Perspectives on Graduate Education
4.1 PhD Education
The 1996 report made several recommendations for improving graduate education for students interested in taking a job in industry, including coursework in an application, experience with formulating and solving real-world problems, and coursework in computer or computational science.
In the current survey, we asked three related questions to gauge to what extent these recommendations have become a part of graduate education. First, we asked if the graduates had been involved in industrial-related programs. Of the respondents, 28% participated in industrial internships, 7% had an industrial mentor, 7% participated in problem sessions, and 5% participated in an industrial workshop. Multiple answers were allowed. However, 59% either did not respond or indicated that the question was not applicable.
On the other side of the coin, many of the companies we visited in on-site interviews stressed the advantage of internships, and many of them offer such internships: for example, Boeing, D.E. Shaw, Cray, IBM, GM, AT&T, Intel, Akamai, HP Labs, Google, and Solidworks. Likewise, workshops have proven to be a successful platform transferring knowledge from academia to industry and giving students experience at solving industrial problems. Leaders include the mathematical problems in industry workshops in the United States, the industrial problem solving workshops of the Pacific Institute for the Mathematical Sciences in Canada, and the European Study Groups with Industry.
In view of the appreciation that companies express for internships and workshops, and the variety of opportunities, it is disappointing that participation in such programs has not become more universal, at least among students considering an industrial career.
I think it is important to bridge the gap between theory and practical applications—most people do not realize this.
Programming experience (preferably on team software project) is very important and frequently omitted in a mathematically oriented curriculum.
We asked graduates about graduate-level training outside of their major. In this case, 79% of the graduates had at least one such experience, (see Table 9). Often this took the form of training in programming, scientific computing, and other computer sciences. Finally, we asked how valuable this training was for obtaining a job in industry, and 65% of graduates considered it very valuable or valuable. We also asked how important they found the experience of working in a team, and 70% rated this as very valuable or valuable.
We contacted one graduate program that ranks very high in the percent of graduates entering industry to see if that department has any special insights into the preparation of students for industrial jobs, particularly ideas that might be portable to other institutions. The Department of Computational and Applied Mathematics at Rice University sent 8 of its 20 graduates (40%) into industry from 2004 to 2008, and 6 out of 11 from 2009 to 2010. Some points made by department chairman Matthias Heinkenschoss were:
- The CAAM department enjoys strong contacts with local companies, such as BP, Shell, ExxonMobil, and Chevron. While the specific companies will differ, the concept is certainly generalizable to other departments.
- Students do not, however, only do local internships. About half of the internships in which students participate are outside of Houston.
- It is important to keep in touch with alumni to build up “pipelines” into specific companies and industries.
- Students going into industry take the same courses as other students. However, the required courses include topics like numerical methods and high-performance computing, which might not be required in a traditional pure-math department.
- All students have to write a Master’s thesis at the end of their second year and take a thesis-writing course (which also covers other communication skills, such as the art of making a 5 minute presentation).
- Finally, CAAM is an applied-math department, rather than a program or a group within a department.
Of course the last-mentioned feature is very far from portable, and we do not advocate that other institutions should emulate this model. However, traditional math departments that have applied-math programs or groups should consider ways to make those programs sensitive to the needs of graduates going into industry.
4.2 The Professional Masterís Degree
In the 1996 report, we surveyed Master’s graduates in mathematics and their supervisors. For this report we did not survey Master’s graduates. We focused instead on an emerging trend in Master’s education.
Shortly after the 1996 report was published, the Alfred P. Sloan Foundation launched its Professional Science Masters (PSM) program to establish an innovative Master’s degree in the sciences and mathematics that would equip graduates for work outside academia. PSMs are rigorous, interdisciplinary programs that give students advanced training in science and mathematics, while emphasizing the professional skills that are highly valued by employers in a wide range of fields.
In 2005, the Council of Graduate Schools (CGS) assumed the task of making the PSM degree an accepted academic offering. In 2007, the National Professional Masters Association (NPSMA) was formed as a voice for program directors, faculty, administrators, alumni, and students. Its objective was to support PSM initiatives through conferences, workshops, gathering of data, and development of best practices. Both of these organizations received initial funding from the Sloan Foundation.
There are now more than 230 programs at nearly 110 colleges and universities in 30 states and the District of Columbia, as well as in Canada, the United Kingdom and Australia. These include 23 programs in the mathematical sciences and several closely related programs in the computational sciences and bioinformatics. See [“PSM Programs” 2012].
A recent survey of the alumni of PSM programs, [NPSMA 2009], provides some insight into the jobs taken by graduates. Of the 281 respondents to an online survey, 80% held non-academic jobs; 62% were in industry, 9% in the nonprofit sector and 9% in government. Most jobs were in large organizations. The median salary was approximately $63,000, and the first and third quartiles were about $43,000 and $74,000 respectively. However, the mode (19%) was in the over-$90,000 category. Of the respondents in the NPSMA survey, 19% came from programs in the mathematical or computational sciences.
The PSM curriculum has a scientific component that includes depth in mathematics and breadth in science, engineering, or business, as well as a skills-based component in management, business and professional skills. PSM programs emphasize writing and communication skills, and require a final project or team experience. They provide opportunities for a structured internship. In addition to an innovative, targeted curriculum, a PSM program is expected to have an active advisory board that includes leaders from industry, business, and government. It is also required to collect and publish data on enrollment, degree completion, and employment history.
A recent National Research Council report, Science Professionals: Master’s Education for a Competitive World, emphasized the importance of PSM degrees:
Policymakers, universities, and employers should work together to speed the development of professionally oriented master’s degree programs in the natural sciences. Graduates of these programs—which build both scientific knowledge and practical workplace skills—can make a strong contribution to the nation’s competitiveness. [NRC 2008]
Of the Master’s programs in the mathematical and computational sciences that are not affiliated with the PSM program, some are very traditional, but others are very much focused on preparing students for jobs in particular industries. Perhaps the most prominent of these are in finance, where they go by variants on the names “mathematical finance,” “computational finance,” “financial engineering,” or “quantitative finance.” A few mathematical finance programs are affiliated with PSM, but the majority of them are not. For example, all seven PSM programs in financial mathematics participate in the National Financial Mathematics Career Fair, held at the Courant Institute every fall, but 42 other Master’s programs that are not affiliated with PSM also participate.So, if the curriculum expectations are met, why hire a Master’s graduate? In an article in Advanced Trading, [Gibbs 2008], Emanuel Derman, the director of the Master’s program in financial engineering at Columbia University and head of risk management at Prisma Capital Partners, says he “looks to hire quants who have learned the basics in areas such as modeling but who also understand why the model behaves as it does and which factors are driving the market. … You can’t learn everything in school—a lot of the schoolwork is theoretical. So students go through the program and get experience in the real financial world.” This rationale applies not just to “quants” but also to most Master’s graduates in the mathematical and computational sciences who intend to follow a non-academic career. A balance has to be struck in a Master’s curriculum between understanding of theory, understanding of business (or of a particular business), and developing practical experience.