Chapter 1: A Time for ReckoningThis chapter provides an introduction to the motivation and purpose of the book, as well as an overview of its contents. 
Chapter 2: PrimitivesThis chapter describes techniques related to multiplication, division and repeating decimals, greatest common divisor (GCD), errorchecking and divisibility tests, and factoring numbers. 
Chapter 3: RootsThis chapter provides a brief description of methods for finding the roots of perfect powers, then delves into methods for mentally approximating square roots, a general method for mentally extracting square roots to any number of digits that is more powerful than the traditional method, an iterative technique for reciprocal square roots, and extensions of these methods to cube and higherorder roots. 
Chapter 4: Logarithms and Their InversesAfter a brief review of logarithms, this chapter discusses general approximation techniques for common and natural logarithms that are suitable for mental calculation, then details more accurate relations involving neighboring and intermediate values, offers methods for the more difficult problem of finding inverse logarithms, and concludes with an example of using logarithms and inverses to find higherorder roots of numbers. 
Chapter 5: Trigonometric Functions and Their InversesThis chapter provides convenient 3 to 4digit approximations to the sine, cosine, tangent, arcsine, arccosine and arctangent functions in units of degrees or radians. Graphs provide error curves for each method as a means of evaluating them. 
Chapter 6: Concluding RemarksThe main text of the book ends with a list of the best of the cited references in the text, an encouragement to search out these references (which are now gathered on this site), and a plea for the reader to experiment with number relationships as a means of exploring new algorithms and approximations that may be useful to us all. 
Appendix: Finding Rational Approximations to Precomputed ConstantsOften we encounter multidigit numbers, such as scaling factors, that are difficult to use directly as a divisor or multiplier because of the number of digits involved. This appendix describes the general procedure (using continued fractions) for generating wholenumber fractions that approximate multidigit numbers to a required accuracy and in practice involve multiplication and division by reasonably small whole numbers. 
Online: Web Material on Additional TopicsThis area contains materials relating to advanced mental calculation that either do not appear in the book or are covered in greater detail here. Work by others is also hosted here with their permissionplease contact me if you have an idea or writeup for this section. 
Acknowledgements of Contributors to this Book Section:
Contributors to individual chapter pages are given on those pages. However, the following individuals offered advice that was incorporated in creating the structure and content of this section. Feel free to contact me with any more suggestions.
John McIntosh has provided extensive feedback on the book. His website contains many very interesting and original essays on similar areas of mathematics, of which the top mathematics level is here. He has also written an essay summarizing things he found particularly interesting in the book, with additional interesting commentary of his ownit can be found here.
Grant Nixon published a very nice review, and followed up with very interesting correspondence on the book.
Thomas Wall and John O., in their Amazon.com reviews of the book, commented on the need for additional material, such as exercises and errata, that would benefit the reader. This led in part to the creation of this webpage.
Works Citing This Book:
Ron HaleEvans, Mind Performance Hacks: Tips & Tools for Overclocking Your Brain  Referenced 

David Pimm, Symbols and Meanings in School Mathematics , Routledge, London, 1995  Book excerpts quoted in discussions of modern mathematics education 

Dell, Dick, ed., The World Book of Math Power, Vol. 2, World Book, Chicago, 1996  Suggested book "intended for those in high school, college, or professional occupations who are intrigued by mathematics" in Sources of Mathematical Materials.  
Wikipedia (German Edition), Kopfrechnen (“ Mental Arithmetic ”), Web Translation: “Genuine Mental Arithmetic: Techniques are offered only rarely for the general mental arithmetic. This area normally covers all functions, which more on the average train pocket calculators control must. One of the few good works in this area is the book Dead Reckoning  Calculating Without Instruments of Ronald W. Doerfler. Unfortunately no German translation of this book exists.”  
Harold Thimbleby, “Calculators are Needlessly Bad,” International Journal of HumanComputers Studies (2000)  Referenced  
School of Mathematics and Statistics, University of St Andrews, Scotland, History of Mathematics Site, “Memory, mental arithmetic and mathematics.”  Referenced  
“Percent Change: Big Lies We Are Taught in Government Schools,”  Referenced  
"Dead Reckoning," an essay by John McIntosh on his website summarizing things he found particularly interesting in the book, with additional interesting commentary of his own. 