Mathematics Digital Library:About

I started this project for several reasons, and I will try to explain them on this page.

All my life, I have had no problems buying books. When I was studying, my parents ensured that I always had all the books and other resources I needed. No matter how expensive it was, they would go out of their way to get their hands on it, even sourcing them from abroad, which wasn't easy in the 1970s. Over the years, I realised that this is not so for many students around the world. For some students, books are a luxury.

After graduating from the National University of Singapore, I worked as a chemical engineer in McDermott Southeast Asia for a short time, and then became a lecturer.

The first subject I taught was engineering mathematics. Because I was teaching mathematics, I started collecting math textbooks so that I would have many examples and exercises to give to the students. I noticed that one's proficiency in mathematics depended on how much one "practiced". Humans are really super efficient pattern recognition machines! When they practice more, the also recognise more! Also, whenever I visited a country, I would try to go to a bookstore to buy at least one math textbook bring back home with me. That became, to me, a souvenir from that country. In addition, I scoured secondhand bookstores (mainly in Bras Basah Complex in Singapore) to see if there were any books that I could add to my collection. When the World Wide Web started, things got a lot easier, and I visited online stores like BookFinder and AwesomeBooks to add to my collection. After 30 years of teaching (and travelling), I realised that I had amassed over 600 math textbooks from Singapore, Malaysia, United Kingdom, United States, Indonesia, Thailand, Vietnam, Myanmar, the Philippines, Taiwan, China, India, Israel, Australia, Japan, France and the Czech Republic. During my free time, I would page through the books in my collection.

A few things struck me.

First, the price of textbooks. Math textbooks can be very expensive! Take Thomas' Calculus, for example (I used the 5th edition of this textbook when I was an undergraduate). The 14th edition cost a whopping US$179.44 on Amazon. Apostol's Calculus (Volume 1) costs US$239.39! Students from developing countries will never be able to afford these excellent textbooks -- they're far too expensive! One reason the price is so high is because it's so huge -- usually over a thousand pages! In addition to being expensive, they're thick, heavy and unwieldy to lug around. I wonder if publishers realise that students today don't like to carry textbooks around (even light ones)! Could we make textbooks thinner, and cheaper? I started thinking -- if we were to remove pages from a textbook to make them thinner, which pages could be dispensed off?

Second, the amount of repetition in these books. There are so many examples and questions that were repeated across the different textbooks. Authors re-create so many questions and solutions when they write a math textbook. Is this re-creation necessary? It would be much better if authors spent time creating better explanation on the concepts rather than creating more questions. There is already an amply supply of questions in the textbooks published over the past centuries (yes, centuries -- hundreds of years!).

Third, the lack of solutions to the questions in exercises. Authors usually provide final answers (usually, just the final number) to selected questions (e.g., the odd-numbered questions), but what students need are the full solutions, the steps that progressively lead to the solution. Some publishers publish a "students guide" or "solutions manual" to supplement the textbook, but even these do not have the step-by-step solutions for all the questions. The final answers are only useful for the good students. They use the final answer as a check. They are not useful for the student who does not even know how to start on the question. There is a good reason why authors don't provide the full solution to all questions -- space just doesn't allow it. Imagine how thick textbooks would be if all the questions came with its complete solution! I estimate doing that would add at least 4,000 pages to the textbook, or four volumes of 1,000 pages each!

The thing is that most students learn mathematics by studying examples, and it would be great if clearly explained solutions could be found. This is the idea behind The Mathematics Digital Library. We provide questions publicly online for anyone to solve, and we provide a platform where teachers and students can solve the questions. These (the questions and the solutions) are then made available to everyone. What about the the authors of textbooks, you might ask ...? They can then concentrate on writing and explaining mathematics, instead of reinventing questions for the textbooks they write. In their textbooks, they can refer students to the questions on this database, instead of re-compiling sets of questions, and re-inventing the wheel. Students can come use the solved problems on this site as examples to learn from.

Fourth, there is a huge overlap in the mathematics curriculum of many countries. To put it simply, most countries teach their students the same stuff, when it comes to mathematics! This means once digitized, the questions will benefit students everywhere! They do have to have Internet connectivity, and a device to access the Internet with, but with just these two requirements, they're can access the library!

Mathematics textbooks have been around for a long time. The first ever calculus textbook was published way back in 1696 (over three centuries ago!) by Guillaume de l’Hôpital under the name Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes (Boyer, 1946). It's available (for free) here. Mathematics questions (and solutions) have been recycled from textbook to textbook for a long time, and its time this stops!

Where do the questions on The Mathematics Digital Library come from, you might ask. They come from the textbooks in my collection. You only need to know MathJax to work on the solutions. MathJax is easy to learn. As this database is built on a Wiki, any one can contribute, and that includes you!

