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Das kleine Einmaleins des klaren Denkens: 22 Denkwerkzeuge fur ein besseres Leben

Das kleine Einmaleins des klaren Denkens: 22 Denkwerkzeuge fur ein besseres Leben

          
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About the Book

數學是最迷人的思考活動,將手邊有限的訊息加以消化、理解、進一步掌握,找出問題並尋求解答。本書將介紹22個容易理解、但極為有效的思考工具,讀者們只需具備基礎數學知識跟一顆嘗試冒險的心,即可徹底學會數學抽象化思考的技巧,運用邏輯能力將問題化為捷徑。本書是寫給不排斥數學,但總是不得其門而入的讀者。你將學到數學家如何思考問題以及求解,深入體會數學最迷人的真正精髓。這本書原本是德國斯圖加特大學2006年的夏季學期中,針對非數學系學生所開設的課程教材改寫而成。(課程名稱為:與數學的相遇)為什麼很多人始終無緣一窺數學堂奧?為什麼你看得懂別人的算式,卻沒有辦法解一個別人沒解過的問題?作者在本書向大眾介紹22個以數學原則做基礎的思考工具,不只可以簡化大多數人面對難題而本能產生的複雜想法,更要活絡你的思路,學習用數學的抽象思考方式解決各種難題。有效的思考工具,就是幫助你運用想像力跟邏輯思維,把問題化繁為簡,再以此進一步求解,例如:Q:一整片格子狀巧克力,若要全部折斷成單格的小片,最少需要折幾次才能辦到?→用「類比原理」思考:試著折斷一片巧克力,折斷後的塊數,永遠比折斷次數多1......Q:數學天才高斯七歲的時候,老師要全班同學計算「從1加到100的總和」。高斯只花了幾秒就把答案寫好。他是怎麼算出來?→用「富比尼原理」思考:把數字分組,讓每一組數字的和永遠相同,再計算共有多少組......Q:有2n位大使受邀參加一個慶祝會。每位大使在這群人中最多有n - 1個敵人。要怎樣安排圓桌座位,才能讓每位大使都不會坐在自己的敵人旁邊?→用「單向變化原則」思考:A大使的朋友旁邊,絕不可能都坐著B大使的敵人......22個數學思考工具:1.類比原則:我們能將這個問題回推到另一個已知答案的類似問題嗎?2.富比尼原理:我們可否算出某些東西的數目,但卻是用完全不同的方法去算出來?3.奇偶原理:我們可以從問題是否可能具體區分成兩個互不重疊的類別,來得知問題有沒有解嗎?4.狄利克雷原理:如果 n+1 個物件要任意存放在 n 個格子內,至少會有 1 個格子放了2 個物件。5.排容原理:我們能不能從比較容易計數的子集合,來算出某個集合中的元素個數?6.相反原則:我們可不可以先假設某個斷言的反面是對的,然後透過無懈可擊的邏輯推導,得出與所假設事實矛盾的結論,以此來證明原本的斷言是對的?7.歸納原則:為了證明一堆有序物件當中的全部東西皆具有某種性質,可以先證明第一個東西有此項性質,然後再證明,若其中任意一個東西具有該性質,則下一個東西也有此性質。8.一般化原則:解決一般問題時,可不可以先刪去一些條件或是改變一些約束條件,然後再把求得的解運用在眼前的特殊情形?9.特殊化原則:解題時可以先看特殊情況,然後從特殊情況的結果推廣到一般情況的求解嗎?10.變化原則:我們是不是可以透過控制改變問題的某些層面,從新的角度來觀察,對原本的問題有更深入的理解,進而解開問題?11.不變性原理:系統裡有沒有一些性質,是在系統本身允許改變時也保持不變的,而從這些性質可以推導出系統可能的發展結果嗎?12.單向變化原則:在系統經歷了可允許的改變下,系統中有沒有一些性質只會以一種特定方式改變,且從這些變化可以推斷出系統可能的發展?13.無窮遞減法則:我們可不可以先替某件事給個例子,然後假設從這個例子一定可以推到越來越小例子,但實際上不可能永無止境地越推越小,因而證明這件事不可能發生?14.對稱原理:在給定系統裡有沒有某些對稱性質,可以讓我們從中取得資訊?15.極值原理:我們能不能從給定問題的極端情形,研究出所有情形的相關資訊?16.遞迴原理:解題時可以將問題一步一步推到更簡單的版本嗎?17.步步逼近原則:解題時,可以先找出一個近似解,然後在後續步驟中持續改進嗎?18.著色原理:我們可以透過使用顏色,在問題的結構中建構出模式,然後從中汲取解題的資訊嗎?19.隨機化原則:我們可以在問題裡引進一個隨機的機制,使問題簡化嗎?20.轉換觀點原則:解題時可以從目標往起點反向進行,然後再翻轉思考方向嗎?21.模組化原則:解題時可以將問題分解成許多子問題,解決之後再將這些部分解合併成完整的解?22.蠻力原則:我可以透過試遍所有可能的解法來解題嗎?


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Product Details
  • ISBN-13: 9783406586842
  • Publisher: Beck C. H.
  • Binding: Paperback
  • Language: German
  • Width: 335 mm
  • ISBN-10: 3406586848
  • Publisher Date: 9/24/2013
  • Height: 191 mm
  • Weight: 25 gr

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Das kleine Einmaleins des klaren Denkens: 22 Denkwerkzeuge fur ein besseres Leben
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