Customer Reviews

Theory of Algebraic Numbers

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This review refers to the 1965 Hardcover version of the book.

It's quite apparent that the 40 years that have passed since this book was printed have very much dated it's content. The definitions of many key concepts (such as an ideal) contain the right ideas, but are not formulated in the modern viewpoint. These, however are only minor setbacks. The main flaw of this book is its subject matter. There are 11 chapters, and it was not until the eighth that the ideas start getting deeper. Even these last 4 chapters do not delve very far into the heart of things.

The text is written with the reader in mind (almost excessively so). Useful equations are clearly labeled and the steps in the proof are clearly outlined, though sometimes to an unnecessary degree.

I would recommend this book for a mathematics hobbyist, or perhaps an undergraduate number theory course. For anyone with a stronger background, they wil not glean much.

Proceeding from the Fundamental Theorem of Arithmetic, into Fermat's Theory for Gaussian Primes, this book provides a very strong introduction for the advanced undergraduate or beginning graduate student to algebraic number theory. The book also covers polynomials and symmetric functions, algebraic numbers, integral bases, ideals, congruences and norms, and the UFT.