zbMATH — the first resource for mathematics

Using the mathematics literature. (English) Zbl 1118.00001
Books in Library and Information Science 66. New York, NY: Marcel Dekker (ISBN 0-8247-5035-7/hbk). viii, 389 p. (2004).
The volume provides an interesting guide to the mathematics literature. Hints for searching and accessing all types of mathematical publications are given. The first three chapters are of general nature while the following concentrate on different mathematics subject areas, providing lists of references, in many cases with comments, subdivided into main subareas, types of publications, expectations from the reader and more. Sometimes some general information on the subject area is given or could be recognized from the subdivision.
The collection is a valuable source of information and should be available at all mathematical libraries, at least for Anglo-American universities. As far as refers to the printed literature the references mainly represent what may be available at such a library. Almost all books are from publishers in North America or Great Britain. But this is an effect, which could not be avoided, when selecting references and recommending them for a certain group of users. For example, a European counterpart of the collection may be different, not speaking about other parts of the world.
Short descriptions of the single contributions will be given below.
The first three general chapters start with an interesting essay by the editor of the collection dealing with mathematics culture. This presents philosophical, historical and sociological aspects of mathematics enhanced by well-selected citations from outstanding mathematicians. Many people (including the reviewer) probably will not share the view of the author, but this belongs to the nature of the subject. The second chapter, also by the editor, gives limits how to find mathematics information: basic explanations, equations, algorithms, people, societies, publishing aids etc. In the third chapter on searching the research literature Molly T. White exhibits the history and the search functionalities of the reference data bases in mathematics and the possibilities to find mathematics papers on the web.
The rest of the chapters describe recommended resources in different subjects. Fernando Gouvêa composed the collection for history in mathematics, giving a small comment to almost all citations. The same applies to number theory written by Jay Goldman and Kristine K. Fowler. The chapter on combinatorics by Kristine K. Fowler and Victor Reiner provides citations only. It should be remarked that this chapter also swallows discrete geometry, convexity and optimisation, which may be considered as misleading by geometers and other specialists. The chapter on abstract algebra written by Edgar Enochs and Kristine K. Fowler is enriched by comments again. Chapter 8 by Thomas Garrity combines algebraic and differential geometry. Though the part on differential geometry contains several of the reviewer’s favorites the selection as a whole is a little strange and leaves a lot of gaps. A short chapter with comments on real and complex analysis is written by John McDonald. Both kinds of differential equations are handled by Jan Figa including comments again. Allen Hatcher collected the recommendations in topology. There follow the surveys on probability and stochastic processes by Randall J. Swift and on numerical analysis by Kendall Atkinson. Mathematical biology gets special attention in the nicely elaborated article by Claudia Neuhauser and Kristine K. Fowler. This is the only applied area handled in more detail. The collection ends with an article on mathematics education by Kelly Gaddis, Jane-Jane Lo and Jinfa Cai with a lot of citations and interesting comments. An author index and a subject index are added for the convenience of the reader.
Obviously there are some gaps in the coverage of the subjects of interest in mathematics. But even to collect the current selection is a tremendous work which will be appreciated by most mathematicians.
00A05 Mathematics in general
97-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematics education