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怎樣才算最好

by 梁承裕 ...

Series Book 7 - 數學其實一直都在
導航推薦的「最佳路線」，究竟是最短、最快、最便宜，還是風險最低？只要改變時間、金錢和安全的權重，同一張地圖便會給出不同答案。「最好」需要由人先定義；有人必須說明目標、限制、可接受風險，以及願意花多少計算時間，電腦才知道應該尋找甚麼。《怎樣才算最好？》由日常選擇走進最佳化。最短路線未必最快，現實問題也總有一句「但是」：預算有限、資源不足、物理規律不能違反，不同人的利益亦不完全相同。書中會解釋如何把目標寫成可比較的量，如何處理限制，以及多個互相衝突的「好」為甚麼未必能壓成唯一分數。梯度可以提示下一步往哪裏走，但方向會受座標尺度影響；走到一個谷底，也不代表已找到全世界最低的位置。當可能組合多得無法逐一測試，計算預算本身便成為問題的一部分。有些候選答案每試一次，都要重新模擬整個世界；算法因而需要近似、替代模型和更聰明的搜尋。讀者亦會看到個人與系統的衝突：一個人最快的路，可能令所有人一起變慢；便宜 ... Read more

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導航推薦的「最佳路線」，究竟是最短、最快、最便宜，還是風險最低？只要改變時間、金錢和安全的權重，同一張地圖便會給出不同答案。「最好」需要由人先定義；有人必須說明目標、限制、可接受風險，以及願意花多少計算時間，電腦才知道應該尋找甚麼。《怎樣才算最好？》由日常選擇走進最佳化。最短路線未必最快，現實問題也總有一句「但是」：預算有限、資源不足、物理規律不能違反，不同人的利益亦不完全相同。書中會解釋如何把目標寫成可比較的量，如何處理限制，以及多個互相衝突的「好」為甚麼未必能壓成唯一分數。梯度可以提示下一步往哪裏走，但方向會受座標尺度影響；走到一個谷底，也不代表已找到全世界最低的位置。當可能組合多得無法逐一測試，計算預算本身便成為問題的一部分。有些候選答案每試一次，都要重新模擬整個世界；算法因而需要近似、替代模型和更聰明的搜尋。讀者亦會看到個人與系統的衝突：一個人最快的路，可能令所有人一起變慢；便宜
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倒過來的數學

by 梁承裕 ...

Series Book 3 - 數學其實一直都在
醫生沒有切開身體，CT卻畫出內部影像；科學家不能鑽到地心，仍嘗試由地震波推測地下結構。這些答案都不是直接看見的。儀器只收到投影、走時、波形或回聲，人們再由留下的痕跡，倒過來推問原來的世界可能是甚麼樣子。《倒過來的數學》從「正着算」與「倒着推」的差別開始。若已知一個世界，可以預測它會產生甚麼資料；若手上只有資料，符合它的世界卻可能不止一個。本書以有限角度CT和地震探測為兩條主線，討論儀器究竟量到甚麼、增加資料是否必然增加知識、最早到達的波與完整回波各自帶來甚麼線索。讀者亦會遇上反問題最棘手的兩件事：不同答案可能產生相同資料，而量測只差一點，重建結果卻可能相差很遠。資料不足時，算法通常會偏好較平滑、較簡單或較符合先驗知識的答案。這種做法可以令問題變得可解，卻同時加入了資料本身沒有提供的假設。電影裏把模糊影像無限放大、按一下便看清人臉的情節，因此值得重新審視。書中不把重建圖像當成世界本身 ... Read more

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醫生沒有切開身體，CT卻畫出內部影像；科學家不能鑽到地心，仍嘗試由地震波推測地下結構。這些答案都不是直接看見的。儀器只收到投影、走時、波形或回聲，人們再由留下的痕跡，倒過來推問原來的世界可能是甚麼樣子。《倒過來的數學》從「正着算」與「倒着推」的差別開始。若已知一個世界，可以預測它會產生甚麼資料；若手上只有資料，符合它的世界卻可能不止一個。本書以有限角度CT和地震探測為兩條主線，討論儀器究竟量到甚麼、增加資料是否必然增加知識、最早到達的波與完整回波各自帶來甚麼線索。讀者亦會遇上反問題最棘手的兩件事：不同答案可能產生相同資料，而量測只差一點，重建結果卻可能相差很遠。資料不足時，算法通常會偏好較平滑、較簡單或較符合先驗知識的答案。這種做法可以令問題變得可解，卻同時加入了資料本身沒有提供的假設。電影裏把模糊影像無限放大、按一下便看清人臉的情節，因此值得重新審視。書中不把重建圖像當成世界本身
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會流動的數學

by 梁承裕 ...

