Math Girls
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Summary
Math Girls is the first volume in a series of popular mathematics novels by Japanese technical writer and programmer Hiroshi Yuki. It was first serialized on the author's personal website starting in 2002 and was collected into a book after an enthusiastic reader response. The Chinese edition was translated by Zhu Yifei and brought in by Posts & Telecom Press under its "Turing New Knowledge" imprint. The book unfolds as a novel: the protagonist "I" is a high school student who loves mathematics, and together with the quick-witted genius girl Miruka, the earnest and inquisitive junior schoolmate Tetra, the programming-savvy Risa, and the quirky cousin Yuri, he engages in conversations and derivations around mathematical problems in everyday settings such as the library, a café, and the music room. The content progresses from easy to difficult, beginning with sequence puzzles, prime numbers, and absolute values, and with the vibration and rotation represented by ω, then using generating functions to derive the general term formula for the Fibonacci sequence, discussing basic inequalities, the contrast between differentiation and differences, convolution and the binomial theorem, and finally advancing to harmonic numbers and the ζ function, Taylor expansion and the Basel problem (the sum of the reciprocals of all natural numbers squared equals π²/6), up to partition numbers and the estimation of their upper bounds. The book preserves the complete thinking process of "thinking wrong—getting stuck—having an insight," so readers can derive, make mistakes, and correct themselves alongside the characters. The book was recommended by the Mathematical Society of Japan; the original series has sold on the order of a hundred thousand copies, and the first two Chinese volumes have a Douban rating of about 8.9.
Editor's review
很多人对数学的感情，停止在某一张写满符号的试卷上：不是讨厌，而是「我大概不是这块料」。这本书正是冲着这种无力感来的。作者结城浩本身就是长年写代码、写技术书的程序员，他不用「定义—定理—证明」的冷面孔讲数学，而是让几个高中生在樱花树下、图书室和咖啡店里为一个问题争得面红耳赤——泰朵拉会替读者问出那个不好意思问的「等一下，这一步为什么可以这样」，米尔嘉则给出干净漂亮的解法，两种思路互相碰撞。 它的难度爬升非常平滑：从「1、1、2、3、5」这种小学生都认识的数列出发，一路走到用生成函数推出斐波那契通项、把全体自然数平方的倒数加起来得到π²/6。你不需要全部看懂，但跟着人物完整走一遍「不懂—卡住—想通」的流程，比背下十个公式更有价值。作为系列第一卷，它既是一本可以当青春小说读的数学书，也是一本可以当数学书读的小说。
Who it's for
A good fit for
- 对数学有兴趣、想补回「理解感」的高中生与大学生
- 曾因数学成绩受挫，但隐约觉得数学不该这么无趣的成年人
- 喜欢看故事、轻小说，又想顺带学点硬知识的人
- 家里有孩子、想准备一本不会毁掉数学兴趣的课外书的家长
- 习惯编程思维、对递归与生成函数好奇的程序员
Not a good fit for
- 只想读「十分钟速通某某定理」式快餐读物的读者
- 完全不愿跟着推导、只想看结论和公式表的人
- 期待纯代数习题集或考试刷题训练的学生
Reading tips
- 先当小说通读一遍，遇到公式看不懂就跳过去，读完一章再回头补推导，压力会小很多。
- 准备纸笔跟着算：第四章的斐波那契生成函数和第九章的巴塞尔问题，亲手写一遍收获最大。
- 读不下去时从第八章「调和数」入手，这一章对无穷级数与ζ函数的引入最直观。
- 读完可接着读第二部《费马大定理》，各册之间没有硬性关联，按兴趣挑主题也可以。
About the publisher
Posts & Telecom Press
China · Founded in 1953
Posts & Telecom Press is known for its strengths in science and technology, computing, and information and communications titles, and has extended its publishing into photography, art, software learning, and inspirational growth, giving it a fairly diverse range. Its catalog includes computing and communications works such as Refactoring and Patterns (Revised Edition) and Huawei Switch Learning Guide (Second Edition), alongside bilingual collector's editions such as The Little Prince (Chinese-English-French illustrated collector's edition), The Great Gatsby, and Three Days to See. Beijing Ten Years: 1980-1990 and Ghost Blade: WLOP Personal Illustration Collection reflect its presence in photography and art. Its authors include Antoine de Saint-Exupéry, Helen Keller, Joshua Kerievsky, Wang Da, Zhang Zhaozeng, and WLOP.
Contents
- To the Reader
- Preface
- Chapter 1 Sequences and Mathematical Models (Under the Cherry Blossoms, At Home, Sequence Puzzles Have No Correct Answer)
- Chapter 2 A Love Letter Called a Mathematical Formula (Mental Arithmetic Puzzle, The Letter, The Lecture Hall, Definition of Prime Numbers, Miruka's Answer, The Library)
- Chapter 3 The Waltz of ω (The Library, Vibration and Rotation, ω)
- Chapter 4 The Fibonacci Sequence and Generating Functions (Finding the Pattern, Sum of a Geometric Sequence, Marching Toward Infinite Series, Grasping the Heart of the Fibonacci Sequence, Closed-Form Expression)
- Chapter 5 Basic Inequalities (At "Kagura," Full of Questions, Inequalities, On Learning)
- Chapter 6 Beside Miruka (Differentiation, Differences, Differentiation and Differences, A Journey Back and Forth Between Two Worlds)
- Chapter 7 Convolution (Deriving the Formula, Generalization, The Binomial Theorem, Solving the Generating Function, The Last Fortress, A Circle of Radius 0)
- Chapter 8 Harmonic Numbers (Treasure Hunting, Partial Sums and Infinite Series, Propositions, The ζ Function, Overrating Infinity, If There Were Only Two Primes in the World, The Planetarium)
- Chapter 9 Taylor Expansion and the Basel Problem (Polynomials of Infinite Degree, Taylor Expansion of sin x, The Fundamental Theorem of Algebra, Tetra's Attempt, Challenging Infinity)
- Chapter 10 Partition Numbers (Partition Numbers, The Fibonacci Hand Gesture, The Generating Function of Partition Numbers, A Journey in Search of a Better Upper Bound)
- Epilogue
- Afterword
- References and Further Reading
FAQ
这本书是小说还是数学书？
两者皆是。它以高中校园为背景，用人物对话推进情节，但对话内容就是货真价实的数学推导，从数列、生成函数到泰勒展开与巴塞尔问题，并非虚构的「伪数学」。
数学基础不好能读吗？
可以。书中从简单的数列规律讲起，泰朵拉这个角色常常替读者提出「笨问题」，作者会把每一步都停下来解释。但后几章涉及无穷级数、微积分与复平面，需要一定的耐心。
需要按顺序读整个系列吗？
不必。第一卷没有副标题，之后各册分别聚焦费马大定理、哥德尔不完备定理、随机算法、伽罗瓦理论等主题，彼此独立，可以按兴趣挑读。
中文版由谁翻译，评价如何？
中文版由复旦大学日语系硕士朱一飞翻译，人民邮电出版社「图灵新知」书系出版，全书约32.5万字、327页；前两部中文版在豆瓣评分约8.9。
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