Three Infinities in Mathematics: Projective Geometry, Infinitesimal Analysis, Set Theory
暫譯: 數學中的三個無窮大：射影幾何、無窮小分析、集合論
Panza, Marco, Struppa, Daniele C.
- 出版商: Springer
- 出版日期: 2026-05-26
- 售價: $3,050
- 貴賓價: 9.5 折 $2,897
- 語言: 英文
- 頁數: 431
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3032002761
- ISBN-13: 9783032002761
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相關分類:
離散數學 Discrete-mathematics
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相關主題
商品描述
This book is intended as conceptual introduction to three mathematical theories arising from the attempt to understand (actual) infinity. Though the treatment does not avoid technical aspects, it tries to explain their origins and purposes. The book is divided into three parts, each composed of two chapters and a few appendices. Each part presents in detail one of three moments in which mathematicians made a concerted effort to control the idea of infinity: Projective Geometry, Infinitesimal Calculus, and Set Theory. The text includes exercises and philosophical and/or historical remarks. It is written both for non-mathematicians interested in understanding the most relevant ideas that govern these theories, and for professional mathematicians interested in exploring the possibility of a conceptually-engaged presentation of mathematical contents. The book can be used for advanced undergraduate students, as well as for beginning graduate students.
商品描述(中文翻譯)
本書旨在作為對三個數學理論的概念性介紹，這些理論源於對（實際）無限的理解嘗試。雖然內容不避開技術性方面，但它試圖解釋這些理論的起源和目的。本書分為三個部分，每個部分由兩章和幾個附錄組成。每個部分詳細介紹數學家在控制無限概念方面所做的三個重要努力：射影幾何、無窮小微積分和集合論。文本中包含練習題以及哲學和/或歷史的評論。它既是為了對數學不太熟悉的讀者，幫助他們理解這些理論中最相關的思想，也為專業數學家提供探索數學內容概念性呈現可能性的機會。本書適合高年級本科生以及初級研究生使用。
作者簡介
Marco Panza is currently Kennedy Professor of Philosophy at Chapman University, where he is a member of both departments of philosophy and mathematics, and Director of the Graduate Program MPP (Mathematics, Philosophy and Physics) at the Schmid College of Science and Technology. He is also Emeritus Research Director at the CNRS and a member of the IHPST (CNRS and Univ. of Paris 1, Panthéon-Sorbonne). He held also positions at the University of Geneva, Nantes and at ICREA (Univ. Pompeu Fabra, Barcelona).
He is the author of several peer reviewed articles and books in the domains of history and philosophy of mathematics and logic, and is presently co-editor in Chief of Historia Mathematica.
Daniele C. Struppa is currently the President of Chapman University, where he also holds the Donald Bren Presidential Chair in Mathematics. Before joining Chapman University as its Provost in 2006, he held positions at George Mason University in Virginia, and at the University of Calabria, the Scuola Normale Superiore in Pisa, and the University of Milano, all in Italy. Daniele C. Struppa has published more than 250 peer reviewed articles and books in a variety of topics, but his current emphasis is on Fourier Analysis, with applications to Quantum Physics, and on Hypercomplex Analysis. He was the recipient of the Bartolozzi Prize of the Italian Mathematical Union in 1981, for his work on convolution equations, and more recently one of his papers on the violation of the pigeonhole principle in quantum physics was awarded the 2016 Cozzarelli Prize from the National Academy of Sciences. Daniele C. Struppa is also a Managing Editor of Quantum Studies, Mathematics and Foundations, and is on the Editorial Board of several journals, including Complex Analysis and Operator Theory, and the Milan Journal of Mathematics.作者簡介(中文翻譯)
馬可·潘扎（Marco Panza）目前是查普曼大學（Chapman University）的肯尼迪哲學教授，並且是哲學與數學兩個系的成員，同時擔任施密德科學與技術學院的研究生課程 MPP（數學、哲學與物理）的主任。他也是法國國家科學研究中心（CNRS）的榮譽研究主任，以及 IHPST（法國國家科學研究中心與巴黎一大，潘提翁-索邦大學）的成員。他曾在日內瓦大學、南特大學及 ICREA（巴塞隆納的龐培法布拉大學）擔任職位。
他是數學與邏輯的歷史和哲學領域中幾篇經過同行評審的文章和書籍的作者，目前擔任《數學史》（Historia Mathematica）的共同主編。
丹尼爾·C·斯特魯帕（Daniele C. Struppa）目前是查普曼大學的校長，並擔任數學的唐納德·布倫總統椅。在2006年加入查普曼大學擔任教務長之前，他曾在維吉尼亞州的喬治梅森大學、意大利的卡拉布里亞大學、比薩的高等師範學校以及米蘭大學擔任職位。
丹尼爾·C·斯特魯帕已發表超過250篇經過同行評審的文章和書籍，涵蓋多個主題，但他目前的重點是傅里葉分析，並應用於量子物理，以及超複雜分析。他於1981年因其在卷積方程方面的研究獲得意大利數學聯盟的巴托洛齊獎（Bartolozzi Prize），最近他的一篇關於量子物理中鸽子洞原理違反的論文獲得2016年美國國家科學院的科扎雷利獎（Cozzarelli Prize）。
丹尼爾·C·斯特魯帕也是《量子研究、數學與基礎》（Quantum Studies, Mathematics and Foundations）的管理編輯，並且是幾本期刊的編輯委員會成員，包括《複雜分析與算子理論》（Complex Analysis and Operator Theory）和《米蘭數學期刊》（Milan Journal of Mathematics）。