Series Book 4 - 數學其實一直都在
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車明明向前行，塞車的波卻可能向後傳；一滴墨水落進水中，一方面被水流帶走，另一方面又慢慢散開。世界不停改變，但每一個位置通常只「知道」附近發生甚麼。局部的速度、溫度、濃度和交換規則，累積起來，便把整個系統推向下一刻。《會流動的數學》帶讀者進入偏微分方程所描述的動態世界，卻不要求先修微積分。書中以示蹤物質貫穿不同情境：東西去了哪裏？熱為甚麼總會散開？煙究竟是飄走，還是散走？讀者會比較站在固定位置觀察與跟着流體粒子移動的分別，也會看見守恆、輸送、擴散和反應如何組成幾種基本變化。相同想法還會走進交通、聲音和移動邊界：塞車怎樣形成，聲音穿過不同介質為甚麼轉彎，一條邊界裂開再合起來時，數學如何繼續追蹤它？本書亦談一個很迷人的問題：複雜花紋是否一定需要一位設計者逐點畫出？簡單的局部反應與擴散，已可能長出斑點和條紋；看似混亂的流動，也可能藏着引導物質去向的骨架。不過，方程不會自動等於真實
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算不準的數學

by 梁承裕 ...

Series Book 2 - 數學其實一直都在
一般使用二進制浮點數的電腦，甚至不能把十進制的0.1完完整整地放進記憶體。既然最基本的小數也要近似，我們憑甚麼相信天氣模擬、橋樑計算、醫學影像或科學預測？《算不準的數學》處理所有有限電腦都逃不掉的處境：數字位數有限、格點有限、時間有限，答案卻仍要可靠。本書由浮點數、絕對誤差和相對誤差開始，逐步走進數值計算的現場。一條連續曲線怎樣存進電腦？切線如何變成幾個鄰近數值？把世界切成格子後，格子愈細是否一定愈準？同一個熱傳或波動問題，會帶讀者經過差分、收斂、穩定性、守恆、矩陣與疊代方法。當未知數多達一百萬個，電腦為甚麼有時故意不把方程「解到最盡」？當某一小片區域特別複雜，格子又能否自己集中到最需要的地方？可靠的計算不靠多印幾個小數位。本書會分清輸入本身有多敏感、算法會否放大誤差，以及浮點精度是否足夠；也會示範在沒有標準答案時，如何用網格加密、獨立方法、殘差、守恆量和可重現測試交叉檢查 ... Read more

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一般使用二進制浮點數的電腦，甚至不能把十進制的0.1完完整整地放進記憶體。既然最基本的小數也要近似，我們憑甚麼相信天氣模擬、橋樑計算、醫學影像或科學預測？《算不準的數學》處理所有有限電腦都逃不掉的處境：數字位數有限、格點有限、時間有限，答案卻仍要可靠。本書由浮點數、絕對誤差和相對誤差開始，逐步走進數值計算的現場。一條連續曲線怎樣存進電腦？切線如何變成幾個鄰近數值？把世界切成格子後，格子愈細是否一定愈準？同一個熱傳或波動問題，會帶讀者經過差分、收斂、穩定性、守恆、矩陣與疊代方法。當未知數多達一百萬個，電腦為甚麼有時故意不把方程「解到最盡」？當某一小片區域特別複雜，格子又能否自己集中到最需要的地方？可靠的計算不靠多印幾個小數位。本書會分清輸入本身有多敏感、算法會否放大誤差，以及浮點精度是否足夠；也會示範在沒有標準答案時，如何用網格加密、獨立方法、殘差、守恆量和可重現測試交叉檢查
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Mathematics for Economics, fourth edition

by Michael Hoy, John Livernois, Chris Mckenna, Ray Rees, Thanasis Stengos ...