Many types of content are available for free today on the World Wide Web:

dictionaries (e.g., The Free Dictionary) encyclopedias (e.g., Wikipedia) maps (e.g., OpenStreetMap) music scores (e.g., International Music Score Library Project) It's time for mathematics questions (and their solutions) to get online for free too!

Take a look at this set of questions that I have digitized. You can now contribute the solutions.

I will be starting to digitize the questions from the textbooks I own. Many of them are excellent textbooks, but not easy to find.

Open Educational Resources (OER)

Here are three definitions of open educational resources (OERs):

(i) educational resources, enabled by information and communication technologies, for consultation, use and adoption by a community of users for non-commercial purposes;

(ii) digitised materials offered freely and openly for educators, students, and self-learners to use and reuse for teaching, learning and research; and

(iii) resources that reside in the public domain or have been released under an intellectual property license that permits their free use or re-purposing by others.

An OER may be an entire course, a complete book, or a more granular piece, such as a single learning object.

I'm working on a few technical details with the wiki platform now (specifically, how to organise the content so that the questions can be found!), but will be adding questions soon.

A special thanks to Sophie Hnin for setting up MediaWiki, along with the MathJax extension.

To join me in this effort (adding questions, or solving them), email me at ascklee@gmail.com.

Thank you.

Chu Keong

References:

Bover, C.B. (1946). The First Calculus Textbooks. The Mathematics Teacher, 39(4), 159-167.

Three students who are doing their Critical Inquiry project with me is responsible for jump-starting the work on The Mathematics Digital Library. They are Bian Qiuyu, Chen Xiaofeng and Zhang Suyu. ...

This project has been made possible because of the efforts of several people.

因为一些原因，我开始着手建立这个网站。

对我来说，无论是在人生中的哪个阶段，买书一直都是一个令人头疼的难题。在我的学生时代，我的父母总是倾尽全力为我提供我所需要的书籍以及其他学习材料。不管那些书有多贵，他们都会想方设法买到它们，有时甚至需要从海外购入。这在70年代是一件很不容易的事情。而这些年来，我意识到，这个世界上的许多学生并不能像我一样幸运。对于一些学生来说，书本是一种奢侈品。

从新加坡国立大学毕业后，我在McDermott东南亚分公司任职了一段时间的化学工程师，并在此之后成为了一名讲师。

我教的第一个科目是工程数学。作为一名数学老师，我需要收集数学教材，并从中寻找例题和习题给学生讲解。在这个过程中，我意识到一个人的数学水平高低取决于他花了多少功夫去练习。人类是超高效的模式识别机器 - 当我们练的越多，理解到的也就越多。我会在每一个我去过的国家的书店里买至少一本当地的数学教材。这些教材之于我，是纪念品之于旅人。除此之外，我也会去二手书店（主要在新加坡Bras Basah Complex）搜罗可以纳入我数学书收藏的书。

万维网的兴起使这一切都变得简单了起来。我开始去BookFinder和AwesomeBooks这些网上书店购入书籍。在30年的教学（和旅行）生涯中，我收集了来自新加坡、马来西亚、英国、美国、印度尼西亚、泰国、越南、缅甸、菲律宾、中国、印度、以色列、澳大利亚、日本、法国和捷克共和国这16个国家的数学教材，共计600本。我会在闲暇时翻阅这些藏书。

有一些事实引发了我的思考。

首先是实体教材的价格。数学教科书的价格往往很高。举个例子，第十四版《托马斯微积分》（我在本科时用的是第五版）在亚马逊网站上的售价高达179.44美元，而《阿波斯托尔微积分(第1卷)》售价更是达到了239.39美元。一些来自发展中国家的同学很难负担起这样的教材，而造成这样昂贵价格的原因之一是动辄上千的页数。这使得书本不仅价格高昂，更是笨重到难以携带。令我好奇的是出版商们是否有意识到当代学生不愿携带这样厚重的书（甚至连轻薄的书本也不愿携带），并进一步引发了我的思考：我们是否可以将书本变得更轻薄、更价廉？如果我们要通过减少书页来达到降低价格的目的，那么哪些页面是可以被减除的？

其次是教材中大量重复的内容。许多的相同例题和习题出现在不同的教科书中，且作者在编撰的时候重新编写了大量的数学题和答案，这真的是必要的吗？我认为应当将时间花在更好地解释数学概念上，而非不断产生更多的数学练习题，因为几个世纪以来我们已经积累了大量的数学题目（没错，几个世纪，也就是好几百年）。

