Mathematics

CRC Concise Encyclopedia of Mathematics, Second Edition by Eric W.
Weisstein
(Chapman & Hall CRC) Allows readers to implement the formulas presented,
perform calculations, construct geographical displays of results, and generate
remarkable mathematical illustrations. More than 1000 new pages of terms
defined, illustrated, and referenced. Essentially the print version of
the contents of the website:
www.mathworld.wolfram.com

The second edition of the
CRC Concise Encyclopedia of Mathematics has been designed with the user in
mind and for ease of accessibility. Listed below are various changes in the new
edition that will make the book easier for the reader to use while navigating to
different areas of interest

The MathWorld website, produced by Wolfram Research, Inc..
and Dr. Eric Weisstein, can be found at
http://mathworld.wolfram.com. Wolfram Research, Inc. retains the copyright
in certain entries therein; CRC Press LLC has certain exclusive rights to
publish all of said entries in all media and formats other than free
distribution over the internet.

The
CRC Concise Encyclopedia of Mathematics is a compendium of mathematical
definitions, formulas, figures, tabulations, and references. It is written in an
informal style intended to make it accessible to a broad spectrum of readers
with a wide range of mathematical backgrounds and interests. Although
mathematics is a fascinating subject, it all too frequently is clothed in
specialized jargon and dry formal exposition that make many interesting and
useful mathematical results inaccessible to laypeople. This problem is often
further compounded by the difficulty in locating concrete and easily understood
examples. To give perspective to a subject, I find it helpful to learn why it is
useful, how it is connected to other areas of mathematics and science, and how
it is actually implemented. While a picture may be worth a thousand words,
explicit examples are worth at least a few hundred! This work attempts to
provide enough details to give the reader a flavor for a subject without getting
lost in minutiae. While absolute rigor may suffer somewhat, I hope the
improvement in usefulness and readability will more than make up for the
deficiencies of this approach.

The format of this work is somewhere between a handbook, a
dictionary, and an encyclopedia. It differs from existing dictionaries of
mathematics in a number of important ways. The entries are extensively
crossreferenced, not only to related entries but also to many external sites on
the Internet. This makes locating information very convenient. It also provides
a highly efficient way to "navigate" from one related concept to another.
Standard mathematical references, combined with a few popular ones, are also
given at the end of most entries to facilitate additional reading and
exploration. In the interests of offering abundant examples, this work also
contains a large number of explicit, formulas and derivations, providing a ready
place to locate a particular formula, as well as including the framework for
understanding where it comes from.

The selection of topics in this work is more extensive than
in most mathematical dictionaries (e.g.., Borowski and Borwein's HarperCollins
Dictionary of Mathematics and Jeans and Jeans' Mathematics Dictionary). At the
same time, the descriptions are more accessible than in "technical" mathematical
encyclopedias (e.g., Hazewinkel's Encyclopaedia of Mathematics and Iyanaga's
Encyclopedic Dictionary of Mathematics). While the latter remain models of
accuracy and rigor, they are not terribly useful to the undergraduate, research
scientist, or recreational mathematician. In this work, the most useful,
interesting, and entertaining (at least to my mind) aspects of topics are
discussed in addition to their technical definitions. For example, in my entry
for pi (it), the definition in terms of the diameter and circumference of a
circle is supplemented by a great many formulas and series for pi, including
some of the amazing discoveries of Ramanujan. These formulas are comprehensible
to readers with only minimal mathematical background, and are interesting to
both those with and without formal mathematics training. However, they have not
previously been collected in a single convenient location. For this reason, I
hope that, in addition to serving as a reference source, this work has some of
the same flavor and appeal of Martin Gardner's delightful Scientific American
columns.

Everything in this work has been compiled by me alone. I am
an astronomer by training, but have picked up a fair bit of mathematics along
the way. It never ceases to amaze me how mathematical connections weave their
way through the physical sciences. It frequently transpires that some piece of
recently acquired knowledge turns out to be just what I need to solve some
apparently unrelated problem. I have therefore developed the habit of picking up
and storing away odd bits of information for future use. This work has provided
a mechanism for organizing what has turned out to be a fairly large collection
of mathematics. I have also found it very difficult to find clear yet accessible
explanations of technical mathematics unless I already have some familiarity
with the subject. I hope this encyclopedia will provide jumping-off points for
people who are interested in the subjects listed here but who, like me, are not
necessarily experts.

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