Mathematics Digital Library:About

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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:

  1. dictionaries (e.g., The Free Dictionary)
  2. encyclopedias (e.g., Wikipedia)
  3. maps (e.g., OpenStreetMap)
  4. 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.