• To encourage students to read maths game / puzzle book in their leisure time;
• To give a brief introduction to maths game / puzzle books which can be found in school library so that students can be more easy to understand the books;
• To encourage to better use the library resource to enrich maths horizon

我所介紹的這本書名叫“數學女孩﹣費馬最後定理”。
這是一本關於數學與愛情結合在一身的小說。可能你會即時萌生起大惑不解的問號，數學與愛情有關聯嗎？如果是物理學家寫愛情小說，那又如何呢？最少＜＜神探伽理略＞＞之中不也是有警官小姐和物理學家的愛情故事吧？
這本書是最受日本中學生歡迎的科普作品之一，它運用了小說中人物的對話來深入淺出地解說了不同的數學原理，例如運用時鐘來說明整數的性質 （完全循環的條件），運用果汁機來道出畢氏定理。除此之外，作者還用其他生動有趣的例子來講及反證法、餘數的定義、無窮遞減法、歐拉公式等，以至利用這些數學基礎來說明一個困擾了數學家三百多年的一個疑惑：何為費馬最後定理！
在此，讓我們一起探討書中的幾個有趣問題吧。
找到受同伴排擠的數字
題目1.1（見書第3頁）：
題目1.2（見書第4頁）：
題目1.3（見書第5頁）：
題目1.4（見書第6頁）：
題目2.1（見書第8頁）： 時鐘巡迴, 一個時鐘，中間相隔一個點，用線將點連結起來的結果是這樣的：

題目2.2（見書第8頁）：
一個時鐘，中間相隔二個點，用線將點連結起來又如何？那麼相隔三個點呢？四個點呢？五、六、七．．．個點呢？
最後，希望你在閱讀這本書及解難時可發掘出箇中的樂趣！

本書講述高中生主角與同學米爾迦、學妹蒂蒂和初中生表妹由梨在日常學生生活中討論、一起學習數學的故事。全書以主角第一人稱全以對話形式嘗試帶領讀者一起思考探索數學的世界。
書中提到的課題有: 畢氏定理、互質、反證法、複數、同餘、群、環、體、無窮遞減法、歐拉公式和費馬最後定理。正如作者所言，書中的數學問題「從簡單到小學生都懂得的部分到困擾了數學家們長達三百五十年的世紀之謎」，「如遇到無法理解公式涵意的時候，不妨先跳過卡住的部分，暫且隨著故事情節發展往下走」或許之後會發現有趣的事唷。對初中生而言，至少頭四章應該都是能夠應付的。

微積分的歷史步道

蔡聰明

三民書局

中四選修單元一或單元二的同學，都有機會學習到微積分•微分學起源於求曲線的切線斜率問題，積分學則源於求面積與體積的問題。微積分的共同特色是都要經歷「無窮步驟」，落實於無窮小的演算與極限操作，極具難度。

從古希臘開始，數學家經年的奮鬥到了十七世紀，由牛頓與萊布尼茲發展出微積分，並看出它們的互逆性，得到微積分根本定理,從而了解求切、求積、求極、變化與運動現象等問題。牛頓由運動學切入微積分;而萊布尼茲由差和分的連續化得到微積分,雖然是殊途同歸,但基本思想還是有所差異.此外,牛頓隱藏追求普遍方法,但熱衷解決特殊問題;萊尼茲強調普遍方法,用它來解特殊問題.我們都公認,微積分是由他們兩個人各自以不同的方式獨立地發展出來的,到近1880年，微積分的基礎才鞏固下來．

其後的數學家建議用極限概念,由此定義出無窮小.連續.導數.與積分,從而建立微積分.利用極限，我們可以處理一些難纏的概念問題．例如：一尺之棰，日取其半，萬世不竭，但可窮盡．但一尺之棰，逐日取1/4, 1/8, 1/16,....就不能窮盡了.

作者將微積分的發展過程放在歷史的脈絡中，適當地點出它的學習動機與需求。當學生只作機械式運算微積分的時候，不妨看看這本書，微積分的歷史進展及意義。

Sterling

If you used not to read math leisure readings because of the following reasons:
(i)        scared about the complicated mathematical symbols and content;
(ii)       it usually needs to take me long time to read, usually stop at some places that take time to think before move on; and
(iii)      the content and the page outline are dull,
then this would be a new light for you in looking at math books.

