Number Theory: A Lively Introduction with Proofs, Applications, and Stories
暫譯: 數論：生動的介紹，包含證明、應用與故事
Pommersheim, James, Marks, Tim, Flapan, Erica
- 出版商: Wiley
- 出版日期: 2010-02-15
- 售價: $6,520
- 貴賓價: 9.5 折 $6,194
- 語言: 英文
- 頁數: 763
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0470424133
- ISBN-13: 9780470424131
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相關主題
商品描述
Readable discussions motivate new concepts and theorems before their formal definitions and statements are presented. Many theorems are preceded by Numerical Proof Previews, which are numerical examples that will help give students a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before the statement and proof are formalized in more abstract terms. In addition, many applications of number theory are explained in detail throughout the text, including some that have rarely (if ever) appeared in textbooks.
A unique feature of the book is that every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth Explorations, in which a series of exercises develop a topic that is related to the material in the section.
商品描述(中文翻譯)
《數論：生動的介紹，包含證明、應用與故事》是一本新書，提供了一個嚴謹但易於理解的初等數論介紹，並附有相關的應用。可讀的討論在正式定義和陳述之前，激發新的概念和定理。許多定理之前都有《數值證明預覽》，這些數值範例將幫助學生具體理解定理的陳述及其證明背後的思想，然後再以更抽象的術語形式化陳述和證明。此外，書中詳細解釋了數論的許多應用，包括一些在教科書中很少（如果有的話）出現的應用。
這本書的一個獨特特點是每一章都包含一個《數學神話》，這是一個虛構的故事，以友好、吸引人的方式介紹一個重要的數論主題。許多練習題集包含深入的《探索》，其中一系列練習發展與該部分材料相關的主題。
作者簡介
Tim Marks is a Research Scientist at Mitsubishi Electric Research Laboratories in Cambridge, Massachusetts. Previously, he taught high school mathematics and physics for three years, and he worked for three years as a mathematics textbook editor at McDougal Littell/ Houghton Mifflin. Marks and Pommersheim have taught number theory at the Johns Hopkins University's Center for Talented Youth (CTY) summer program for 19 years. Marks earned his A.B. degree from Harvard University. He completed his Ph.D. and postdoctoral research at the University of California, San Diego.
Erica Flapan joined the mathematics department at Pomona College in 1986. She held post-doctoral positions at Rice University and the University of California, Santa Barbara. Flapan has taught a wide range of mathematics courses and has numerous publications in topology and its applications to chemistry, including her book When Topology Meets Chemistry. She developed a course entitled Problem Solving in the Sciences," which aims to teach students the mathematics they need in order to succeed in science and economics. Flapan obtained her Ph.D. in knot theory from the University of Wisconsin and is the Lingurn H. Burkhead Professor of Mathematics at Pomona College.
作者簡介(中文翻譯)
詹姆斯·波默斯海姆是瑞德學院的凱瑟琳·皮戈特數學教授。他曾在高等研究院、麻省理工學院和加州大學伯克利分校擔任博士後職位，並在新墨西哥州立大學和波莫納學院的數學系任教。波默斯海姆在多個領域發表了研究論文，包括代數幾何、數論、拓撲學和量子計算。他喜歡教授數論給不同程度的學生：大學數學及數學教育學生、優秀的高中生以及高級研究生。波默斯海姆在芝加哥大學獲得博士學位，並在那裡師從威廉·富爾頓。
蒂姆·馬克斯是位於麻薩諸塞州劍橋的三菱電機研究實驗室的研究科學家。此前，他曾教授高中數學和物理三年，並在麥克杜格爾·利特爾/霍頓·米夫林擔任數學教科書編輯三年。馬克斯和波默斯海姆在約翰霍普金斯大學的天才青年中心（CTY）夏季計劃中教授數論已經19年。馬克斯在哈佛大學獲得A.B.學位，並在加州大學聖地亞哥分校完成博士學位及博士後研究。
艾瑞卡·弗拉潘於1986年加入波莫納學院的數學系。她曾在萊斯大學和加州大學聖巴巴拉分校擔任博士後職位。弗拉潘教授了多種數學課程，並在拓撲學及其在化學中的應用方面發表了多篇論文，包括她的著作《當拓撲學遇上化學》（When Topology Meets Chemistry）。她開發了一門名為“科學中的問題解決”的課程，旨在教授學生在科學和經濟學中成功所需的數學。弗拉潘在威斯康辛大學獲得了結理論的博士學位，並是波莫納學院的林根·H·伯克海德數學教授。
