Favourite Links and References for Mathematics

Here is my list of what I believe to be the most important or useful links and references for mathematics.

In no particular order…

Numbers

Book
The Book of Numbers
by John H. Conway (Author), Richard Guy (Author)
Springer
Hardcover; 311 pages
ISBN-10: 038797993X
ISBN-13: 978-0387979939
~ £22
This is a wonderful reference for many families and sequences of numbers, and for types of number.

Book
On Numbers and Games
by John H. Conway (Author)
A K Peters
Hardcover; 242 pages
ISBN-10: 1568811276
ISBN-13: 978-1568811277
~ £50
This is a book about ‘surreal numbers’ and a generalisation ‘games’. Surreal numbers include the reals, ordinals and infinities, and infinitesimals. This class is generated by a single construction step that is a combination of the notions of an ordinal constructor and the Dedekind cut.

(Alternative) Book
Surreal Numbers
by Donald E. Knuth (Author)
Addison Wesley
Paperback; 128 pages
ISBN-10: 0201038129
ISBN-13: 978-0201038125
~ £14
This book is a lighter introduction to surreal numbers in the form of a tale.

Integer Sequences

Book
The Encyclopedia of Integer Sequences
by N. J. A. Sloane (Author), Simon Plouffe (Author)
Academic Press
Hardcover; 587 pages
ISBN-10: 0125586302
ISBN-13: 978-0125586306
~ £64
This book contains over 5000 sequences ordered lexicographically, with some illustrations and notes on selected sequences.

Associated Website
The On-Line Encyclopedia of Integer Sequences
http://www.research.att.com/~njas/sequences/

Numerical Constants

Websites
Inverse Symbolic Calculator [ISC]
http://glooscap.cs.dal.ca:8087/index
http://oldweb.cecm.sfu.ca/projects/ISC/

Dictionaries and References

Book
Handbook of Mathematical Functions
by Milton Abramowitz (Editor), I.A. Stegun (Editor)
Dover Publications
Paperback; 1046 pages
ISBN-10: 0486612724
ISBN-13: 978-0486612720
~ £28
Of particular note is the chapter on elementary functions.

Replacement Book and Associated Website
Handbook of Mathematical Functions and
Digital Library of Mathematical Functions (DLMF)
NIST / Cambridge University Press
expected 2009/2010
http://dlmf.nist.gov/

Book
Concise Encyclopedia of Mathematics
by Eric W. Weisstein (Author)
CRC Press
Hardcover: 1969 pages
ISBN-10: 0849396409
ISBN-13: 978-0849396403
This is a dictionary-style encyclopaedia of mathematics.

Associated Website
http://mathworld.wolfram.com/
Unfortunately, but unsurprisingly, this is biased towards Mathematica.

Website
Wikipedia Mathematics Portal
http://en.wikipedia.org/wiki/Portal:Mathematics

Website
Math Overflow
http://mathoverflow.net

and see in particular this page for further maths references.

Combinatorics

Book
Introductory Combinatorics
by Kenneth P. Bogart (Author)
Brooks Cole
Hardcover; 654 pages
ISBN-10: 0121108309
ISBN-13: 978-0121108304
~ $43
An excellent book on the foundations of combinatorics.

Paper
A Survey of Combinatorial Gray Codes
by Carla Savage
http://www4.ncsu.edu/~savage/AVAILABLE_FOR_MAILING/survey.ps
(also available from citeseer)

Finite Calculus

Book
Concrete Mathematics: Foundation for Computer Science
by Ronald L. Graham (Author), Donald E. Knuth (Author), Oren Patashnik (Author)
Addison Wesley
Hardcover; 672 pages
ISBN-10: 0201558025
ISBN-13: 978-0201558029
~ £51
This book describes itself as a meeting of continuous and discrete mathematics.

Paper
Finite Calculus: A Tutorial for Solving Nasty Sums
by David Gleich
http://www.stanford.edu/~dgleich/publications/finite-calculus.pdf

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