The Math book is not a technical one in terms of its content, but a book which is written for a general audience who do not necessarily have much background in mathematics. It contains 250 single-page articles on milestones in the history of mathematics. Each article, arranged in chronological order, is followed by a related full-page color image – some of them are stunning computer generated images. Each article is short and self-contained, and is easy to read in a few minutes at a time. You can just pick some of those that you are familiar with such as Tic Tac Toe, Pythagorean Theorem and Triangles, Law of Cosine,  Platonic Solids, Zero, Discovery of Series Formula for p, Logarithms, Pascal’ Triangles, Discovery of Calculus, Euler’s number e, Pigeonhole Principle, Rubik’s Cube etc. Though there are contents which are related to advanced math topics, the author is trying to press it and to explain the simplest overview of them and their significance in the development of mathematics at different stages. He rarely attempts to actually convey understanding of them so that it is easy for the reader to read through.

I would especially recommend this book to those who are currently or would like to study math extensive modules in senior secondary. It will not immediately drive you to the success in studying mathematics, but could be able bring you to a delighted realm in mathematics if you already have a slight inclination towards it.

這本書其實是兩個作者所著的，第一部是Lundy, M寫的「神聖的幾何」；而第二部是Sutton, D所整理的「柏拉圖與阿基米德立體」。
 　　在「神聖的幾何」中，大部份是提到平面的幾何圖形，雖然都是一些平時就看得到的正方形、三角形、圓形，但經過作者的介紹，讓讀者了解許多其中的奧秘，例如：以六個或十二個圓圍繞著一個圓，在古代教徒裡所代表的意義、如何劃出正七邊形、拼貼、螺旋線以及許多不可思議的巧合，也可能正因為有這麼多巧合，所以古代教徒們才會認為這些巧合都是神的旨意。
第二部從介紹「柏拉圖立體」開始，其實就是五種多面體，這些或許沒什麼，但柏拉圖給予元素的意義，例如：四面體代表火、八面體代表空氣、二十面體代表水、立方體代表土，最後十二面體代表神秘的第五元素－ether。除了這些神秘的色彩，作者後段所介紹的全是這些立體圖的變化，例如：有對偶性、可以嵌套、可旋轉、星狀化、可截面、可擴張、可展開，還有阿基米德立體，雖然作者很細心地介紹這些立體圖的變化，但從平面的書本上閱讀，還是很不容易，讀者必須有很棒的三維想像力。

The International Mathematical Olympiad (IMO) is a worldwide mathematics competition which held in over 80 countries annually. The paper consists of six problems, which chosen from various areas of secondary school mathematics. The solutions are usually short and elementary. No knowledge of higher mathematics is required.

This book is target to those who are interested in knowing more about this competition. Moreover, the problems in this book are good for form one to four students in revising Hong Kong secondary mathematics curriculum. Analyses and explanations in examples are easy to understand. The intermediate-level practice questions encourage students to enhance their problem-solving skills.

Numb3rs -- Season 2, episode 5 – ‘Assassin’

“We all use math every day; to predict weather, to tell time, to handle money. Math is more than formulas or equations; it's logic, it's rationality, it's using your mind to solve the biggest mysteries we know.”  - opening credits.

The opening credits gives a neat little answer to the question “When do we ever use Maths in real life?” Of course, it doesn’t answer the question “When will I ever need to use the cosine formula?” (the answer is probably never, BTW), but it does demonstrate how many people think Maths is so much more complex than it is. I’ve had many a student who claims that they “can’t do Maths”, and yet are able to tell me strange and complicated things such as the fact that I get things cheaper per item at the supermarket if I use a certain credit card on certain days of the week, in combination with certain other products when they are on special offer, plus I get more free stamps to boot!

