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商品描述
Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics.
Aligning with the trend toward smaller, essential texts in mathematics, the author strives for clarity of exposition. Proof techniques and proofs are presented slowly and clearly.
The book employs a versatile approach to the use of algebraic ideas. Instructors who wish to put this material into a broader context may do so, though the author introduces these concepts in a non-essential way.
A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems urges students realize unique factorization into primes is a more subtle idea than may at first appear; students will find this chapter interesting, fun and quite accessible.
Applications of number theory include several sections on cryptography and other applications to further interest instructors and students alike.
商品描述(中文翻譯)
《數論入門》涵蓋了一門入門級數論課程的基本內容，包括可除性和質因數分解、同餘和二次互反律。教師還可以從一系列額外的主題中選擇。
與數學中對更小、更基本的教材的趨勢相一致，作者力求清晰地陳述。證明技巧和證明過程被慢慢且清晰地呈現。
本書採用了一種多功能的代數思想方法。希望將這些材料放入更廣泛的背景中的教師可以這樣做，儘管作者以非必要的方式介紹了這些概念。
最後一章討論了代數系統（如高斯整數），假設讀者之前沒有接觸過抽象代數。研究一般系統促使學生意識到唯一質因數分解比起初看起來更為微妙；學生們會發現這一章有趣、有趣且相當易於理解。
數論的應用包括幾個關於密碼學和其他應用的部分，以進一步引起教師和學生的興趣。
作者簡介
Mark Hunacek has advanced degrees in both mathematics (Ph.D., Rutgers University) and law (J.D., Drake University Law School). He is now a Teaching Professor Emeritus at Iowa State University, and before entering academia he was an Assistant Attorney General for the state of Iowa.
作者簡介(中文翻譯)
Mark Hunacek擁有數學（Rutgers大學博士學位）和法律（Drake大學法學院法學博士學位）的高級學位。他現在是愛荷華州立大學的名譽教授，之前在學術界之前，他曾是愛荷華州助理檢察總長。
