The Skeleton Key of Mathematics: A Simple Account of Complex Algebraic Theories (Dover Books on Mathematics) by D. E. Littlewood

by Dudley E. Littlewood

As the title promises, this helpful volume offers easy access to the abstract principles common to science and mathematics. It eschews technical terms and omits troublesome details in favor of straightforward explanations that will allow scientists to read papers in branches of science other than their own, mathematicians to appreciate papers on topics on which they have no specialized knowledge, and other readers to cultivate an improved understanding of subjects employing mathematical principles. The broad scope of topics encompasses Euclid’s algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers; groups; the Galois theory of equations; algebraic geometry; matrices and determinants; invariants and tensors; algebras; group algebras; and more."It is refreshing to find a book which deals briefly but competently with a variety of concatenated algebraic topics, that is not written for the specialist," enthused the Journal of the Institute of Actuaries Students’ Society about this volume, adding "Littlewood’s book can be unreservedly recommended."

Genres: Science, Mathematics

Paperback Bunko

First published November 11, 2002

About the author

Dudley Ernest Littlewood, D.E. Littlewood

Reviews

[Keith Peters · Rating 2 out of 5]

I was of two minds about this book. I love reading old math books to get a historical perspective on how math has developed on the 50-100 year time scale. I figure it's like an English major reading Chaucer in the original middle english.

And on that front the book didn't disappoint. It was very amusing to see the author assume familiarity with manifolds, but not matrices. And to hear talk about relativity and nuclear energy as hot new topics.

But, ultimately, the author's description of a "simple account of complex algebraic theories" falls short. Unless by simple you mean short. He skips proofs of results in the name of simplicity, but in turn moves very quickly through the material leaving a lot of reading between the lines to the user. And that's not including some of the ambiguous definitions and expressions he uses.

Ultimately, it was nice to see a historical perspective and to see a few things that haven't survived the conversion to the standard educational process, but I can't recommend it for others.

[Megan · Rating 3 out of 5]

This is an interesting survey of several central mathematical concepts, but I don't think it's as useful as a reference or "key" as the title would have you believe. It kind of reads like someone's senior thesis sometimes; fair enough explanations without really enough detail or background, and a little jumpy in proofs and topics. Still it's not totally worthless; the concept is really interesting and it's a nice survey of some ideas that any math grad that's not actively using their degree probably hasn't encountered in a while. However, I think this book would need far more concrete examples of interdisciplinary nature and more coherence between chapters to be truly useful to anyone outside of math. It might only work - and even then only slightly - to serve its intended purpose for mathematicians, enabling them to pick up and read the specialized texts of other scientists, but personally I'm not so sure very good mathematicians couldn't do that already anyway.

[Nick · Rating 2 out of 5]

Not exactly what I expected. We'll see how it ends up.