Strong libraries are of vital importance to an effective undergraduate environment in which students are expected to acquire the disposition for life-long learning. To accomplish this goal, colleges must develop curricula--in mathematics as in any other subject--that encourage students to learn to use a library. However, before that can happen, colleges must develop libraries worth using.
Unfortunately, undergraduate students rarely use library resources in their mathematical studies. Conventional curricula and common teaching practices rely almost exclusively on textbooks--despite substantial evidence that more engaging assignments based on richer resources lead to better understanding. Moreover, typical undergraduate libraries have very thin and eccentric mathematics collections, partly because many librarians have little knowledge of mathematics and many mathematicians have little interest in libraries. Collections are typically shaped more by the happenstance of research interests of new faculty than by careful planning that emphasizes balance of the collection as a whole. This process yields spotty collections that are often inappropriate for undergraduate education.
Building a strong undergraduate library is much like building a strong undergraduate curriculum. One must plan for the whole while ensuring balance of all the parts. In building libraries as in planning curricula, one must make tough choices. As not every good course can be taught, neither can every good book be purchased. Course-related library assignments are an essential bridge between textbook-based homework and undergraduate research experiences that are so crucial to career choices made during college years. Moreover, research experiences for undergraduates require strong libraries that reflect the best of current mathematical practice.
The current national imperative for revitalizing mathematics education adds a special sense of urgency to the need for balanced, contemporary undergraduate mathematics collections. A good undergraduate library provides resources for students to broaden their mathematical horizons; opportunities for assignments that move beyond mere exercises to writing, reacting, and research; and sources for faculty who are engaged in scholarship and curriculum development. Library improvement in the mathematical sciences is a necessary (but by no means sufficient) step along the path towards curriculum reform.
Twenty-five years ago the Mathematical Association of America addressed a similar need by preparing Basic Library Lists for two-year and four-year colleges. The goal then was to encourage all colleges to build mathematics collections adequate to ensure that no student would be denied access to appropriate mathematical materials. The four-year college List was revised once, but even that revision is now fifteen years old. Since the Basic Library List was last revised, over 15,000 books have been published in the mathematical sciences, many reflecting topics and specialties that have only recently become prominent.
Mathematics itself has undergone several major changes. Computers have emerged as a significant force in mathematics, introducing algorithmic thinking, discrete mathematics, data analysis, and mathematical logic as important and growing parts of the mathematical sciences. The increasing applicability of mathematics has created new demand for courses in mathematical modeling, in statistics, and in mathematical biology. The joining of applied mathematics with computing has created whole new disciplines on the periphery of mathematics, such as the theory of computation, simulation, scientific computation, and dynamical systems.
Powerful new methods of computational and applied mathematics have the potential to attract many good students to careers in mathematics. Unfortunately, these advances are often invisible to students at the early, formative stage of their college studies, since all they see in introductory courses are calculus textbooks. Because of the long delay for modern topics to get into regular texts, it is very important that colleges be encouraged to develop instructional styles that introduce beginning students not only to textbooks, but also to library resources. For that to make educational sense, it is important that libraries use their limited budgets to build collections that will stimulate the interests of all prospective mathematics students, both those who might be attracted to major in a mathematical science as well as the many others who study mathematics for different purposes.
Library Recommendations for Undergraduate Mathematics contains approximately 3000 titles arranged in 25 chapters and 230 sections. Books have been selected according to several different objectives:
Whereas the former Basic Library List included about 1000 volumes, the present volume includes three times as many titles. This growth is both appropriate and necessary, given the dramatic increase in the breadth and applicability of the mathematical sciences. To help libraries on limited budgets, books have been marked with asterisks to indicate priority:
| *** | Essential (approximately 200 titles) |
| ** | Highly recommended (approximately 400 titles) |
| * | Recommended (approximately 800 titles) |
| Listed (approximately 1600 titles) |
The final section contains recommendations for periodical and journal subscriptions in the mathematical sciences, marked in similar priority categories.
By its very nature, Library Recommendations for Undergraduate Mathematics offers a comprehensive survey of the best literature in the mathematical sciences. Although intended primarily for libraries, the volume is also an excellent source of inspiration for self-study by anyone wishing to explore a new field or to catch up on the recent literature in a subject. The volume provides a truly panoramic window on the world of mathematics.
This volume was prepared under the supervision of a special subcommittee of the MAA's Committee on the Undergraduate Program in Mathematics (CUPM). Primary judgments for titles to be included in each chapter were provided by over 100 college and university mathematics faculty working in 25 teams according to subject area. Initial nominations were drawn primarily from Telegraphic Reviews published in the American Mathematical Monthly and from the earlier Basic Library List. These initial nominations numbered in excess of 15,000 titles. After preliminary screening, titles were arranged by topic to provide 25 lists totaling approximately 4500 nominations to the discipline review teams. These teams then added another 1500 nominations before beginning the major task of establishing priorities. The recommendations published here represent approximately half of the titles originally considered by the review teams.
