We are all familiar with mathematics and mathematical success stories, but likely we are less familiar with mathematical projects and perhaps we never have thought about managing mathematics. Phil Dyke manages to put these four big words in the short title of his book in which he summarizes, analyzes and details twenty years worth of his life as a supervisor of all kinds of mathematical projects. The book is written not only for mathematics instructors but their undergraduate students as well.
Three main types of projects are defined and described: Individual projects, group projects and case studies. The chapter on individual projects is mainly directed at the student, offering advice on how to choose a project, stressing the importance of the project report and the difficulties of writing mathematics, outlining expectations and student responsibilities concerning mathematical depth. Assessment suggestions are directed toward both students and instructors. The cartoon on page 4 shows a professor hiding out from his students on a window ledge — "Overworked academics are hard to find", reads the caption and underlines the message that an individual project, while straightforward in choice, execution and evaluation, requires considerable effort from both the student and the supervisor. Many fairly detailed project examples and suggestions for project topics are given.
Group projects, fairly new in mathematics education, offer the student at least some opportunity for debate about different mathematical approaches to a problem — in a differential equations course, every problem will be solved via differential equations. As member of a group the student can form and voice an opinion. The methods proposed by group members might differ markedly without any of them being labelled wrong, which is unusual in the mathematics curriculum, but might be of fundamental importance in the development of the student in preparation for success in the workplace. Group projects, while more economical with respect to advising time per student, are more difficult to assess than individual projects. The role of the instructor here shifts from instruction to management. Besides mathematics, mathematical writing, and oral presentation, the project also requires that the students practice team work, time management and peer assessment — which means that the students must also acquire their share of management skills. Detailed suggestions for setting up group projects, specifying their expectations concerning mathematical content, the length of the written report, the oral presentations and the final assessment are provided, with descriptions of several group projects the author has advised.
The author defines Case Studies to be a half-way house between a formal lecture course and a group project. The lecturer, in two or three lecture hours, introduces a mathematical topic. The students then, either individually or in groups, work on their own to understand the material presented to them and to solve some follow-up problems. Assessment is by oral examination or open book test. For instructors unfamiliar with projects in mathematics, this type of course is most likely the place to get experience, since the scope is well defined and the outcome easily controllable. The student has the opportunity to explore a specific topic of mathematics on his own, the results are expected to be new to the student but not new to mathematics. Again the chapter ends with detailed examples of case studies covering a wide range of topics, but excluding statistics and operations research. Moreover, suggestions for test questions in form of exercises are provided.
Three actual project reports from the author's vast experience are printed as appendices, each framed by a preamble and an epilogue describing the background of each student author and the fate of the project with the assessors.
This book is a valuable resource for all who are involved in project work in mathematics. Even if we are alarmed by the shift from instruction to management, we have to acknowledge that there is an impressive amount of mathematics contained in the project reports and their value in the students' education is beyond doubt. Maybe we all should try our hands at this kind of management!
Brigitte Servatius (firstname.lastname@example.org) is professor of mathematics at the Worcester Polytechnic Institute. She is the editor of Student Research Projects for the College Mathematics Journal.