Algebraic Number Theory

by Ian Stewart

Contents: Preface. Reader's Guide. Index of Notation. The Origins of Algebraic Number Theory. Part I: Numbers. Quadratic and Cyclotomic Fields. Geometric Methods. Lattices. Minkowski's Theorem. Part II: Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Part III: Number-Theoretic Applications. Computational Methods. Fermat's Last Theorem. Dirichlet's Units Theorem. Appendix. Quadratic Residues. References. Index.

Genres: Mathematics, Algebra, Textbooks, Reference

288 pages, Paperback

First published January 1, 1979

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.

Reviews

[Jon-Erik G. Storm]

I have been working on understanding the proof of Fermat's Last Theorem for several years. I'm pretty strong in analysis and algebra, but I really know nothing about modularity. Hoping this one teaches me enough to get me there.

P.S. I need some work on modular forms to really understand the proof, but this gave me enough context to understand the broader strokes. I'm good with the elliptic curves, numbers, and algebra and this book explains it well too.

[George Law]

A very good account of algebraic-number theory, a branch of mathematics whose genesis was motivated by the search for a proof of Fermat’s last theorem, as well as a brief discussion of the ideas used by Andrew Wiles for his Wolfskehl Prize winning proof. I thought the theory of ideals could be developed a bit further, but I understand that the central theme of the book is on FLT.

[Chris]

A captivating beach read for the algebraically literate non-specialist.

[Amar Pai]

Good overview of algebraic number theory as it applies to FLT, however not exactly pitched at beginners. You'll want to have a grounding in abstract algebra & linear algebra at the minimum. Still, even if you don't, you can get a good sense of the "big picture" and a high-level understanding of the advances in mathematics that were directly or indirectly related to attempts to solve FLT. Overall a fascinating read if you're a math geek who wants something a little deeper than Simon Singh's pop treatment of Wiles' proof.

[Peng Gao]

The book with shorter title seems more useful but cannot find it in this database