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9781470473327 Academic Inspection Copy

Integer and Polynomial Algebra

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This book is a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields. In addition to introducing students to the rigorous foundations of mathematical proofs, the authors cover several specialized topics, giving proofs of the Fundamental Theorem of Algebra, the transcendentality of $e$, and Quadratic Reciprocity Law. The book is aimed at incoming undergraduate students with a strong passion for mathematics.
Kenneth R. Davidson, University of Waterloo, ON, Canada. Matthew Satriano, University of Waterloo, ON, Canada.
The integers Modular arithmetic Diophantine equations and quadratic number domains Codes and factoring Real and complex numbers The ring of polynomials Finite fields Bibliography Index
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