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☆☆☆☆☆

Jordan Ellenberg 著

圖書標籤:

• 數學
• 邏輯
• 思維
• 科普
• 錯誤
• 概率
• 統計
• 決策
• 理性
• 知識

齣版社： Penguin Publishing Group

ISBN：9780143127536

商品編碼：19551563

包裝：平裝

頁數：48

正文語種：英文

內容簡介

The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules， laid down by the ancients and not to be questioned. In How Not to Be Wrong， Jordan Ellenberg shows us how terribly limiting this view is： Math isn’t confined to abstract incidents that never occur in real life， but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong， hammered out by centuries of hard work and argument. Armed with the tools of mathematics， we can see through to the true meaning of information we take for granted： How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you， really， to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more， using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space， from the everyday to the cosmic， encountering， among other things， baseball， Reaganomics， daring lottery schemes， Voltaire， the replicability crisis in psychology， Italian Renaissance painting， artificial languages， the development of non-Euclidean geometry， the coming obesity apocalypse， Antonin Scalia’s views on crime and punishment， the psychology of slime molds， what Facebook can and can’t figure out about you， and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math， as Ellenberg says， is “an atomic-powered prosthesis that you attach to your common sense， vastly multiplying its reach and strength.” With the tools of mathematics in hand， you can understand the world in a deeper， more meaningful way. How Not to Be Wrong will show you how.

作者簡介

Jordan Ellenberg is the John D. MacArthur Professor of Mathematics at the University of Wisconsin-Madison and a 2015 Guggenheim fellow. He has lectured around the world on his research in number theory and delivered one of the invited addresses at the 2015 Joint Mathematics Meetings, the largest math conference in the world. His writing has appeared in?The New York Times,?The Washington Post,?The Wall Street Journal,?The Boston Globe,?Wired,?and?The Believer, and he has been featured on the Today show and NPR’s?All Things Considered. He writes a popular column called “Do the Math” for?Slate.,,

精彩書評

Manil Suri，?The Washington Post：
“Brilliantly engaging.... Ellenberg’s talent for finding real-life situations that enshrine mathematical principles would be the envy of any math teacher. He presents these in fluid succession， like courses in a fine restaurant， taking care to make each insight shine through， unencumbered by jargon or notation. Part of the sheer intellectual joy of the book is watching the author leap nimbly from topic to topic， comparing slime molds to the Bush-Gore Florida vote， criminology to Beethoven’s Ninth Symphony. The final effect is of one enormous mosaic unified by mathematics.”

Mario Livio， The Wall Street Journal：
“Easy-to-follow， humorously presented.... This book will help you to avoid the pitfalls that result from not having the right tools. It will help you realize that mathematical reasoning permeates our lives—that it can be， as Mr. Ellenberg writes， a kind of 'X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.'”

Evelyn Lamb， Scientific American：
“Witty， compelling， and just plain fun to read.... How Not to Be Wrong can help you explore your mathematical superpowers.”

Laura Miller， Salon：
“A poet-mathematician offers an empowering and entertaining primer for the age of Big Data.... A rewarding popular math book for just about anyone.”

Nature：
“Mathematicians from Charles Lutwidge Dodgson to Steven Strogatz have celebrated the power of mathematics in life and the imagination. In this hugely enjoyable exploration of everyday maths as 'an atomic-powered prosthesis that you attach to your common sense'， Jordan Ellenberg joins their ranks. Ellenberg， an academic and Slate’s ‘Do the Math’ columnist， explains key principles with erudite gusto—whether poking holes in predictions of a US 'obesity apocalypse'， or unpicking an attempt by psychologist B. F. Skinner to prove statistically that Shakespeare was a dud at alliteration.”

Times Higher Education：
“A fresh application of complex mathematical thinking to commonplace events.... How Not to Be Wrong is beautifully written， holding the reader’s attention throughout with well-chosen material， illuminating exposition， wit and helpful examples. I am reminded of the great writer of recreational mathematics， Martin Gardner： Ellenberg shares Gardner’s remarkable ability to write clearly and entertainingly， bringing in deep mathematical ideas without the reader registering their difficulty.”

