A Computational Introduction to Number Theory and Algebra

A Computational Introduction to Number Theory and Algebra
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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

"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...