors in a clean room to working on grid-based computing. 
  
• Undergraduate research opportunities (many with funding) abound—both during regular term and over the summer, through the Program for Research in Science and Engineering (PRISE), an opportunity for Harvard undergraduates to join a 10-week residential research community here on campus.
• Past senior projects in Applied Mathematics take full advantage of the collaborative nature of faculty: CEO Equity Initiatives and Company Performance; Multi-Stage Information Acquisition in Auction Design; Determining U.S. Black Carbon Emissions Using an Inverse Method; and Efficient Algorithms for Brownian Dynamics Simulations Based on Higher-Order Solutions of the Fokker-Planck Equation.
• Learning happens beyond the classroom. Students participate in events such as the ACM Programming Competitions and the Consortium for Mathematics and Its Applications (COMAP) Mathematical Modeling Competition.

Why should I study Applied Mathematics in a given area (like economics or computer science) rather than concentrate in that area?

One should study applied mathematics because one is fascinated with the power and impact that mathematical arguments have had on the world around us. This concentration is inherently interdisciplinary because it combines courses in mathematics with courses in an area of application.

How demanding is the workload for a typical course?

Concentrators can expect to invest the same amount of time in their courses as students pursuing the natural sciences (e.g., biology) or the physical sciences (e.g., physics and chemistry). Students—even in an honors track—are able to balance their academics with outside interests.

Do I need a background in mathematics?

Although there are students who start in Math 21a (or even 23a, 25a, or 55), the program is designed so that students from all levels can complete it.

Can students "minor" in Applied Mathematics?

Yes. The secondary field in Mathematical Sciences is jointly sponsored by the the Mathematics Department and the Applied Mathematics concentration.

Secondary fields are a new program in Harvard College. They are intended to provide the opportunity for students to pursue focused study in one area outside of the concentration, without requiring students to combine their academic interests in a joint thesis project.

What are the requirements for Applied Mathematics?

The following publications describe the concentration in Applied Mathematics and its requirements.

• Applied Mathematic Guidelines
  A detailed description of the concentration requirements that includes ideas for area of application and possible courses to take to satisfy the requirements.

• Guidelines for Area (d) of Applied Mathematics-Economics
  Information on courses that can be used to satisfy the area of application for economics.

• Requirements
  Official requirements for the concentration as published in the Harvard College Handbook for Student.

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