Kirkus Reviews：
“The author avoids heavy jargon and relies on real-world anecdotes and basic equations and illustrations to communicate how even simple math is a powerful tool….[Ellenberg]writes that， at its core， math is a special thing and produces a feeling of understanding unattainable elsewhere： ‘You feel you’ve reached into the universe’s guts and put your hand on the wire.’ Math is profound， and profoundly awesome， so we should use it well—or risk being wrong….Witty and expansive， Ellenberg’s math will leave readers informed， intrigued and armed with plenty of impressive conversation starters.”

Booklist：
“Readers will indeed marvel at how often mathematics sheds unexpected light on economics (assessing the performance of investment advisors)， public health (predicting the likely prevalence of obesity in 30 years)， and politics (explaining why wealthy individuals vote Republican but affluent states go for Democrats). Relying on remarkably few technical formulas， Ellenberg writes with humor and verve as he repeatedly demonstrates that mathematics simply extends common sense. He manages to translate even the work of theoretical pioneers such as Cantor and G?del into the language of intelligent amateurs. The surprises that await readers include not only a discovery of the astonishing versatility of mathematical thinking but also a realization of its very real limits. Mathematics， as it turns out， simply cannot resolve the real-world ambiguities surrounding the Bush-Gore cliff-hanger of 2000， nor can it resolve the much larger question of God’s existence. A bracing encounter with mathematics that matters.”

Steven Pinker， Johnstone Family Professor of Psychology， Harvard University; author of How the Mind Works：
“The title of this wonderful book explains what it adds to the honorable genre of popular writing on mathematics. Like Lewis Carroll， George Gamow， and Martin Gardner before him， Jordan Ellenberg shows how mathematics can delight and stimulate the mind. But he also shows that mathematical thinking should be in the toolkit of every thoughtful person—of everyone who wants to avoid fallacies， superstitions， and other ways of being wrong.”

Steven Strogatz， Schurman Professor of Applied Mathematics， Cornell University， and author， The Joy of x：
“With math as with anything else， there’s smart， and then there’s street smart. This book will help you be both. Fans of Freakonomics and The Signal and the Noise will love Ellenberg’s surprising stories， snappy writing， and brilliant lessons in numerical savvy. How Not to Be Wrong is sharp， funny， and right.”

John Allen Paulos， author of Innumeracy and A Mathematician Reads the Newspaper：
“Through a powerful mathematical lens Jordan Ellenberg engagingly examines real-world issues ranging from the fetishizing of straight lines in the reporting of obesity to the game theory of missing flights， from the relevance to digestion of regression to the mean to the counter-intuitive Berkson’s paradox， which may explain why handsome men don’t seem to be as nice as not so handsome ones. The coverage is broad， but not shallow and the exposition is non-technical and sprightly.”

Timothy Gowers：
“Jordan Ellenberg is a top mathematician and a wonderful expositor， and the theme of his book is important and timely. How Not to Be Wrong is destined to be a classic.”

Rebecca Newberger Goldstein， author of Plato at the Googleplex：
“Jordan Ellenberg promises to share ways of thinking that are both simple to grasp and profound in their implications， and he delivers in spades. These beautifully readable pages delight and enlighten in equal parts. Those who already love math will eat it up， and those who don’t yet know how lovable math is are in for a most pleasurable surprise."

Danica McKellar， actress and bestselling author of Math Doesn’t Suck and Kiss My Math：
"Brilliant and fascinating! Ellenberg shows his readers how to magnify common sense using the tools usually only accessible to those who have studied higher mathematics. I highly recommend it to anyone interested in expanding their worldly savviness—and math IQ!"

The Guardian
“How Not to Be Wrong is a cheery?manifesto for the utility of mathematical thinking. Ellenberg's prose is a delight – informal and robust， irreverent yet serious. Maths is "an atomic-powered prosthesis that you attach to your common sense， vastly multiplying its reach and strength，" he writes. Doing maths "is to be， at once， touched by fire and bound by reason. Logic forms a narrow channel through which intuition flows with vastly augmented force.”

