A Toolkit in 0s and 1s
In the late 1930s, Harvard graduate student Howard Aiken was dreaming of a computing machine. His doctoral thesis in physics required numerical solutions to nonlinear differential equations, involving tedious calculations beyond the capacity of calculators. It was clear to Aiken that these mathematical operations could be standardized and mechanized, so he began designing a machine to carry them out. The potential, he thought, was immense: he could already envision applications in mathematics, science, and even sociology. Certain areas of science, he argued, were at an impasse, limited by the mathematical power of computing equipment.
Aiken’s computing machine, now better known as the Harvard Mark I, was built by IBM and presented to Harvard in August 1944. In the next 15 years, the Mark I and its successors ran calculations for scientific research as well as for the U.S. military, including a series of implosion calculations for Los Alamos National Laboratory (later revealed to be part of the atomic bomb project). Aiken himself, as a professor of applied mathematics, directed Harvard’s Computation Laboratory—built to house the Mark I, and later renamed in his honor—until 1961. In 1947 and 1949 respectively, he developed a master’s, and then a doctoral, program in computer science, the first of their kind in the nation. The age of computing had begun.
Yet in the decades following Aiken’s retirement, large-scale computing largely left Harvard behind. Computer science—especially the theory of computation and the development of software systems—took off as an academic discipline in the 1970s, but computational science lagged behind, burdened by its roots in calculation. Early computing machines like the Mark I seemed like enormous calculators; though powerful, they remained merely tools, and few people thought to study their use. Computational methodology persisted in scattered academic fields, but was employed mostly on an ad hoc basis, lacking an academic foundation of its own.
Now, nearly 70 years after the Mark I was built, computational science has come into its own, says Efthimios Kaxiras, Van Vleck professor of pure and applied physics and founding director of Harvard’s Institute for Applied Computational Science (IACS). No longer do computers merely speed up processes that could be done by hand, as in Aiken’s time; computation, once just a tool, has become so powerful that it is changing the nature of inquiry. “The hardware, algorithms, and ideas behind computing have all evolved so that computers can now solve real problems,” Kaxiras explains. So-called “big data” is opening new lines of research in fields from basic science to advertising; already, it has given rise—via complex computational models, coupled with statistics—to developments like election forecasts more accurate than ever before. People are calling computation the “third leg” of science, he says, adding it to the traditional modes of theory and experiment.
But harnessing the potential of computation requires more sophisticated training. To that end, the School of Engineering and Applied Sciences has launched a new degree program, the master of science in computational science and engineering (CSE), to provide rigorous training in the use of computational methods to solve research problems. The 28 students in its inaugural class, drawn from a pool of 147 applicants, began their studies this fall. The year-long program combines a core of project-based computer science and applied math courses with electives that allow students to explore connections to other fields, from engineering to economics and global health. “The program is meant to be a toolkit,” says Rosalind Reid, former IACS executive director (she recently became executive director of the Council for the Advancement of Science Writing). “And it’s a toolkit taught via application.”
The program itself is the product of careful design by IACS, which was founded in 2010 to oversee interdisciplinary research and educational initiatives related to computing. “The new degree is grounded in real needs,” Kaxiras says. IACS convened a panel of experts from industry and national research laboratories to assess the current research environment and brainstorm what an academic program could accomplish. (The advisory board has met periodically since to continue the dialogue.) The unanimous suggestion, he says, was to create a master’s degree—a recommendation supported by academics on the grounds that computational science and engineering still lack the clear career path and disciplinary focus needed to justify a doctoral degree (though Kaxiras predicts that this will soon change).
The Institute itself has begun laying the intellectual groundwork for this new field by developing courses in areas like scientific computing, data science, and numerical methods. “Computational science is always changing, and its needs and topics are changing,” says Kaxiras, “but the key ideas remain the same.” There’s a need, he explains, for sophisticated techniques from computer science and applied math that are properly matched to the complex problems at hand. For instance, situations from card games to market investments are often represented by systems of equations impossible for even the most high-powered computers to solve mathematically because of the near-infinite range of possibilities. Kaxiras has therefore developed and taught a course on stochastic optimization: a set of probabilistic methods that tries a large number of possible strategies to come up with a best guess—all that’s possible, he says, for many real-world problems.
