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Honsberger Revisited:Mathematical Gems Polished

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Honsberger Revisited:Mathematical Gems Polished Honsberger Revisited:Mathematical Gems Polished

作者:Liong-shin Hahn 
出版社:國立台灣大學出版中心
出版日期:2011-12-01
語言:繁體書   
圖書介紹 - 資料來源:TAAZE 讀冊生活   評分:
圖書名稱:Honsberger Revisited:Mathematical Gems Polished

本書(中譯名:重訪亨斯貝爾格--磨亮數學寶石)是美國 New Mexico 大學退休教授 Liong-Shin Hahn(韓良信)從著名數學家 Ross A Hongsberger 所著的五本書中選出好題目,加以探索、分析、解題、延伸之後,寫下的一本「讀數」札記。

Hongsberger 的這五本書分別是(1) Mathematical Delights(2004出版) (2) In Polya's Footsteps(1997出版) (3) Mathematical Chestnuts from around the world(2001出版) (4) Mathematical Diamonds(2003出版) (5) From Erdös to Kiev(1996出版)。

  韓教授將上述這五本書的書名作為本書的章名,每一章的題目都是從 Hongsberger 對應的書中挑出來的,並且提供了比原書更好,更精緻,且更具啟發性的解法。作者特別強調「重訪」這本書完全可以獨立閱讀,當然也可以與 Hongsberger 的原書平行閱讀。

除了上述五章本文之外,「重訪」一書另有A、B、C三個附錄。附錄A收集了115個挑戰題,粗分為52題幾何題,20題代數題,18題數論題,20題組合題和5題微積分題,解題所需的工具是高中數學。
附錄B是對附錄A的詳解。附錄C是整本「重訪」一書解題所需的定理,作者將這些定理作了很好的證明和延伸,這些定理包含了中學教育最核心的議題:

c.1 三角形相關定理
c.2 圓形相關定理
c.3 三角學相關定理
c.4 圓錐曲線相關定理
c.5 Jensen不等式的各種面貌

本書不單是一本解題手冊,而是藉解題來呈現作者認為最重要的數學,適合對數學有興趣的高中生、大學生以及中學的數學教師研讀。

The author's purpose is to share the thrills and excitement of ingenious solutions to intriguing elementary problems that he has had the good fortune to have conceived in the pursuit of his passion over many years. His satisfaction lies in the beauty of these gems, not in the incidental fact that they happen to be his own work. A wonderful solution is a glorious thing, whoever might have thought of it, and the author has worked diligently to make easy reading of the joy and delights of his often hard-won success.

As Director, responsible for composing the problems for the New Mexico Mathematics Contest before his retirement, the author consulted the wonderful books by Professor Ross Honsberger whenever he needed an inspiration. As a result, the New Mexico Mathematics Contest rose to national prominence and the author received the “Citation for Public Service” from the American Mathematical Society in 1998. In this volume he collected his treatments of over a hundred problems from the treasure trove of Professor Honsberger.

Perhaps it is best to quote Professor Honsberger, “This is a book for everyone who delights in the richness, beauty, and excitement of the wonderful ideas that abide in the realm of elementary mathematics. I feel it is only fair to caution you that this book can lead to a deeper appreciation and love of mathematics.”

作者簡介:

Liong-shin Hahn was born into a family of physicians in Tainan, Taiwan. He calls himself the black sheep of the family, because, like his father, Shyr-Chyuan Hahn, M.D., Ph.D., all five of his brothers became physicians. After graduating from Tainan First Senior Middle School and the National Taiwan University, he attended Stanford University and obtained his Ph.D. there under Professor Karel deLeeuw. He spent most of his career at the University of New Mexico, and while away from that institution, he held visiting positions at the University of Washington (Seattle), the National Taiwan University, the University of Tokyo, Sophia University (Tokyo) and the International Christian University (Tokyo). As director of the mathematics contest sponsored by the University of New Mexico, he consulted frequently the superb books by Professor Ross Honsberger that seeded the birth of this book. He authored Complex Numbers and Geometry (Mathematicial Association of Americia, 1994), New Mexico Mathematics Contest Problem Book (University of New Mexico Press, 2005), and co-authored with Bernard Epstein Classical Complex Analysis (Jones and Bartlett, 1996). He was awarded the Citation for Public Service from the American Mathematical Society in 1998. His marriage to Hwei-Shien Lee (yet another M.D.) yielded three sons and seven grandchildren.


推薦序
Introduction

What is it about math problems that makes them so addictive?

When I get going on a problem, I’d rather stay at it than eat!

Liong-shin Hahn and I are kindred spirits who have lived like this for the last fifty years. As you might expect, Liong-shin has become very adept at solving problems, and in this volume he has collected his treatments of some hundred problems that caught his eye in my books. If you would like a sample of his ingenuity, take a look at Exercise 49 (pages 14...
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作者序
Preface

Before my retirement, I was responsible for composing the problems for the New Mexico Mathematics Contest1. Whenever I needed an inspiration then, I always turned to the wonderful books by Professor Ross Honsberger. I knew his books were a treasure trove of interesting problems with brilliant solutions. So it was only natural that when I retired and wanted to prevent dementia, I chose problems from his books for my “Problem-of-the-Day” activity. I would not peek at the solution unless...
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目錄
Contents
Introduction vii
Preface viii

1 Mathematical Delights 1
1.1 Triangles in Orthogonal Position 1
1.2 Pan Balance 6
1.3 Schoch 3 7
1.4 A Nice Problem in Probability 10
1.5 Three Proofs of the Heron Formula 13
1.6 Incenter 18
1.7 On Median, Altitude and Angle Bisector 19
1.8 A Geometry Problem from Quantum 23
1.9 Monochromatic Triangle 25
1.10 Sum of the Greatest Odd Divisors 26
1.11 Prime Numbers of the Form m2k + mknk + n2k 27

2 In P olya's Footst...
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商品資料
  • 作者: Liong-shin Hahn
  • 出版社: 國立台灣大學出版中心 出版日期:2011-12-01 ISBN/ISSN:9789860311686
  • 語言:繁體中文 裝訂方式:平裝
  • 類別: 中文書> 科學> 數學
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