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Integer and Polynomial Algebra
Kenneth R. DavidsonMatthew Satriano
出版American Mathematical Society, 2023-10-30
主題Mathematics / General
ISBN14704733219781470473327
URLhttp://books.google.com.hk/books?id=HEPsEAAAQBAJ&hl=&source=gbs_api
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註釋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.