But I digress…Numb3rs (note the fancy 3 instead of the e) is a US TV show that uses Maths to solve crimes. The premise is simple; every episode, FBI agent Don Eppes is challenged with solving a new crime, and he needs the help of his genius Mathematician younger brother Charlie (who is also a university professor) to crack the case. Each week, new mathematical theories are introduced and utilized to solve different crimes from murder to theft. Charlie (our Maths genius) will dazzle us with complicated maths speak (which is strangely easy to guess the meaning of) that most people won’t be too put off by, leaving us with moments where we might think “so THAT’S where Maths can be useful!” To top it all off, the Maths in each episode is guaranteed to be correct. The Wolfram website even has a dedicated blog explaining the maths behind each episode and how it was used to solve it!

In the episode ‘Assassins’ which I’m reviewing, two of my favourite topics are broached; crytanalysis (how to break a code) and game theory are used to decipher a hitman’s messages and then to second, and triple guess him into apprehending him before he can kill his target. In this episode, the maths is an ok match for the plot, but this is not always the case. While the maths is always correct, the story is written and then the Maths is added into the script. So while I can see the connection between the theory and the application, it does sometimes leave me with a sense of “Yeah! Right! As if that’s ever gonna happen!” It’s often a case of overcomplicating a rather simple problem, or rather, it takes Charlie half an episode to come up with complicated equations that takes up 3 blackboards to come up with an answer that police profiler could come up with in a few minutes.

With those down points aside, I must say that the Maths is quite seamlessly integrated into a polished TV series. The dialogue is snappy, the plot moves on at a smooth pace, and it never really gets stuck on certain parts for too long. So for fans of crime series like CSI or Bones, or for those who want to get a glimpse of what Maths CAN be used for, Numb3rs is definitely worth a try!

為什麼要學數學？想必有很多同學都不明白，而且當中不少認為數學艱深、乏味、欠實際。如果你心裡有這樣想法，本書或能改變你對數學和其應用的了解，
先跟你玩個遊戲：http://mathsking.net/mind.htm
這奇妙的讀心術遊戲可能你曾玩過，但可有想過到底為何它會知道你在想什麼？還是其實它根本就不知道你心中的兩位數是什麼也能一定顯示對的符號？想知道背後的原因，快去圖書館看看(P.125)
一直在課堂上所學的有理數、無理數(rational & irrational numbers)、畢氏定理(Pythagoras theorem)，同學一定很熟練它們的運算和操作了。但可知道它們被發現的因由、派系爭鬥的歷史和它們如何被廣泛應用在大大小小的研究、建設上？透過這些短淺而有趣的歷史小故事，精簡而常見的生活難題，也許會令你對一直以為沉悶的數學改觀，更有興趣。

從幼稚園開始，香港學生便要學習數學，但不少學生升讀中學後都經常問?一個問題：學習這些數學課題有何用？我們日常生活不只要需要運用加減乘除了吧？其實在日常生活中，我們可以用數學方法去理解周遭的事物。譬如我們可以從黃金分割(golden section)理解女士們愛穿高跟鞋的理由，什麼高度的高跟鞋才會令自己身段顯得較美。喜歡打籃球的同學亦可以二次函數(quadratic function)理解為何較高的拋物線會有較大的「穿針」機會，並因應自己的跳躍高度計算出最有利的投籃距離和角度。讀完此書，大家便會發現我們過去所學的數學並一無事處，可以跟數學扯上關係的東西其實多的是，關鍵是懂不懂用和會不會用

想要快樂，最好乾脆放棄數學，真的是這樣嗎？如果你對數學一點興趣也沒有，那麼你要好好地了解和認識它，打好數學的根基。看了這本書後，你會學懂怎樣解應用題、轉換單位和了解除法、分數、率、比其實一樣等，更可能培養出高中之前必須具備的數學基礎。
以下是加法的筆算。在不同的字母中，隱藏著不同的數字，在相同的字母中隱藏著相同的數字。請問以下的字母中，藏了什麼樣的數字？
            S E N D
+        M O R E__
          M O N E Y
雖然作者是位日本人，他會用日元來作例子，但內容都和我們的課題相同。內附很多圖畫和表來解釋很多數學概念，令你快樂地學習數學！