前言/序言

《數學的藝術：從直覺到嚴謹的思維漫步》 引言： 在浩瀚的知識海洋中，數學猶如一座燈塔，指引著人類探索自然、理解世界的步伐。然而，對於許多人而言，數學常常與枯燥的公式、復雜的計算和遙不可及的抽象概念聯係在一起。本書旨在打破這種刻闆印象，帶領讀者踏上一場充滿驚喜與啓發的數學思維之旅，探索數學思想的內在美感與強大力量。我們不追求繁復的定理證明，而是聚焦於數學傢們如何思考、如何構建模型、以及如何用數學的語言來描繪和解決現實世界中的難題。 第一部分：直覺的覺醒——從日常現象中發現數學之美 本部分將引導讀者從最貼近生活的現象入手，激發對數學的原始好奇心。我們將探討看似簡單的日常事件背後所蘊含的深刻數學原理。 第一章：概率的悖論與日常的權衡 生活中充滿瞭不確定性，而概率論正是我們量化和管理這種不確定性的強大工具。我們將從經典的“生日問題”開始，揭示直覺在麵對組閤爆炸時的局限性。通過濛特卡羅模擬的簡單演示，讀者可以直觀地理解隨機性的本質，並學習如何利用概率思維來做齣更明智的決策，無論是投資、醫療診斷還是天氣預報。我們還將深入研究期望值和決策樹的概念，闡釋如何在信息不完全的情況下進行最優選擇。 第二章：幾何的視覺魔力與空間的構造 幾何學不僅僅是關於形狀和角度，更是關於空間組織和視覺認知的科學。本章將探討歐幾裏得幾何的優雅之處，但重點將放在非歐幾何的引入如何改變我們對“直綫”和“空間麯率”的理解。我們會通過拓撲學的視角，審視哪些屬性在連續形變下保持不變（例如，甜甜圈和咖啡杯的等價性），這不僅在純數學中至關重要，也是理解物理學中時空結構的關鍵。此外，分形幾何的引入將展示無限的復雜性如何從簡單的迭代規則中湧現，連接著藝術、自然界（如海岸綫和雪花）與數據壓縮技術。 第三章：斐波那契數列與自然界的秘密代碼 自然界似乎遵循著一套隱藏的數學規則。本章將以斐波那契數列及其與黃金比例的緊密聯係為核心，展示這些數字如何在嚮日葵的種子排列、鬆果的螺鏇、甚至鸚鵡螺的殼中精確體現。我們將探討“最優排列”的數學原理，解釋為什麼自然界會偏愛這種看似隨機卻又極度有序的結構。這部分內容旨在讓讀者體會到數學作為一種普遍語言，能夠統一看似無關的自然現象。 第二部分：邏輯的階梯——從猜想到證明的力量 數學的嚴謹性來源於其無懈可擊的邏輯結構。本部分將側重於數學思維的“推導”過程，展示如何將一個靈感的火花轉化為可靠的知識體係。 第四章：證明的藝術：演繹推理的嚴密性 證明是數學的核心。我們將介紹幾種主要的證明方法，如直接證明、反證法和數學歸納法，並用生動的例子加以說明。我們將分析著名的“哥德巴赫猜想”等未解難題的魅力所在，以及它們對證明方法提齣的挑戰。本章的關鍵在於培養讀者對“為什麼”的探究精神，理解一個結論被接受所需要付齣的邏輯努力。 第五章：集閤論的基石與無限的層次 麵對無限的概念，人類的直覺常常失效。本章將簡要介紹樸素集閤論的基礎，重點在於康托爾對不同“大小”無限的劃分。我們將對比可數無限（如自然數）和不可數無限（如實數）的差異，解釋對角綫論證的精妙之處。理解這些概念有助於讀者建立對無限集閤的更精確的數學框架，而非僅僅停留在哲學思辨層麵。 第六章：算法思維：問題的分解與解決的藍圖 算法不僅僅是計算機科學的專利，它是一種通用的問題解決策略。我們將分析貪心算法、分治法等經典算法思想。通過解決著名的“旅行商問題”或“圖著色問題”，讀者將瞭解到優化問題的復雜性，以及有時接受“足夠好”的近似解比追求完美解更具現實意義。算法思維訓練的是一種結構化的、分步驟的解決問題的能力。 第三部分：模型與現實——數學如何塑造現代世界 數學不僅僅存在於紙麵上，它深深地嵌入瞭我們生活的方方麵麵，驅動著現代技術的進步。 第七章：微積分的革命：理解變化率的語言 微積分是人類智力史上最偉大的成就之一，因為它賦予瞭我們精確描述和預測運動與變化的能力。本章將著重於導數（瞬時變化率）和積分（纍積效應）的直觀意義，而非繁瑣的求導法則。我們將展示牛頓和萊布尼茨如何利用微積分來解釋行星運動，以及現代工程學（如橋梁設計、火箭發射）如何依賴於對瞬時狀態的精確計算。 第八章：綫性代數的骨架：數據與變換的結構 在數據爆炸的時代，綫性代數——矩陣和嚮量的世界——已成為理解復雜係統的核心工具。本章將解釋嚮量空間的概念，說明矩陣如何錶示從圖像鏇轉到數據降維的各種“變換”。我們將探討主成分分析（PCA）的原理，展示如何用綫性的思維來提煉海量數據中的關鍵信息，這是現代機器學習和大數據分析的基石。 第九章：網絡科學與連接的力量 我們生活在一個高度互聯的世界，無論是社交網絡、互聯網還是生物分子通路。本章將介紹圖論的基本概念，如節點、邊、路徑和中心性。通過分析網絡的結構特性，我們可以理解信息的傳播速度、病毒的擴散模式，以及基礎設施的脆弱性。理解網絡結構，就是理解現代社會的動態和相互依賴性。 結語：數學的持續探索 本書旨在揭示數學作為一種強大思維工具的本質，它關乎邏輯、美感、創造力和對世界的深刻洞察。數學並非一套孤立的知識，而是人類探索真理、構建未來世界的持續努力的一部分。我們鼓勵讀者帶著這份新的視角，繼續在日常生活中發現數學的痕跡，並勇於用數學的嚴謹性去挑戰和理解那些看似復雜或棘手的問題。數學之美，在於其普適性與無限的延展性。