An updated edition of a widely used textbook, offering a clear and comprehensive presentation of mathematics for undergraduate economics students.This text offers a clear and comprehensive presentation of the mathematics required to tackle problems in economic analyses, providing not only straightforward exposition of mathematical methods for economics students at the intermediate and advanced ... Read more

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An updated edition of a widely used textbook, offering a clear and comprehensive presentation of mathematics for undergraduate economics students.This text offers a clear and comprehensive presentation of the mathematics required to tackle problems in economic analyses, providing not only straightforward exposition of mathematical methods for economics students at the intermediate and advanced
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Infinite Ascent

A Short History of Mathematics

by David Berlinski ...

Series Book 22 - Modern Library Chronicles
In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure.Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated ... Read more

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In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure.Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated
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Fractions For Dummies

by Mark Zegarelli ...

An easy, straightforward, and fun guide for learning fractions and its counterpartsFractions For Dummies is the perfect strategy guide for both understanding and using one of math's most common (and most challenging) topic areas. You'll explore current solving strategies for fraction-related problems, and you'll also discover how to solve problems involving fractions' closely related cousins, ... Read more

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La engañosa sencillez de los triángulos

De la fórmula de Herón a la criptografía

by Ágata Timón, Manuel de León ...

Los triángulos han despertado la curiosidad de las mentes más brillantes desde la Antigüedad clásica hasta la actualidad, en problemas de investigación teórica (en el cálculo de áreas y volúmenes de objetos complejos, en las curvas elípticas, en la fractalidad) y en su aplicación a cuestiones reales, como el desarrollo de los sistemas de GPS, el diseño y la arquitectura. Sin embargo, esta magia de ... Read more

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Calculus Made Easy

Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning Which are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus

by Silvanus Phillips Thompson ...

Calculus Made Easy by Silvanus Phillips Thompson is an accessible and engaging introduction to the fundamental principles of calculus, offering readers a clear and simplified approach to understanding this essential branch of mathematics.Calculus Made Easy by Silvanus Phillips Thompson is a timeless classic that makes the complex world of calculus accessible to students and learners of all levels. ... Read more

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Prime Wave

Prime Numbers

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Series series Prime Numbers
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GRADE 12 (MHF4U) SECONDARY SCHOOL MATHEMATICS TESTS AND EXAMS (FUNCTIONS)

INCLUDING MR W'S EASY TO FOLLOW STEP BY STEP SOLUTIONS

by Dennis Weichman ...

Series series MR W'S MATH STUDY GUIDES
WHO IS MR.W?Dennis Irwin Weichman (MR. W) holds a Bachelors degree and Masters degree in mathematics from the University of Western Ontario. His series of Math Study Guides capture his teaching methodology best practices from 30 years as a high school teacher and 20 years as a private math tutor.It all started with the idea of simplifying the process of teaching math using a step by step approach. ... Read more

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Sample EBOOK - SECONDARY SCHOOL MATHEMATICS - SAMPLES FROM EACH BOOK IN MR W'S MATH STUDY GUIDE SERIES

INCLUDING MR W'S EASY TO FOLLOW STEP BY STEP SOLUTIONS

by Dennis Weichman ...

Series series MR W'S MATH STUDY GUIDES
WHO IS MR.W?Dennis Irwin Weichman (MR. W) holds a Bachelors degree and Masters degree in mathematics from the University of Western Ontario. His series of Math Study Guides capture his teaching methodology best practices from 30 years as a high school teacher and 20 years as a private math tutor.It all started with the idea of simplifying the process of teaching math using a step by step approach. ... Read more

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The Joy Of X

A Guided Tour of Math, from One to Infinity

by Steven Strogatz ...

“Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!”—Scientific AmericanMany people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series ... Read more

$12.19 USD

“Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!”—Scientific AmericanMany people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series
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See Ya Later Calculator

Simple Math Tricks You Can Do in Your Head

by Editors of Portable Press ...

