Elementary Number Theory
暫譯: 初等數論

Effinger, Gove, Mullen, Gary L.

Elementary Number Theory
  • 出版商: CRC
  • 出版日期: 2021-09-09
  • 售價: $2,580
  • 貴賓價: 9.5 折 $2,451
  • 語言: 英文
  • 頁數: 242
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1032017236
  • ISBN-13: 9781032017235

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相關主題

商品描述

Elementary Number Theory, Gove Effinger, Gary L. Mullen

This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject.

Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter.

The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.

商品描述(中文翻譯)

《初等數論》，Gove Effinger，Gary L. Mullen

本書旨在作為本科生對數論的入門教材。作者在這一數學領域浸淫多年，希望本書能激勵學生（以及教師）學習、理解並熱愛這一真正美麗的學科。

每一章在介紹之後，清晰地分為幾個部分，發展出一個新的主題，這些部分包括理論材料以及大量的例子，每個例子都詳細解釋。在每一章的結尾，除了對主題的總結外，還有若干已解決的問題，這些問題也都詳細解答，隨後是一組補充問題。這些補充問題讓學生有機會測試自己對材料的理解；部分問題的解答會在章末提供，但並非所有問題都有解答。

前八章討論了一些初等數論中的標準材料。其餘章節則討論一些可能被認為稍微進階的主題。本書以一章關於數論中的開放問題作結。強烈建議學生（當然還有教師）仔細研究這一章，充分意識到並非所有數學問題和難題都已解決！在數學領域，尤其是數論中，仍有許多需要學習的知識和許多問題等待解答。

作者簡介

Gove Effinger received his Ph.D. in Mathematics from the University of Massachusetts (Amherst) in 1981 and subsequently taught at Bates College for 5 years and then Skidmore College for 29 years. He is the author of three books: An Elementary Transition to Abstract Mathematics (with Gary L. Mullen, CRC Press), Additive Number Theory of Polynomials over a Finite Field (with David R. Hayes), and Common-Sense BASIC: Structured Programming with Microsoft Quick BASIC (with Alice M. Dean), as well as numerous research papers. His research focus has primarily been concerned with the similarities of polynomials　over a finite fields and ordinary integers.

　

Gary L. Mullen is Professor of Mathematics at the Pennsylvania State University, University Park, PA. He has taught both undergraduate and graduate courses there for over 40 years. In addition, he has written more than 150 research papers and co-authored seven books, including both graduate as well as undergraduate textbooks. He also served as department head for seven years and has served as an editor on numerous editorial boards, including having served as Editor-in-Chief of the journal Finite Fields and Their Applications since its founding in 1995.

作者簡介(中文翻譯)

戈夫·艾芬傑於1981年在麻薩諸塞大學（阿默斯特）獲得數學博士學位，隨後在貝茨學院任教5年，然後在斯基德莫爾學院任教29年。他是三本書的作者：《初步過渡到抽象數學》（與加里·L·穆倫合著，CRC出版社）、《有限域上的多項式加法數論》（與大衛·R·海耶斯合著）以及《常識BASIC：使用Microsoft Quick BASIC的結構化程式設計》（與愛麗絲·M·迪恩合著），並發表了多篇研究論文。他的研究重點主要集中在有限域上的多項式與普通整數之間的相似性。

加里·L·穆倫是賓夕法尼亞州立大學（University Park, PA）的數學教授。他在那裡教授本科和研究生課程超過40年。此外，他撰寫了超過150篇研究論文，並共同編著了七本書，包括研究生和本科教科書。他還擔任了七年的系主任，並在多個編輯委員會中擔任編輯，自1995年創刊以來擔任期刊《有限域及其應用》的主編。

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