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War Stories from Applied Math: Undergraduate Consultancy Projects

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Robert Fraga, editor
Mathematical Association of America
Publication Date: 
Number of Pages: 
MAA Notes 71
[Reviewed by
William J. Satzer
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War Stories from Applied Math is a compilation of papers arising primarily as adaptations of transcripts from a 1996 workshop on undergraduate consultancy projects in applied mathematics. The book’s subject is setting up and running a program that allows undergraduate students to work on problems from real-world sources. People involved from both academic and industry sides share their experience, insights and concerns.

The “war stories” of the title suggest that this is a collection of reminiscences about battles. Although all the programs have encountered their share of difficulties, on the whole they have been remarkably successful. Perhaps the best known program is the Mathematics Clinic at Harvey Mudd College, which has been operating since the 1970s, is formally structured, and has probably the best supporting resources. Another successful program at Marquette University is described as a small, do-it-yourself operation with a low profile and an informal, flexible approach. What the programs have in common are a strong desire to expose undergraduates to applications of mathematics, at least a few committed faculty members, and the organizational skills necessary to keep all the pieces in place. It is highly desirable for at least one of the faculty members to have contacts with industry; not much is required to get started — one connection will inevitably lead to others. Alumni and alumnae are often good initial contacts.

One description of the range of good and bad projects comes from George Corliss at Marquette: “The worst projects my students do are those which are finished about the middle of the semester, leaving the students with nothing to do. The best projects are the really hard, wide-open ones that the client company wouldn’t dare to submit to a consulting group because the client couldn’t write down the job description of exactly what was wanted, and the consulting company wouldn’t know how to price the project. It’s no problem to turn students loose on it.”

A comment from Robert Borrelli, speaking of Harvey Mudd’s program, warns that technical issues are not always the biggest concern: “I can tell you now, after all these years of experience, that we’ve never, ever had a project fail because of technical difficulties. We’ve come close to failure twice because of personnel problems… Currently, in industry the same thing happens. In fact, it’s a common occurrence.”

It sure is.

One of the representatives from the client side emphasizes how important teamwork and understanding team members’ roles are in making the projects work. He notes that mathematicians, oriented more than engineers or scientists toward working alone, are often not comfortable working in teams. Nonetheless, students often find the non-technical aspects of projects (learning to coordinate with team members, communicating with their client, learning how to present results) among their most valuable experiences.

Perhaps the best real war stories come from the two chapters on project deliverables. Not surprisingly, relationships with clients are among the most challenging aspects of the projects. You must find potential clients, discuss and define possible projects with them, identify specific items that the project will deliver, communicate regularly with the clients along the way to make sure they agree with the direction you’re taking and be prepared to change direction if they disagree.

The panel discussion presented in one chapter offers — perhaps indirectly — some valuable insights into the relationships between project faculty members and clients. The perspectives of the two groups are often quite different, and the language they use is often subtly different. Learning to speak the client’s language is a key part of successful projects.

This is a valuable resource for anyone running, planning or thinking about setting up student consultancy projects. The book offers the benefit of many years of collective experience in making these projects work. Although virtually everyone involved is positive about the programs, no one minimizes the difficulties.

A couple of other things are worth noting. One should be cautious with the notion of “real world” applications. Certainly they are not exclusively industrial. Many good applications arise in colleges and universities. (A noteworthy project at Marquette involved work with the university library.) Hospitals and medical schools also offer many opportunities. On the other hand, some potential industrial applications couldn’t be further from the “real world”.

Also, the “mathematics” part of “applications of mathematics” should be taken broadly to include statistics, operations research, as well as some aspects of computer science, software development, and occasionally even some engineering.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.