It is the immodest hope of the authors that this Dictionary will not only prove valuable as a reference book for students of mathematics at all levels from secondary school to master's degree, but also offer much to interest a more general readership. We have no illusions that a reference book can supplant authoritative textbooks, but we nonetheless believe that the Dictionary will serve a distinct, complementary, and useful purpose. We have thus attempted to include anything we consider of interest or mnemonic value to the reader: there are formal accounts of certain terms of elementary arithmetic (in terms unavoidably reminiscent of Tom Lehrer's 'New Math'), informal accounts of a number of common logical paradoxes, and less than hagiographic biographies of the luminaries in the history of mathematics.

Our more serious aspiration was the inclusion of any term that an undergraduate might encounter not only within, but also in reading around, any course at any college or university, and we have also deliberately set out to tailor the explanation of each term to the mathematical knowledge of the reader who is likely to consult it. But this ideal overreaches the practicalities, since syllabuses vary greatly in scope, level, and order of presentation, and there are also various demarcation disputes, particularly at the intersection of applied mathematics and physics. In resolving these conflicts, we gave some weight to the existence of the other volumes of the present series; for that reason there is little computing or economics, but a considerable amount of logic. However, our prime consideration remained the likelihood of a mathematics student encountering a given term, so that our comparative liberality towards mechanics and statistics is a consequence of the prominence of these subjects in many undergraduate syllabuses. Thus in general we believe we have erred on the side of inclusiveness, albeit that some lacunae undoubtedly remain,however inadvertently, and that for some advanced terms we have taken refuge in mere indications of the context in which the term occurs, and limitations of space and the demands of readability have dictated that some definitions are relatively informal.

Preface

Dictionary of Mathematics

  Symbols and Conventions

 Table of Derivatives and Integrals

  Hilbert Problems

  Millennium Problems

  Forty-four useful constants

  Web Resources