Smarandache sequences are a family of sequences of integers around which
one can formulate various number-theoretical questions. For example, on
page 6 of this book, we find the "Smarandache Symmetric Sequence",
New
technologies create new possibilities. Early in 1999, John B. Cosgrave,
using off-the-shelf mathematical software and mathematical ideas due to
H. C. Pocklington, found a prime number with exactly 2000 digits. With the
year 2000 on the horizon, it was inevitable that the number of digits would
be related to the millennium. Cosgrave himself called it his "millennium
prime," and its discovery garnered him some attention. For example, Ivars
Peterson mentioned it in one of
his MathTrek columns. Excited by his discovery, Cosgrave wrote a long email message to his niece and nephew explaining some of the ideas that led to the discovery of the millennium prime. This email message now forms the major portion of the booklet A Prime for the Millennium, published by Folding Landscapes Press in Ireland. The booklet is charming, the story well told, and profits from the sales go to the Irish Cancer Society. Not a bad deal at all; check it out. (Fernando Q. Gouvêa)
Smarandache sequences are a family of sequences of integers around which
one can formulate various number-theoretical questions. For example, on
page 6 of this book, we find the "Smarandache Symmetric Sequence",
Pluckings from the Tree of Smarandache Sequences and Functions is Charles Ashbacher's third book on "Smarandache Notions." In this book, he tries to make some progress on questions such as the one above, questions which are generally very difficult. Ashbacher plays with the various notions, obtains partial results, does computer experiments. There are a few theorems, but mostly there are questions, conjectures, and examples. Most of the mysteries being studied remain mysterious.
Hermann Grassmann's Extension Theory (Ausdehnungslehre), first
published in 1862, is a legendary book in the history of mathematics.
Extending the ideas in his earlier book Linear Extension Theory,
Grassmann here introduces a whole "calculus of extensive magnitudes" that
is one of the historical roots of modern linear and multilinear algebra. In
contrast to Grassmann's earlier book, this one is more mathematical and
less philosophical. It also goes much deeper into the subject, including
applications of Grassmann's ideas to what we would describe as
multivariable calculus. Grassmann's earlier book and some of his shorter
works had already been translated into English by Lloyd C. Kannenberg a few
years ago and published as A
New Branch of Mathematics (Open Court, 1995). Here the same translator
brings us Grassmann's more mature book. This new book in the "Sources"
subseries is a most welcome addition to the AMS/LMS History of
Mathematics series. A must-buy for those seriously interested in the
history of mathematics. (Fernando Q. Gouvêa)
A Prime for the Millennium, by John B. Cosgrave. Folding Landscapes, Ireland, 2000. Paperback, 48pp, $27 (including airmail postage) or $24 (including surface mail postage). ISBN 09-530509-0-4.
See also John B. Cosgrave's page about his booklet.
Pluckings from the Tree of Smarandache Sequences and Functions, by Charles Ashbacher. American Research Press, 1998. Paperback, 87pp, $9.95. ISBN 1-879585-61-8.
Extension Theory, by Hermann Grassmann. History of Mathematics, volume 19. American Mathematical Society and London Mathematical Society, 2000. Softcover, 411pp, $75.00. ISBN 0-8218-2031-1.
Fernando Gouvêa (fqgouvea@colby.edu) is Associate Professor of Mathematics at Colby College in Waterville, Maine. His special interests include number theory, history of mathematics, science fiction, and Christian theology.
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Read This! is the MAA Online book review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouvêa, Dept. of Mathematics, Colby College, Waterville, ME 04901. Publishers, please check our reviews information page.
MAA Online is edited by Fernando Q. Gouvêa (fqgouvea@colby.edu). Last modified: Wed May 17 22:58:20 -0500 2000