In computational science, he continues, there’s a need for people who can “marry the hardware to the right software and the right algorithm.” For instance, big data now requires immense computing power, well beyond what any single processor can accomplish alone. “How do you break down a problem to take advantage of parallel computing?” he asks. “It requires a different way of thinking from the sequential mode of thinking we’re accustomed to. These developments have elevated the discipline and approach to something with serious intellectual potential.” Wang professor of computer science Hanspeter Pfister, the current IACS director, has developed and taught courses in visualization, computer graphics, parallel programming, and computational science; this fall, he and Joseph Blitzstein, professor of the practice in statistics, introduced a new course in data science that is jointly offered by the computer science and statistics departments.
Meanwhile, the new degree is promising as much for its applications as its academic focus. “Students come up with amazing and innovative ideas about how to apply what they’ve learned,” Kaxiras reports: in the final project for his class, they developed methods to optimize everything from class time and room assignments (to minimize between-class travel) to resource distribution and routes to first-aid facilities (in case of a major disaster).
The inaugural master’s-degree students come from diverse academic backgrounds; about a third earned undergraduate degrees outside the STEM (science, technology, engineering, and mathematics) fields. Most have taken time off since college, and a third already hold advanced degrees in fields as diverse as finance, sociology, and science writing. Physician Ryan King, for example, felt unfulfilled in the purely clinical aspect of his residency and found himself drifting back to his undergraduate studies in chemical engineering at Tulane University. “I hope to add engineering to medicine,” he says. As a medical student, he had observed that much of healthcare is empirical, and he believes it could benefit from a stronger foundation in computer models and simulation. He has already arranged to work with associate professor of radiation oncology Lance Munn on a research project to create computational models of metastasis. He’s not sure yet whether his path will take him back into medicine, or into academia—“I think this year will help me refine what I want to do”—but like many of his classmates, he is interested in learning the approaches that will allow him to choose what problems to tackle.
“Many data-science students come from fields in science that they naturally gravitate to, that form how they think and what problems they choose to approach,” says Reid. At the same time, she says that science and computer science speak different languages, even though computational science must make use of both. “We’re trying to create multilingual people here,” she explains. Daniel Weinstock, the program’s assistant director of graduate studies, who holds a Ph.D. in theoretical and computational chemistry, points out that computation “is frequently taught for the purpose of problem-solving, but only informally. The [program’s] courses give students rigorous training in a computational area that they can then take back to their disciplines.” Pfister adds that IACS intends to foster collaborations across schools at Harvard, and to connect students with alumni and practitioners in industry through internships and research projects.
Several students have already worked in industry, giving them valuable perspectives on the importance of computation in the marketplace. After graduating from the University of California, Berkeley, in 2011, Anita Mehrotra joined the technology-consulting firm Accenture’s research and development labs, where she witnessed firsthand the growing need for data scientists and statisticians. Peter Bull, who graduated from Yale in 2008, worked for five years as a software engineer at Microsoft, where he became interested in learning how to manage and gain insights from large amounts of data. He sees some connections between data science and his undergraduate focus on philosophy: “Both represent rigorous, technical approaches to finding answers to humanistic questions,” he says, and he’s excited by the potential of big data to transform epidemiology and public health. Mehrotra, who studied math and economics, says she’s “always enjoyed using economics to understand how people interact, and their impact on the world around them,” and hopes that by strengthening her background in programming and Bayesian statistics she will be able to explore projects with social impact in fields like developmental economics, education, and public health. She calls the Harvard program the “perfect mix” of strong applied-math and computer-science classes in an interdisciplinary setting. “The degree can really take you anywhere,” says Bull, echoing many of his classmates.
“I think these [computational-training] courses are meeting a real need, and proof of that is the great number of students who are attending,” says Kaxiras. This fall, over 400 students enrolled in the new data science course; more than half were undergraduates, and the rest a mix of students from the graduate and professional schools, as well as the Extension School. Next fall, a two-year master of engineering degree program will join the current one-year master of science program in CSE, and a secondary-field citation is also available for other graduate students. Kaxiras says he receives frequent inquiries from other institutions seeking to develop similar programs. “The need is urgent,” he says. “There are so many things happening in science, engineering, and the wider world that rely on computation, and the more people you have who are highly trained, but not narrowly focused, the more exciting the possibilities will be.”
He is happy to see the surge in interest. “When I first came to Harvard over 20 years ago, there was quite a bit of skepticism that this type of scientific approach could yield interesting results and really advance the scientific endeavor,” he says. “I think there’s real potential in the future for scientific breakthroughs using computational approaches. It’s mind-boggling.”
For those interested in the master of science and master of engineering degrees, the School of Engineering and Applied Sciences is holding an information session on Friday, November 8. See also this announcement about the master of engineering degree, which begins accepting applications this fall.
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