Algebraic Number Theory (Springer Undergraduate Mathematics Series) 2014th Edition by Frazer Jarvis (PDF)

Description

This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

User’s Reviews

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

⭐Very clear and friendly introduction to ANT. It does not assume too much background and can be read by CS Majors who might not have taken a course in Commutative Rings/Modules.

⭐Very readable introduction to the subject. The presentation of the Number Field Sieve is nicely done, the clearest I’ve seen.

⭐This book has excellent content at a reasonable price.

⭐Chapter9まで読了。代数体の拡大のうち、Ｑ上の拡大のみに絞っているので、ディリクレの単数定理まで比較的早く到達できるが、Ｑ上でない一般の代数体上については他の本で補っていく必要はある。Chapter5のイデアルの(絶対)ノルムの有限性のあたりで証明が急に不親切に感じられたので、単因子論について載っている他の本を参考にした。Chapter7のミンコフスキーの理論は証明などでそれまでに比べて色々と不備が感じられた。ノイキルヒの代数的整数論などで補完。不備は見られるが代数的整数論の導入としては役立ったので☆4つ

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Algebraic Number Theory (Springer Undergraduate Mathematics Series) 2014th Edition PDF Free Download
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Algebraic Number Theory (Springer Undergraduate Mathematics Series) 2014th Edition 2014 PDF Free Download
Download Algebraic Number Theory (Springer Undergraduate Mathematics Series) 2014th Edition PDF
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