Careful organization and clear, detailed proofs make this book ideal either for classroom use or as a stimulating series of exercises for mathematically-minded individuals. Modern abstract techniques focus on introducing elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
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25 of 25 people found the following review helpful:
3.0 out of 5 stars
Uncompromising and difficult,
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This review is from: Algebraic Number Theory (Dover Books on Mathematics) (Paperback)
Make no mistae about it, this is a very difficult book. It is pitched at a highly advanced level and assumes a good deal of ring and field theory and makes no concessions by way of pausing to briefly summarise what is assumed at any point. Parts of the book also progress very quickly and consist of streams of definitions with next to no examples followed by a chunk of theorems that depend on the terms introduced to such an extent that the material has to be re-read many times to glean any understanding. Although in terms of the amount of material covered this is a comprehensive text, it is far too concise for student use. It might have some limited appeal as an advanced postgraduate reference book, but for anyone not already well up to speed in algebraic number theory this will be heavy going indeed.
11 of 15 people found the following review helpful:
4.0 out of 5 stars
A high level book,
This review is from: Algebraic Number Theory (Dover Books on Mathematics) (Paperback)
This book seems to be a good description of Algibraic valuations. Potential buyers should know that it assumes what seems to be a knowlage of graduate-level mathematics, particularly a thurogh knowlage of mathematical fields.
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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Citations (learn more)
36
books
cite this book:
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- The Mathematical Experience, Study Edition by Philip J. Davis on page 207, and Back Matter
- Mathematics of Physics and Engineering by Edward K. Blum on page 432, and Back Matter
- Algebraic Number Theory by H. Koch in Back Matter
- Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics) by Wladyslaw Narkiewicz in Back Matter
- Gauss and Jacobi Sums (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Bruce C. Berndt in Back Matter
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