The math book for anyone who thinks they hate math, full of easy, entertaining and practical tricks for mentally solving problems in seconds.No matter how much you might try to avoid numbers, we all use math every day to calculate a tip, figure out an interest rate, or estimate the cost of the groceries in your cart. But the good news is, math can be easy—and even fun—if you know how to do it all ... Read more

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The math book for anyone who thinks they hate math, full of easy, entertaining and practical tricks for mentally solving problems in seconds.No matter how much you might try to avoid numbers, we all use math every day to calculate a tip, figure out an interest rate, or estimate the cost of the groceries in your cart. But the good news is, math can be easy—and even fun—if you know how to do it all
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Fermat's Enigma

The Epic Quest to Solve the World's Greatest Mathematical Problem

by Simon Singh ...

xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy ... Read more

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Principes mathématiques de la Philosophie Naturelle

by Isaac Newton ...

Isaac Newton (4 janvier 1643 G – 31 mars 1727 G, ou 25 décembre 1642 J – 20 mars 1727 J)N 1 est un philosophe, mathématicien, physicien, alchimiste, astronome et théologien anglais, puis britannique.Cet ouvrage: Principes mathématiques de la Philosophie Naturelle 2,3, écrit en 1686, est considéré comme une œuvre majeure dans l'histoire de la science. C'est dans celui-ci qu'il décrit la loi ... Read more

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... Read more
The Princeton Companion to Mathematics

Edited by Timothy Gowers, June Barrow-Green, Imre Leader ...

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and ... Read more

$79.19 USD

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and
... Read more
Math Review

by BarCharts,Inc ...

This guide includes the essentials covered in all the basic areas of math. It contains information on set theories, real numbers, integers, fractions and much more. ... Read more

$4.95 USD

This guide includes the essentials covered in all the basic areas of math. It contains information on set theories, real numbers, integers, fractions and much more.
... Read more
Math Fundamentals 1

by BarCharts,Inc ...

$4.95 USD
Birds

by Jim Flegg ...

Series series Collins Gem
The ideal portable companion, the world-renowned Collins Gem series returns with a fresh new look and updated material.This is the perfect pocket guide for keen birdwatchers and nature enthusiasts to identify the most commonly seen species in Britain and Europe.Authoritative text and beautiful photographs show the distinguishing features of each bird, including notes on appearance, colour and ... Read more

$3.77 USD

The ideal portable companion, the world-renowned Collins Gem series returns with a fresh new look and updated material.This is the perfect pocket guide for keen birdwatchers and nature enthusiasts to identify the most commonly seen species in Britain and Europe.Authoritative text and beautiful photographs show the distinguishing features of each bird, including notes on appearance, colour and
... Read more
I Used to Know That: Maths

by Chris Waring ...

Series Book 19 - I Used to Know That
If memories of learning algebra bring you out in a cold sweat and thoughts of quadratic equations cause you feelings of fear and dread, I Used to Know That: Maths can help. A light-hearted and informative reminder of the things that we learnt in school but have since become relegated to the backs of our minds, this book will help you to brush up on your mental arithmetic, including percentages, ... Read more

$7.19 USD

If memories of learning algebra bring you out in a cold sweat and thoughts of quadratic equations cause you feelings of fear and dread, I Used to Know That: Maths can help. A light-hearted and informative reminder of the things that we learnt in school but have since become relegated to the backs of our minds, this book will help you to brush up on your mental arithmetic, including percentages,
... Read more
The Abacus

The World's First Computing System

by Jesse Dilson ...

An easy-to-use guide to the world's first computer, from its historical origins and how it works to how to use it to perform an array of mathematical feats.The abacus is as efficient and useful a tool today as it was when it was first devised many centuries ago. Whether you're a computer expert or you're mastering arithmetic and word problems for the first time, it won't take long to learn the ... Read more

$17.29 USD

An easy-to-use guide to the world's first computer, from its historical origins and how it works to how to use it to perform an array of mathematical feats.The abacus is as efficient and useful a tool today as it was when it was first devised many centuries ago. Whether you're a computer expert or you're mastering arithmetic and word problems for the first time, it won't take long to learn the
... Read more
GRADE 9 (MPM1D) SECONDARY SCHOOL MATHEMATICS TESTS AND EXAMS

INCLUDING MR W'S EASY TO FOLLOW STEP BY STEP SOLUTIONS

by Dennis Weichman ...

