A Computational Introduction to Number Theory and Algebra

Author of "Algebraic Number Theory: A Computational Approach" here, in case anybody has any questions. Here's the history of that book. I first taught an undergraduate class at Harvard in maybe 2002 and went over the first 20 pages of Swinnerton-Dyer's brief course on algebraic number theory book -- expanding it into course-length notes. I taught the course next to grad students at UC San Diego, and added more content inspired by the excellent "Algebraic Number Theory" by Cassels-Frohlich. Then I taught it again twice at Univ of Washington, adding more modern computational content, and resulting in a rough draft of this book. Finally, Travis Scholl (a UW grad student) and I spent the last year polishing it and making it look a bit nicer. The book is under contract to be published by the American Mathematical Society soon.

From the preface:

Prerequisites. The mathematical prerequisites are minimal: no particular mathematical concepts beyond what is taught in a typical undergraduate calculus sequence are assumed.

The computer science prerequisites are also quite minimal: it is assumed that the reader is proficient in programming, and has had some exposure to the analysis of algorithms, essentially at the level of an undergraduate course on algorithms and data structures.

Even though it is mathematically quite self contained, the text does presuppose that the reader is comfortable with mathematical formalism and also has some experience in reading and writing mathematical proofs. Readers may have gained such experience in computer science courses such as algorithms, automata or complexity theory, or some type of “discrete mathematics for computer science students” course. They also may have gained such experience in undergraduate mathematics courses, such as abstract or linear algebra. The material in these mathematics courses may overlap with some of the material presented here; however, even if the reader already has had some exposure to this material, it nevertheless may be convenient to have all of the relevant topics easily accessible in one place; moreover, the emphasis and perspective here will no doubt be different from that in a traditional mathematical presentation of these subjects

From the third review hyperlink (first two are dead): https://amca01.wordpress.com/2009/10/03/book-review-a-comput...

"Although the text requires not much specific mathematical background, I would hesitate to use it except in an advanced class, or for students whose mathematical ability was already high. The material moves swiftly – while never compromising rigour – and the multiple strands assume considerable ability on the part of the reader."

Math textbooks must be reviewed by an expert; yet it's impossible for an expert to see them as a beginner would. If they can see it's difficult for a beginner, it definitely is...

I read a bit the chapter about the distribution of prime numbers. I could follow because I have an Msc in maths (not in number theory) but the progression is fast, and while I don't think one needs an advanced background to read it, one needs to be used to formal reasoning, and I feel like the author is moving fast, so I guess for someone with a low background in maths it would be a hard (but not impossible) read.

Depends what you mean by AI. Back in the day, a computer algerbra system was considered AI, in which case, this book is very relevant. But I can't think of another interpretation of AI that would make this book relevant.