An Excursion Through Elementary Mathematics, Volume I: Real Numbers and Functions
暫譯: 初等數學漫遊，第一卷：實數與函數

Caminha Muniz Neto, Antonio

An Excursion Through Elementary Mathematics, Volume I: Real Numbers and Functions
  • 出版商: Springer
  • 出版日期: 2018-05-08
  • 售價: $2,320
  • 貴賓價: 9.5 折 $2,204
  • 語言: 英文
  • 頁數: 652
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3319852612
  • ISBN-13: 9783319852614

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商品描述

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more.


As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.


The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

商品描述(中文翻譯)

本書提供了對於全球數學奧林匹克中探討的基礎數學的全面深入概述。它擴展了通常在高中階段遇到的主題，甚至可以用作大學第一學期課程的準備。這第一卷涵蓋了實數、函數、實分析、方程組、極限和導數等內容，還有更多主題。

作為一個系列的一部分，本書與該領域的其他出版物不同，並非僅僅是問題的選集或針對特定問題的技巧和竅門。它從最基本的理論原則開始，既不過於一般化也不過於公理化。只有在有助於理論應用的情況下，才會討論例子和問題。命題會詳細證明，並隨後應用於奧林匹克問題或其他奧林匹克級別的問題。

本書還探討了一些在國家和國際數學奧林匹克中提出的最難問題，以及與內容相關的許多重要定理。附錄中提供了對所有困難問題的提示或完整解答，為本書畫上句點。

作者簡介

Antonio Caminha M. Neto received his PhD from the Federal University of Ceará, Brazil in 2004. In the same year he joined the University as a Professor of Mathematics, where he is now a member of the Differential Geometry Research Group. The author of several research papers, Caminha is distinguished by a CNPq Research Grant on Differential Geometry. He is also an Affiliate Member of the Brazilian Academy of Sciences. Prior to his academic career, Caminha was himself an Olympic competitor, who has placed 4th in the 1990 Brazilian Mathematical Olympiad. Subsequently, as a high school teacher in the 1990s, he coached Brazilian students in preparation for various mathematical competitions, from regional meets to the Iberoamerican Mathematical Olympiad and the International Mathematical Olympiad, where several of them were medalists. He was also a Leader of the Brazilian Team at the 1996 and 1999 South Cone Mathematical Olympiad, and Deputy Leader of the Brazilian Team at the 1995 and 2001 International Mathematical Olympiads. In 2012, Caminha published a six-volume book collection entitled Topics in Elementary Mathematics with the Brazilian Mathematical Society, which gave rise to this book.

作者簡介(中文翻譯)

安東尼奧·卡明哈·M·內托（Antonio Caminha M. Neto）於2004年獲得巴西塞阿拉聯邦大學（Federal University of Ceará）的博士學位。同年，他加入該大學擔任數學教授，並且現在是微分幾何研究小組的成員。卡明哈是多篇研究論文的作者，並因在微分幾何方面的研究獲得了CNPq研究獎助金。他也是巴西科學院的附屬會員。在學術生涯之前，卡明哈曾是一名奧林匹克競賽選手，並在1990年巴西數學奧林匹克中獲得第四名。隨後，作為1990年代的高中教師，他指導巴西學生準備各種數學競賽，從地區賽到伊比美數學奧林匹克和國際數學奧林匹克，其中多位學生獲得獎牌。他還曾擔任1996年和1999年南美數學奧林匹克的巴西隊隊長，以及1995年和2001年國際數學奧林匹克的巴西隊副隊長。2012年，卡明哈與巴西數學學會出版了一套六卷本的書籍《基礎數學主題》（Topics in Elementary Mathematics），這本書的誕生源於此。

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