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

Description

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 ActuariesStudents’ Society about this volume, adding “Littlewood’s book can be unreservedly recommended.”

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an old, elegantly presented, reminder of algebraic theories which should be general knowledge of the mathematics and physics students now. Disgracefully, they are not, and a short, concise review is something which could be readen in a pair of afternoons for the mere pleasure of adquiring a general idea of many theories. This book provides that, if one is prepared to cope with a little antique names. Dr. Littlewoods “Simple Account” should be amply recommended.

⭐The content is good but the kindle version is full of typos, something particularly damaging in a math book.

⭐This book, covers just about everything important in algebra from basic operations on numbers to groups and tensors, both pure and applied, and all in less than 150 pages!Given, the above scope, it moves quickly, but should be completely comprehensible to anyone with a strong High School math background, as long as the student reads slowly and carefully. The advantage of the compression is that it is possible to see the whole field and its connections without getting mired in the details.Fantastic for a broad overview of algebra, prior to studying in more detail (or afterwards, to see how it all fits together). Don’t be put off by the age of the book and, for the money, unbeatable. Littlewood also wrote “A University Algebra,” dating from 1950, which covers similar topics in more detail.

⭐I used the chapter on Galois Theory as a reference for a course I was in because it had such a concrete explanation on how Galois Theory works. However, it didn’t mention anything about field extensions & barely mentioned groups. That’s why I liked this book, it gives concrete versions of things like (off the top of my head) complex variables, matrices, Galois Theory, polynomials, tensors & more. There’s a chapter on each subject & treats it in a very concrete manner. Any math student not totally comfortable with abstractness (as I was, with Galois Theory of equations anyway) would find this book helpful, imo.

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