Book Reviews

Using the Mathematics Literature

Using the Mathematics Literature. Kristine K. Fowler, ed. New York: Marcel Dekker, 2004. 389 pp., $169.95 (ISBN 0-8247-5035-7)

Twenty-five years have passed since Marcel Dekker last published a mathematics volume in its Books in Library and Information Science series (Using the Mathematics Literature: A Practical Guide, Barbara Kirsch Schaefer, ed., 1979). Of course, much has changed since then -- new discoveries, new research directions, new information environments -- so it was important to have an update. Kristine Fowler, an experienced mathematics librarian at the University of Minnesota, has undertaken the task and produced an exceptional guide to the literature.

Using the Mathematics Literature serves as more than a finding aid, more than a list of tools and strategies for finding information. Closer in approach to Alison Dorling's Use of Mathematical Literature (1977), it opens with three chapters on tools and strategies but then continues with twelve signed annotated bibliographies on a range of subjects. Each chapter serves as a road map to its subject matter, highlighting key texts for researchers embarking on new journeys of discovery. The book does an excellent job of guiding its intended audience, described in the preface as "the new mathematics graduate student, [but also] the researcher encountering an unfamiliar area and the new mathematics librarian" (p. iii).

Many important decisions need to be made when compiling such a selective guide, and the editor has made some intelligent choices concerning subjects and contributors. The chapters cover such subjects as the History of Mathematics, Number Theory, Combinatorics, Abstract Algebra, Algebraic and Differential Geometry, Real and Complex Analysis, Differential Equations, Topology, Probability Theory and Stochastic Processes, Numerical Analysis, Mathematical Biology and Mathematics Education. Each chapter begins with a general introduction to the subject, followed by an annotated list of recommended readings.

The recommended readings are judiciously selected and organized. Contributors provide an excellent mix of classic texts and more recent work throughout. For the most part, annotations are descriptive and evaluative. However, the quality of these annotations varies across chapters. Some contributors reveal a thorough understanding of the subject matter through the depth of their annotations. See, for example, Fernando Gouvea's chapter on the history of mathematics or Thomas Garrity's chapter on algebraic and differential geometry. In contrast, the chapter on combinatorics limits its annotations to descriptions of the audience level.

To insure the quality of these chapters, the authority of the contributors is of the utmost importance. Unfortunately, while a biography is included for the editor, only the institutional affiliation is provided for the other contributors. While experienced researchers and librarians may recognize these names, the "new mathematics graduate student" would have to expend some effort to determine their expertise. Even brief biographical information about each contributor would have been useful.

While the author index is comprehensive, the subject index is not as detailed as it should be. For example, if you look up "Zeta functions" in the index, you will find a reference to page 109. However, observant readers will note related works mentioned on pages 94, 102 and 103 as well.

While these and other problems exist, they do not detract significantly from the overall quality of the book. It superbly fulfills its purpose: guiding researchers unfamiliar with a subject to some recommended texts for gaining familiarity. New mathematics graduate students should consult appropriate chapters as introductory reading lists. Librarians should keep the book handy for answering reference questions, especially when referring students to introductory texts. I would recommend this book to all academic libraries.