The process of review has been long and detailed, requiring not only the melding of conflicting opinions by many different experts but also the checking of countless bibliographic details. The result is an amalgam of expert opinion, not a consensus of our many reviewers. Many judgments reflected in these Recommendations are shared by some reviewers but not by others. Our goal was not to make a list of "best books," but to produce a structured set of recommendations that would be useful to undergraduate libraries, that would ensure balance by topic, and that would maintain reasonable limits on the number of recommendations.
Within these constraints, certain informal principles guided the many difficult choices that were required. Routine textbooks were given lower priority than other monographs because it is generally not wise for a library to devote scarce resources to ordinary student texts. In many subjects with dozens of comparable texts, we list a few titles to ensure coverage and omit many others that are essentially similar. In such cases our choices are not primarily a reflection of different quality but of desire to avoid needless duplication. We also tilted choices in favor of recent titles, since this is an area where library committees may be in greatest need of advice. Many old classics which are of great value, especially to libraries that already have them, are not included in our recommendations because new money would probably be more wisely spent on newer books.
Wise use of these Recommendations requires judgment and dialogue between librarians and mathematicians. Many good and valuable books do not appear here, some being cut primarily to meet our self-imposed requirements of total length. Different libraries will view differently the relative priorities of textbooks, of references books, or of advanced monographs. In many situations, libraries may already have comparable books that are not on this list but that nevertheless provide important and equivalent coverage of certain areas. While the collection recommended here does constitute an excellent mathematics library, so would collections with other shapes and other titles. Limited library resources should be used not just to replicate this list as a whole, but to build strength in areas where coverage is thin.
Mathematics is a multi-faceted discipline with innumerable cross-linkages among widely separated specialties. These connections makes the subject fascinating even as they make the task of the bibliographer frustrating. Many titles could easily be listed in several different sections; some seem to fit no section at all. Notwithstanding the difficulties of logically neat classification, titles are listed only once, in some sub-area in which they seem to fit. No cross references have been used, since once begun such a task could go on almost without end.
Each title is listed with spare but adequate bibliographic detail, typically just author(s), title, publisher, and date. Other details such as translators, book series, or special editions are normally omitted. For books that have been revised or reprinted, we normally give only the most recent title with just two dates (and publishers): the first, and the most recent. We leave to librarians and their mathematics department advisors the subtle question of balancing the purchase of new editions against the purchase of new titles.
No attempt has been made to indicate whether books recommended here are still in print. Many are, and many are not. The thriving publication of reprints renders such information ephemeral, outdated before it would appear. Libraries interested in obtaining out-of-print titles can often secure them through used book markets. Perhaps the very presence of an old title among these Recommendations may cause some old classics to be reprinted.
The author index lists each author (or editor) named in the main bibliography together with title of the book and the section in which it appears. This allows anyone checking for particular titles to readily locate them in the main list, where full bibliographic details are provided.
Many people helped with this volume, some of whom I know only through the ubiquitous medium of e-mail. Twenty-five subject-area team leaders undertook the primary responsibility of organizing and amalgamating the diverse recommendations pertaining to each chapter of the bibliography. They were assisted by scores of reviewers who provided advice on various parts of the manuscript. Names of those who helped with various stages of the work are listed on the following pages. Everyone who may benefit from this volume owes these hard-working reviewers a real debt of gratitude.
Policy for the volume was set by a Steering Counting which was established by MAA as an ad hoc Subcommittee of CUPM. Advice from members of the Steering Counting was valuable at all stages of the process. I especially appreciated their counsel at key points where conflicting recommendations regarding policy needed to be resolved.
Typing and checking of innumerable bibliographic details was carried out with unfailing good humor over a period of more than two years by Mary Kay Peterson, who has also prepared every Telegraphic Review that has appeared in the Monthly for the last twenty years. This volume would never have been possible without the consistency provided by her careful attention to details, large and small.
Financial support for preparation of this long-overdue set of recommendations has been provided by grants from the National Science Foundation and the Exxon Education Foundation. Their support made it possible both to prepare the volume and to ensure its distribution to undergraduate libraries.
Despite numerous efforts to check and proof-read this set of recommendations, among the thousands of details there inevitably remain dozens of errors or inconsistencies, missing editions here, or a wrong date there. More substantial errors undoubtedly also occur, improperly categorized titles being the most likely. I hope that these occasional blemishes do not obscure the central purpose and value of the Recommendations as a whole: to provide colleges and universities with useful, contemporary guidance concerning the development of the mathematical sciences collection of an undergraduate library.
Lynn Arthur Steen
St. Olaf College
October 1991