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# Algebraic number theory

Author: Frazer Jarvis Cham : Springer, [2014] ©2014 Springer undergraduate mathematics series Print book : EnglishView all editions and formats The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes 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.  Read more... (not yet rated) 0 with reviews - Be the first.

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Document Type: Book Frazer Jarvis Find more information about: Frazer Jarvis 9783319075440 3319075446 889026619 xiii, 292 pages : illustrations ; 24 cm. 1. Unique factorisation in the natural numbers -- 2. Number fields -- 3. Fields, discriminants and integral bases -- 4. Ideals -- 5. Prime ideals and unique factorisation -- 6. Imaginary quadratic fields -- 7. Lattices and geometrical methods -- 8. Other fields of small degree -- 9. Cyclotomic fields and the fermat equation -- 10. Analytic methods -- 11. The number field sieve -- Appendix A: Solutions and hints to exercises. Springer undergraduate mathematics series Frazer Jarvis.

### Abstract:

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  Read more...

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"Undergraduate mathematics students need both to develop facility with numerical and symbolic calculation and comfort with abstraction. Algebraic number theory offers an ideal context for Read more...

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