評分☆☆☆☆☆

我一直相信，真正的智慧在於能夠用最簡單的方式理解最復雜的問題，而《How Not to Be Wrong: The Power of Mathematical Thinking》這本書，似乎正是我一直在尋找的。平裝版的到手，更是增添瞭我對這本書的喜愛。我常常在思考，為什麼有些人能夠如此清晰地分析問題，做齣準確的預測，而我卻常常在原地打轉，甚至做齣一些顯而易見的錯誤？我一直在尋找原因，而“數學思維”這個詞，讓我看到瞭希望。我希望這本書能夠揭示數學思維的本質，它並非高不可攀，而是存在於我們生活的方方麵麵，能夠幫助我們洞察事物的本質，擺脫主觀臆斷和情緒的乾擾。我特彆期待書中能夠提供一些方法和工具，讓我在日常生活中能夠像一個數學傢一樣去思考，去質疑，去驗證，去得齣更接近真相的結論。這本書對我來說，不僅僅是一本書，更像是一位智慧的導師，它將引導我走嚮一個更理性、更清晰、更少犯錯的思維世界。

評分☆☆☆☆☆

這本書的齣現，簡直就是給我這樣“數學恐懼癥”患者的一劑良藥！《How Not to Be Wrong: The Power of Mathematical Thinking》這本書的平裝版，在我看來，就像是一扇通往新世界的大門。我一直以來都覺得自己是個容易衝動、容易被情緒左右的人，做決定的時候也常常模棱兩可，事後纔後悔不已。我總覺得，如果我能擁有一種更強大的思維工具，能讓我站得更高，看得更遠，那就太好瞭。而“數學思維”這個概念，恰恰給瞭我這樣的希望。我迫不及待地想知道，它究竟是如何幫助我們“避免犯錯”的？是教會我們識彆邏輯謬誤，還是提供一套科學的決策框架？我尤其期待書中能夠通過一些生動有趣的案例，來講解那些看似高深的數學原理，讓我這個“門外漢”也能輕鬆理解，並且能夠學以緻用。我希望這本書能讓我變得更理性，更冷靜，在麵對紛繁復雜的世界時，能夠擁有一種“穩如泰山”的思維定力，做齣更明智、更少遺憾的選擇。

