Introduction to Mathematical Thinking | 誠品線上

Introduction to Mathematical Thinking

內容簡介

內容簡介 數學思維是一種必備知識，也是一種核心技能超過50,000人都在學，最容易上手的數學思維學習書了解事物的本質，正確運用邏輯思考，循序漸進解決問題◎畢達哥拉斯獎、卡爾‧沙根科普獎得主，《數學的語言》作者又一力作◎百萬人爭讀、比臉書和推特用戶成長更快－－超夯線上教育平台Coursera廣受歡迎的公開課空白頁上寫著「此頁留白」，那一頁到底是不是空白的？所有的鳥類都會飛，所有的美洲豹都有斑紋……請證明給我看！有些大象不喜歡鬆餅……每個人都愛著某個人……（大象會爬樹） ⇒ （ 3是無理數）（歐幾里得的生日是7月4日） ⇒ （長方形有四個邊）（凱撒死了） ⇒ （π > 3）若蘋果紅了，則它可以吃了看起來理所當然的事，真的如此確定無誤嗎？◎為什麼要用數學來思考？數學不是只有＋－×÷、函數、微積分，但是，用數學來思考可以幫我們做什麼？●讓我們有能力來提出明確的關鍵性問題●讓我們以數學的嚴謹來識別和描述問題●讓我們用數學的精確來分析和解答問題◎誰需要學習數學思考？讓思考從混亂、令人沮喪、有時看起來不可能，到具有決定性的解析思維能力！●希望提升分析思考技巧和擁有創新思維的人●高中生、大學生，打算主修數學比重高的科目的學生●無法藉由尋找樣板來依循、無法找公式來代換數值或套程序來應用的人◎為什麼要用這本書來學數學思考？完全用不到數學步驟的數學思維入門課，大師親授一流的思考法則！●史丹佛大學教授最熱門的開放式數學課菁華集結●超過50,000人搶讀的線上開放學習平台Coursera課程同名專書●像學習騎腳踏車一樣的數學思維訓練，剛開始總是跌倒，成功卻非遙不可及◎先理解問題的意義，再依序解決問題數學家說，在他還沒有證明，或是尚未看到具有說服力的證明之前，他都無法肯定一個直覺看來正確的數學命題為真。「做數學」常涉及套用步驟和進行繁複的符號運算；「數學思維」則是一種思考事物的明確方法，且思考對象不限於數學。如果你無法藉由尋找一個樣板來依循、一個公式來代換數值進去，或者一個程序來應用，那麼，你該怎麼辦？答案是：思考這個問題！本書作者齊斯‧德福林是史丹佛大學著名數學家、暢銷科普作家，致力於對大眾教授和傳播數學。他在知名線上開放課程平台Coursera所開辦的「數學思維入門」課程，吸引了全球超過50,000人爭相註冊，本書即是針對協助培養「以數學方式思考」的能力所寫的專書。本書的目標是協助發展數學思維的方法，而不是學習記誦一堆千篇一律的規則，窒礙了你的思考！無論是希望提升分析思考技巧的讀者，或者剛由高中進入大學而打算主修數學比重很高科目的學生，都能從書中學習到如何研究一個新問題，換個方式思考直覺看來正確的事物。讓看不見的得以被看見，讓不可解的問題得以被解決，讓我們學習像數學家一樣思考！本中文書介出自《這個問題, 你用數學方式想過嗎? 史丹佛大學教授最受歡迎的4堂思考力訓練課, 打造最強數學思維, 讓你擁有關鍵的邏輯力、證明力、數字力》臉譜出版社出版In the twenty-first century, everyone can benefit from being able to think mathematically. This is not the same as “doing math.” The latter usually involves the application of formulas, procedures, and symbolic manipulations; mathematical thinking is a powerful way of thinking about things in the world -- logically, analytically, quantitatively, and with precision. It is not a natural way of thinking, but it can be learned.Mathematicians, scientists, and engineers need to “do math,” and it takes many years of college-level education to learn all that is required. Mathematical thinking is valuable to everyone, and can be mastered in about six weeks by anyone who has completed high school mathematics. Mathematical thinking does not have to be about mathematics at all, but parts of mathematics provide the ideal target domain to learn how to think that way, and that is the approach taken by this short but valuable book.The book is written primarily for first and second year students of science, technology, engineering, and mathematics (STEM) at colleges and universities, and for high school students intending to study a STEM subject at university. Many students encounter difficulty going from high school math to college-level mathematics. Even if they did well at math in school, most are knocked off course for a while by the shift in emphasis, from the K-12 focus on mastering procedures to the “mathematical thinking” characteristic of much university mathematics. Though the majority survive the transition, many do not. To help them make the shift, colleges and universities often have a “transition course.” This book could serve as a textbook or a supplementary source for such a course.Because of the widespread applicability of mathematical thinking, however, the book has been kept short and written in an engaging style, to make it accessible to anyone who seeks to extend and improve their analytic thinking skills. Going beyond a basic grasp of analytic thinking that everyone can benefit from, the STEM student who truly masters mathematical thinking will find that college-level mathematics goes from being confusing, frustrating, and at times seemingly impossible, to making sense and being hard but doable.Dr. Keith Devlin is a professional mathematician at Stanford University and the author of 31 