# A Computational Introduction to Number Theory and Algebra

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About *A Computational Introduction to Number Theory and Algebra:*

Excerpts from book:

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. My goal in writing this book was to provide an introduction to number theory and algebra,with an emphasis on algorithms and applications, that would be accessible to a broad audience. In particular, I wanted to write a book that would be accessible to typical students in computer science or mathematics who have a some amount of general mathematical experience, but without presuming too much specific mathematical knowledge.

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 has some experience in reading and writing mathematical roofs. 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—these courses overlap with some of the material presented here, but even if the reader already as had some exposure to this material, it nevertheless may be convenient to have all of the relevant material easily accessible in one place, and moreover, the emphasis and perspective here will no doubt be different than in a typical mathematics course on these subjects.

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. My goal in writing this book was to provide an introduction to number theory and algebra,with an emphasis on algorithms and applications, that would be accessible to a broad audience. In particular, I wanted to write a book that would be accessible to typical students in computer science or mathematics who have a some amount of general mathematical experience, but without presuming too much specific mathematical knowledge.

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 has some experience in reading and writing mathematical roofs. 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—these courses overlap with some of the material presented here, but even if the reader already as had some exposure to this material, it nevertheless may be convenient to have all of the relevant material easily accessible in one place, and moreover, the emphasis and perspective here will no doubt be different than in a typical mathematics course on these subjects.