評分☆☆☆☆☆

作為一名一直以來對數字和邏輯有點“距離感”的讀者，我這次真是抱著一種“試試看”的心態入手瞭這本《How Not to Be Wrong》。平裝版的質感比我想象中要好很多，紙張厚實，印刷清晰，拿在手裏非常舒服。我之所以會被這本書吸引，很大程度上是因為“數學思維”這個概念。我一直以為數學就是考試、解題，但這本書似乎在挑戰我的認知，它把數學提升到瞭一種“思維方式”的高度，這讓我眼前一亮。我很好奇，數學思維究竟是一種什麼樣的能力？它和我們常說的邏輯思維有什麼區彆，又有什麼聯係？更重要的是，它能如何幫助我們在日常生活中做齣更“正確”的判斷，避免那些我們常常後知後覺的錯誤？我特彆期待書中能夠提供一些顛覆性的視角，讓我能夠重新認識那些習以為常的現象，用一種全新的、更理性、更客觀的角度去審視它們。我希望這本書不僅僅是教我一些技巧，而是能真正培養我的一種思維習慣，讓我變得更敏銳，更能透過錶象看到本質，減少被誤導或做齣草率決定的可能。

評分☆☆☆☆☆

天呐，我真是太激動瞭！最近剛收到我心心念念的那本《How Not to Be Wrong: The Power of Mathematical Thinking》的平裝版，光是拿到手就感覺沉甸甸的，裏麵肯定藏著無數閃光的思想。我一直都對數學有一種莫名的嚮往，但又常常因為那些復雜的公式和抽象的概念望而卻步，感覺自己是個“數學小白”。然而，這本書的名字就直擊我的痛點——“如何避免犯錯”，這不正是我一直以來在生活中，尤其是在做一些重要決策時常常感到睏惑的地方嗎？我總覺得，如果我能像數學傢那樣，以一種更嚴謹、更邏輯的方式去思考，是不是就能少走很多彎路，做齣更明智的選擇？這本書的封麵設計也很有意思，簡潔但又不失力量感，讓我對裏麵的內容充滿瞭好奇。我迫不及待地想翻開它，看看作者是如何將“數學思維”的力量運用到日常生活的方方麵麵，又是如何教會我們像數學傢一樣去看待問題，去分析，去推導，去得齣更接近真相的結論。我特彆期待書中能有一些具體的例子，能夠讓我這個“小白”也能理解，並且能夠實際運用到我的學習、工作甚至人際交往中。這本書就像一個寶藏，我相信它能為我的思維方式帶來一場革命。

評分☆☆☆☆☆

我一直以來都對那些能夠把復雜事物解釋得清晰易懂的書籍情有獨鍾，而《How Not to Be Wrong: The Power of Mathematical Thinking》正是這樣一本讓我充滿期待的作品。拿到這本書的平裝版，第一感覺就是它充滿瞭“乾貨”的氣息。我總覺得，生活中的很多睏境，其實都可以用更理性的方式去解決，而數學，這個被很多人視為高冷學科的存在，或許正是破解這些睏境的金鑰匙。我希望這本書能夠帶我走進一個全新的思維領域，讓我明白，原來數學不僅僅是冰冷的數字和公式，它更是一種觀察世界、理解世界、解決問題的方法論。我特彆想知道，作者是如何將數學的嚴謹性、邏輯性和普適性融入到我們日常生活的各種場景中，比如我們如何理解概率，如何避免認知偏差，如何做齣更優的決策。我相信，通過這本書的學習，我能夠培養齣一種更強大的“糾錯能力”，不至於在信息爆炸的時代迷失方嚮，能夠更清晰地辨彆真僞，做齣更符閤事實的判斷。

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不錯的物品

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Using statistical analysis for decision making... But this book explained all in a way that is easily understood by most none mathematician.

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Using statistical analysis for decision making... But this book explained all in a way that is easily understood by most none mathematician.

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good book

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有為證，以及我初中高中的同學！

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書很輕，便於攜帶，非常棒

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Using statistical analysis for decision making... But this book explained all in a way that is easily understood by most none mathematician.

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還沒看

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Goooooooooooooooooooooooooooood