Series series MR W'S MATH STUDY GUIDES
WHO IS MR.W?Dennis Irwin Weichman (MR. W) holds a Bachelors degree and Masters degree in mathematics from the University of Western Ontario. His series of Math Study Guides capture his teaching methodology best practices from 30 years as a high school teacher and 20 years as a private math tutor.It all started with the idea of simplifying the process of teaching math using a step by step approach. ... Read more

$17.99 USD

WHO IS MR.W?Dennis Irwin Weichman (MR. W) holds a Bachelors degree and Masters degree in mathematics from the University of Western Ontario. His series of Math Study Guides capture his teaching methodology best practices from 30 years as a high school teacher and 20 years as a private math tutor.It all started with the idea of simplifying the process of teaching math using a step by step approach.
... Read more
我的幾何人生：從貧窮少年到數學皇帝，丘成桐自傳

The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry

by 丘成桐, 史蒂夫・納迪斯（Steve Nadis） ...

Translated by 夏木清 ...

「在哈佛，丘成桐一個人就是一個數學系！」——美國數學家 Isadore Singer丘成桐是當代最具影響力的數學家，成就卓越，獲獎無數，被紐約時報譽為「數學皇帝」。他在27歲時破解卡拉比猜想，30歲即成為普林斯頓大學終身教授，33歲更榮獲菲爾茲獎，是首位華人得主。他的研究為包括幾何學、弦論、廣義相對論眾多領域都提供洞見，也為黑洞理論做出重要貢獻。《我的幾何人生》以直率而真誠的筆觸，紀錄這位傑出數學家與眾不同、充滿意外的勵志故事與傳奇人生。書中講述他如何從貧窮的中國鄉村成長，因父親早逝，由母親一手撫養，度過顛沛流離的貧困童年。而後遠渡重洋，在異國求學，並在27的年輕之姿，在世界數學界一鳴驚人，獲得美國頂尖大學教職，並不斷解決科學上的難題，取得驚人突破。除了舉世矚目的個人成就外，他更投入大量的精力與心血，支持青年學子，培養新一代的數學家。丘成桐也特別撰寫〈我與臺灣〉篇章 ... Read more

$13.74 USD

「在哈佛，丘成桐一個人就是一個數學系！」——美國數學家 Isadore Singer丘成桐是當代最具影響力的數學家，成就卓越，獲獎無數，被紐約時報譽為「數學皇帝」。他在27歲時破解卡拉比猜想，30歲即成為普林斯頓大學終身教授，33歲更榮獲菲爾茲獎，是首位華人得主。他的研究為包括幾何學、弦論、廣義相對論眾多領域都提供洞見，也為黑洞理論做出重要貢獻。《我的幾何人生》以直率而真誠的筆觸，紀錄這位傑出數學家與眾不同、充滿意外的勵志故事與傳奇人生。書中講述他如何從貧窮的中國鄉村成長，因父親早逝，由母親一手撫養，度過顛沛流離的貧困童年。而後遠渡重洋，在異國求學，並在27的年輕之姿，在世界數學界一鳴驚人，獲得美國頂尖大學教職，並不斷解決科學上的難題，取得驚人突破。除了舉世矚目的個人成就外，他更投入大量的精力與心血，支持青年學子，培養新一代的數學家。丘成桐也特別撰寫〈我與臺灣〉篇章
... Read more

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怎樣才算最好

倒過來的數學

會流動的數學

算不準的數學

Mathematics for Economics, fourth edition

Infinite Ascent

Fractions For Dummies

La engañosa sencillez de los triángulos

Calculus Made Easy

Prime Wave

GRADE 12 (MHF4U) SECONDARY SCHOOL MATHEMATICS TESTS AND EXAMS (FUNCTIONS)

Sample EBOOK - SECONDARY SCHOOL MATHEMATICS - SAMPLES FROM EACH BOOK IN MR W'S MATH STUDY GUIDE SERIES

The Joy Of X

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Fermat's Enigma

Principes mathématiques de la Philosophie Naturelle

The Princeton Companion to Mathematics

Math Review

Math Fundamentals 1

Birds

I Used to Know That: Maths

The Abacus

GRADE 9 (MPM1D) SECONDARY SCHOOL MATHEMATICS TESTS AND EXAMS

我的幾何人生：從貧窮少年到數學皇帝，丘成桐自傳