再次，数学题的解答也有一些匮乏。编者通常只是在特定的题目（如奇数相关的题）下给出最终解，然而学生需要的是完整的解决方案，是逐步走向最终答案的步骤。有的出版社会出版 "学生指南 "或 "解题手册 "作为教材的补充，但即便如此，也没有所有问题的分步解法。最终答案只适用于那些优秀的学生用来校对正误，而对没有解题头绪的同学来说，它们没有任何意义。编者不将完整步骤放上书本的理由也很简单-没有位置。想象一下，如果所有的解题步骤都印刷在教材上，那这本书会有多厚。我估计这样做至少可以使教材增加4000页，也就是四卷，每卷1000页。但事实是，大多数学生是通过学习例题来学习数学的，详尽的解题步骤可以帮助他们很多。这便是创建数字化数学题库的思想启发和基础。我们会通过网站提供公开的数学题目供老师、同学以及大家解决，并分享给大家。你可能会问，那教科书的作者呢？他们可以集中精力编写和解释数学概念，而不是为他们编写的教科书重新设计数学题。 在课本中，他们可以让学生参考数字化数学题库中的问题，而不是重新编排成套的问题。而学生可以把这个网站上的解题作为例子来学习。

最后，很多国家的数学课程之间有很大的重复部分。简单来说，大多数国家教给学生的数学知识东西都是一样的，这意味着一旦实行数字化，全世界的学生都将从中受益。虽然他们必须要有一个联网设备和可供连接的网络，但只要满足了这两个要求，他们便可以访问题库。

数学教科书的出现由来已久。有史以来的第一本微积分教科书早在1696年（3个多世纪前）由Guillaume de l'Hôpital出版，书名为Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes（Boyer，1946）。由此可见，数学问题（和解决方案）一直循环往复地出现在各个教科书中，而我们是时候去停止这种做法了。

你或许会问，数字化数学题库里的题目是从哪里来的？它们其实正来自于我收藏的那些教科书中。你只需要掌握MathJax便可以将你的解答放在网站上，而MathJax是一个很好上手的软件。这个数据库是建立在Wiki上的，这意味着任何人都可以做出贡献，包括你在内。

如今，许多不同类型的内容都可以在万维网上免费获得：字典(如《The Free Dictionary》)、百科全书(如维基百科)、地图(如OpenStreetMap)、乐谱(如International Music Score Library Project)。而现在是时候让数学题(及其解法)也能通过网络免费获得了。

你现在可以为这些已经实现数字化的数学题贡献解题方法了。

我将开始着手于数字化我所拥有的教科书中的数学题。其中很多是非常优秀的教科书，但不容易被找到。

开放教育资源（OER）

以下是开放教育资源的三个定义。

(一) 通过信息和通信技术实现的教育资源，供用户群体为非商业目的咨询、使用和采纳。 (二) 免费和公开提供的数字化材料，供教育工作者、学生和自学者以教学、学习和研究为目的利用和再利用。 (三) 属于公共领域的资源，或根据允许他人自由使用或再利用的知识产权许可证发布的资源。

一门课程、一本完整的书都可以被视作一个开放教育资源，它也可以是一个更细小的部分，如一个学习对象。

我现在正在处理维基平台的一些技术细节（尤其是如何组织内容，以便能够更快找到想要的数学题），但很快我就会将数学题添加上去。

感谢Sophie Hnin建立了MediaWiki以及MathJax扩展。

若你想和我一同努力（添加题目，或解决它们），请随时与我邮件联系：ascklee@gmail.com。

谢谢你。

Chu Keong

参考文献： Bover, C.B. (1946). The First Calculus Textbooks. The Mathematics Teacher, 39(4), 159-167.

与我一起做”批判性探究”项目的三位学生负责启动“数字化数学题库”的工作，他们是边秋宇、陈晓枫、张粟毓。

这个项目的完成，离不开大家的努力。

Project Team Members

Bian Qiuyu

Bian Qiuyu is currently a student of the Master of Science (Knowledge Management) programme at the Nanyang Technological University in Singapore. I was a former undergraduate in Creative Media at the Faculty of Communication, University of Macau. I see myself as a relentless idea person, and I’m always looking for a new inspiration. I enjoy recording the flow of time or capturing the freeze frame moments in life with my camera, since video production and photography allow me to bring my understanding of life into reality and show it through my work. I am one of the team members involved in the improvement of "The Mathematics Digital Library" project at NTU. This project was a brave attempt for me. It is also a hands-on opportunity for us to learn about the diversity and richness of knowledge management. I hope that this website will break the limitations of physical textbooks, regions, languages on learning mathematics, thus providing help to students who are interested in mathematics. If you have any ideas or suggestions, please contact me via byunchoowoo98123@gmail.com.