previous books and over 80 research papers. His books have earned him many awards, including the Pythagoras Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is known to millions of NPR listeners as “the Math Guy” on Weekend Edition with Scott Simon. He writes a popular monthly blog “Devlin’s Angle” for the Mathematical Association of America, another blog under the name “profkeithdevlin”, and also blogs on various topics for the Huffington Post.In the twenty-first century, everyone can benefit from being able to think mathematically. This is not the same as "doing math." The latter usually involves the application of formulas, procedures, and symbolic manipulations; mathematical thinking is a powerful way of thinking about things in the world -- logically, analytically, quantitatively, and with precision. It is not a natural way of thinking, but it can be learned.Mathematicians, scientists, and engineers need to "do math," and it takes many years of college-level education to learn all that is required. Mathematical thinking is valuable to everyone, and can be mastered in about six weeks by anyone who has completed high school mathematics. Mathematical thinking does not have to be about mathematics at all, but parts of mathematics provide the ideal target domain to learn how to think that way, and that is the approach taken by this short but valuable book.The book is written primarily for first and second year students of science, technology, engineering, and mathematics (STEM) at colleges and universities, and for high school students intending to study a STEM subject at university. Many students encounter difficulty going from high school math to college-level mathematics. Even if they did well at math in school, most are knocked off course for a while by the shift in emphasis, from the K-12 focus on mastering procedures to the "mathematical thinking" characteristic of much university mathematics. Though the majority survive the transition, many do not. To help them make the shift, colleges and universities often have a "transition course." This book could serve as a textbook or a supplementary source for such a course.Because of the widespread applicability of mathematical thinking, however, the book has been kept short and written in an engaging style, to make it accessible to anyone who seeks to extend and improve their analytic thinking skills. Going beyond a basic grasp of analytic thinking that everyone can benefit from, the STEM student who truly masters mathematical thinking will find that college-level mathematics goes from being confusing, frustrating, and at times seemingly impossible, to making sense and being hard but doable.Dr. Keith Devlin is a professional mathematician at Stanford University and the author of 31 previous books and over 80 research papers. His books have earned him many awards, including the Pythagoras Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is known to millions of NPR listeners as "the Math Guy" on Weekend Edition with Scott Simon. He writes a popular monthly blog "Devlin's Angle" for the Mathematical Association of America, another blog under the name "profkeithdevlin", and also blogs on various topics for the Huffington Post.

作者介紹

作者介紹 Dr. Keith Devlin is a mathematician at Stanford University in California, where he is Executive Director of the university's H-STAR institute. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 31 books and over 80 published research articles. His books have won a number of prizes, including the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.

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