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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