Algebraic Number Theory (English, Serge Lang)

Thorough text on ANT

This book is accessible to beginning graduates with a good background in algebra. If you haven't met number fields at all before, then you won't have much intuition for what's going on as the book has no exercises and explicit examples are fairly sparse. The book is really nicely presented, and the examples given at the end of some chapters show you how the theory is coming together (but I wish there were more such lovely examples!) There are certainly some typos and suboptimally presented proofs, despite the efforts of the second edition's editors, hence only four stars. I have spent several hours here and there working out various things for this reason, although I suspect the reader who gets any way into this book will likely have studied enough mathematics not to be derailed by this. The approach taken is global, and doesn't touch much on local fields, and omits higher ramification groups completely. This works all the way up to giving a thorough exposition of global class field theory in the second section. The third and final section deals with some analytic theory of zeta functions and L-series. A thorough and generally well-written book for a more mathematically mature reader.

satisfied consumer

The book was delivered accordingly. I am happy with the purchased.

Not for beginners, but covers the general field in one small book

I think I just have a thing for these grad text series but...this book is, by far, the most simplified algebraic number theory book I have.By "simplified", I do not mean "made easy", but I mean "organized so only the important parts are covered".It is not for beginners into algebraic number theory since Lang assumes his readers to know concepts and theories covered in more basic books. However, it is great for students who have taken a course in alg number theory to decide their direction of interest in the field.The book is thin and light but it is not a light reading.Lang takes the reader through a fast paced course of the general field and (at least for myself) a pen and paper is necessary to follow along.The organization could use work as his use of symbols and variables are sometimes quite different from most other renown mathematicians in the field. Sometimes his variables are defined somewhere hidden in some paragraph.But it is an old book (my version) and this seems pretty common in older books.

Classic

Awesome text. For the more well-versed reader in Algebraic Number Theory. Great resource for a variety of topics.

5.0 out of 5 starsVery good book for ANT

Extremely good