边秋宇，现为南洋理工大学理科硕士（知识管理）课程学生，曾就读于澳门大学传播系创意媒体专业。我视自己为一个随时都在寻找灵感的创想者。我热爱用相机记录下时间的流动或捕捉生活中的定格瞬间，因为在摄影和视频作品中，我能够表达出自己对生活的理解以及感受。 我是参与完善南大 "数学数字图书馆 "项目的团队成员之一。这个项目对我来说是一次勇敢的尝试，也是一次让我们了解到知识管理的多样性和丰富性的实践机会。希望这个网站能打破实体教材、地区、语言对数学学习的限制，从而为对数学感兴趣的同学提供帮助。 如果您有什么想法或建议，请通过byunchoowoo98123@gmail.com与我联系。

Chen Xiaofeng

Chen Xiaofeng is currently a student of the Master of Science (Knowledge Management) programme at the Nanyang Technological University in Singapore. I am graduated from e-business management and information system in HKBU-BNU United International College. I’m an enthusiast of new media and I hope to work in Internet industry such a fast-growing field so that I can be exposed to the new and changing things. Besides that, I enjoy music and movie in my free time to relax myself. Because of my major, I am quite interested about the process of connecting physical with virtual world including transferring offline information to online version. That is what we want to realize in this website. Instead of physical textbooks, we hope online mathematics questions can be shared among someone who needs it no matter wherever he or she is. For students who are get stuck in learning mathematics, it would be a place for you to practice what you have learnt and find solutions to abundant of questions. For teachers, the well-classified questions site would relieve some burden of colleting practices. Any suggestions and questions, please contact me at cassiee0127@gmail.com without hesitation.

陈晓枫目前就读于南洋理工大学知识管理专业，本科就读于北京师范大学－香港浸会大学联合国际学院的电子商务管理与信息系统专业。我是一名新媒体爱好者，有着对于互联网行业的热情，希望以后可以在这个快速发展的领域里持续地接触最新兴的技术并在其中贡献自己的一份力。除此之外，在闲暇时期，我非常享受音乐与其诠释世间万物的方式。 因为我的专业（电子商务），我对于将现实与虚拟世界紧密连接的过程很感兴趣，其中包括了将线下的信息转化成线上的形式，这正是我们在这个网站里所想实现的结果。我们希望能与所有有需求的人共享这个线上的数学题库。对于身陷数学学习的学生来说，这会是一个可以让你练习所学知识并提供了解题方法的线上数据库。而对于数学老师来说，这个拥有优秀分类的网站会减轻你收集数学题目过程中的负担。 如果有任何的建议和问题，随时可以通过邮件联系我。cassiee0127@gmail.com

Zhang Suyu

Zhang Suyu is currently a student of the Master of Science (Knowledge Management) programme at the Nanyang Technological University in Singapore. And I studied in Nanjing Agricultural University as an undergraduate student between 2016 and 2020, majoring in Tourism Management. I enjoy travelling, watching movies in my spare time, and sometimes I would listen to music to refresh my mind.

I have a strong interest in education industry. When I was an undergraduate student, I did a lot of research on education tourism with my partners. During that time I found technology really plays an important role in the education. And today because of the COVID -19 pandemic, we are involved with internet much more often than before. Therefore, we decided to carry out this project, to explore how to construct a platform of mathematics questions to bring convenience and efficiency to students, teachers as well as other mathematics leaners and researchers on their learning journey, with the help of internet technology. I think this is a very meaningful project which can indeed make a difference in the math education and help those people in need. Therefore, we really welcome everyone to join us and help us to review and enrich this website, to make a difference. Any suggestions and questions, please contact me at z13833957046@gmail.com without hesitation.

张粟毓，现就读于南洋理工大学知识管理专业。在2016年至2020年间，我在南京农业大学攻读了旅游管理专业的本科生。我喜欢在业余时间旅行，看电影，有时我会听音乐来放松。

我对教育行业有非常浓厚的兴趣。在我本科学习期间，我和我的伙伴们就做了一些关于教育旅游的研究。在此期间，我发现科技在教育领域中起着越来越重要的作用。如今，由于新冠病毒大流行，我们与互联网的接触比以前更加频繁。因此，我们决定尝试寻找利用科技来方便教育的途径，基于此，我们小组开展此项目，以探索如何构建一个数学练习题平台，以借助互联网技术为学生，教师以及其他数学学习者和研究人员在学习过程中带来便利和效率。我认为这是一个非常有意义的项目，能够对数学教育带来一定的帮助，特别对于那些有需要的人。因此，我们非常欢迎大家加入我们，并帮助我们检查和丰富此网站，以为教育做出一定的贡献。 如果您有任何建议和问题，请随时通过z13833957046@gmail.com与我联系。