Index to Mathematical Problems 1975-1979


In the preface to the first edition of their book Concrete Mathematics published in 1989, Graham, Knuth, and Patashnik state that they have not been able to pin down the sources of many problems that have become part of the folklore. The same year that book was published, a new company called MathPro Press was founded by Stanley Rabinowitz to reference the world’s problem literature in a way that had never been attempted before. In 1992, Rabinowitz introduced a series of books called Indexes to Mathematical Problems. The first volume in that series, Index to Mathematical Problems 1980-1984, truly marked a sea change: never before had so many problems from so many sources been gathered together into a single volume. To problemists worldwide, the introduction of this remarkable book brought the hope that problems and their references might eventually become very easy to locate.

As one might guess, the production of such an index requires an enormous amount of work. But it was not expected that six years would pass from the time the first volume was published until the time this second one was published. The main culprit behind the delay was a seemingly endless variety of loose ends and details that needed tending to. In addition, the editors were not able to devote as much attention to the project as they would have liked during the past few years, because their full-time jobs demanded most of their time. A great deal of work was performed by generous volunteers. Given the unique and valuable nature of this project, it is hoped that some sort of alliance may be forged with one or more of the various mathematical associations that publish problem columns and contests, in order to accelerate book production in the future.

Except for the specific problems indexed, there are few differences between the first two volumes. A new cross-referencing feature was added to the keyword index that allows users to readily browse all classifications containing a given keyword. This feature adds a new dimension to the classification scheme: while still grouping similar problems together as before, now it can also be used to conduct keyword searches. Partly as a result ot this, and partly because the overall database is growing, more detail was added to the lower-level classification categories in this volume.

Another difference between the two volumes is in the typefaces used. The first volume was typeset with the Computer Modern family of fonts created by Donald Knuth, whereas this volume was typeset with the MathTime family of fonts created by Michael Spivak. Finally, Volume 1 contained a very comprehensive list of journals with problem columns; this section has been omitted from the present volume to avoid redundancy. (The list can also be viewed online.)

It should be noted that the collection of contests referenced in this volume is by no means comprehensive. There are dozens of fine contests held around the globe each year. Ones missing from this volume were either too difficult to obtain, or unknown to us. Readers are encouraged to submit information regarding any contests missing from this series (or journals missing from the list mentioned above), so they may be included in future volumes.

It is hoped that users will find this volume at least as useful as Volume 1, if not more useful. The editors must apologize for any errors or omissions in the presentation. In the end, it seemed better to publish with errors than to err by not publishing at all. Please report any typos or mistakes to MathPro Press so they may be corrected in future editions. We are constantly striving to improve our methods of problem indexing, so all comments and suggestions for future enhancements are heartily welcomed.

Stanley Rabinowitz
Chelmsford, Massachusetts

Mark Bowron
Lauhglin, Nevada

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