問以下的數列是什麼名字？
1，1，2，3，5，8...
答對了，這就是「費波那契數列（Fibonacci sequence)」。

但是你知道關於這個數列的故事嗎？原來這個數列源於數學家費波那契的一本著作內的一個「兔子生兔子問題」。假如每個月一對兔子生下另一對，而這新一對的兔子在二個月後就生下另一對。問一年後有多少對兔子生出來？答案是377對！計算的方法是與你們中一時所學的費波那契數列有關的。

以上的是屬於「數學和數學家的故事1」的其中一部分。書內除了介紹不少數學家的故事，還有很多關於數學的有趣典故。

數學恩仇錄：數學史上的十大爭端

作為一名數學老師，多少對數學歷史總有一點興趣。
為甚麼他們會這樣想？
為何要學這課題？
……
這些問題不但是學生時代出現過，就是現在作為老師的我還常常問自己。從前看數學總是千篇一律，但當閱畢此書後，頓然發現數學也有它「人性」的一面。

作者在書中記錄了十段在近代數學歷史中的精彩事件，縱然當中有鮮為人知的事情，但卻是對數學發展有?深遠的影響。或許你會覺得數學書不值一顧，但正如譯者所言「數學知識不?不要緊，不妨就當小說來讀，其感染力一點也不比虛構小說遜色。」

數學科? 在一些人的眼中, 是沉悶和討厭的。 因為經常做錯數學題, 成績又不太好, 便幾乎失去了學習興趣。所以, 很多老師和同學都認為：要學得好, 不外乎是多整理重點, 多做習題, 多測驗 (即是採用“題海戰術”), 多提問和多做考試檢討。這種學習方法在執行時需要很堅強的毅力。缺點是流于記憶層次, 比較偏重于用來應付考試, 對於真正數學精神的培養和邏輯思考的訓練不一定會有很大的幫助。

於是, 作者提出一種“直觀式系統性數學學習方法”, 並稱之為“學好數學的五個捷徑: 大膽try, 分段think, 圖像look, 運算simplify, 推演logical”, 以求在解題時真正達到靈活思考的層次, 並體會出數學是有用的。作者王擎天博士見解獨到, 經驗豐富, 講解深入淺出, 例子的程度從初中到高中都有。這是一本學習數學學習方法的好書, 相信你閱後一定可以得益!

高等教育出版社

Knowing more about the history of mathematics gets you acquainted with this particular area of study in history. It also let you understand the development of mathematics and discover the reason of learning mathematics. You may then start to appreciate the many mathematicians from various countries across previous 5000 years.

Even though you cannot follow all the mathematics ideas in the book, you can still know more about mathematics from a cultural point of view – how human activities affect the growth of mathematics, how mathematics interact with other disciplines of study, and how different people behave in exploring new aspects of mathematics, etc.

This book is written with mathematics and for mathematics, but not just about mathematics. Have fun!

你心目中的數學奧林匹克比賽的參賽者是怎樣的呢？是天才？是怪人？為什麼他們的數學能力都那麼好？是天資聰敏還是後天努力？這本書追?採訪美國奧數代表隊的幾位成員，記錄了他們的成長故事。既然是關於奧數成員，此書當然也收錄了一些具挑戰性的題目及成員們具創意的思考方法和過程，例如，用”圖像思考”幫助解題。除此之外，本書還有簡單提及一些著名的數學故事，例如Andrew Wiles與世隔絕，用了七年的時間證明了費馬最後定理。

George Polya

Obviously, this is a book about solving mathematic problem. However, the author does not aim to teach the readers some new methods or techniques to solve problems. Instead, he introduces strategies and thinking steps that we can adapt to tackle questions that require us to find a solution or to prove something. Also, this book is intelligently designed for both teachers and students. While showing many different types of problem, the author also includes some dialogues between teacher and students. These dialogues show clearly how students can be guided through questions asked by their teacher. Very often, when coming across complicated questions, students have no idea how to start, how to connect the theories they have learned, how to construct working steps and how to check if their results are correct. If students are capable of asking themselves some useful questions step by step, the problem may not be as scary as they first see it. I highly recommend this book to all of you and I hope that you can equip yourselves good questioning strategies to guide yourselves to solve problems. Even when teacher is not here, you can still solve it!