Ng Tze Beng ,  Associate Professor

Mypic.jpg (64576 bytes)    Education

  Current interests


    1.  Calculus Reform Project.    

Courseware for the laboratory sessions, developed and tested.   Feedbacks are very favourable and positive.    The materials have been very carefully selected and refined.  Still as yet to proceed are the interactive multimedia courseware for the lab sessions, namely 8 modules in all, one for each lab session.

Building of the hyperlearning labs for the department. This is part of the Calculus and Linear Algebra reform project.

The Hyper Learning Labs.

The new labs are now fully functional. With its up to date equipment, the department can now boast of a first class teaching computer labs. We are proud of the fact that we finally have two purpose built hyperlearning labs functioning. Our two modules MA1102 Calculus and MA1101 Linear Algebra are now using the labs to the fullest. The department now have the means to mount more lab based courses. This is a very significant acquisition of the department. It would allow us to plan for, besides basic courses like Calculus and Linear Algebra, applicable mathematics courses where simulation and or modeling or scenario analysis is required, to engineering students, business schools students and science students. Lab sessions could be sessions where real life problems could be modeled and or simulated and real life solution found. This is a very important development in our effort to upgrade and improve the standard of our students. At least two more modules are now using the labs. We hope the labs will be the focus where ideas are tested out and simulated before implementation. We hope to train the students to take more of an active role in this kind of activity, making use of their knowledge to create and innovate and solve real life problem. MA1102 Calculus is now a very rich course with many components built in, the lectures supplemented by lab sessions and web materials in the form of demonstration, more examples, self test kit and quizzes, links to NUSCAST lectures and other interesting calculus web sites. We hope to add more interactive materials assessable over the web.

3.   A formula of Euler -- An application of the use of freshmen calculus -- a powerpoint  experience.

    A simple application of the calculus to the proof of the limits of the infinite series---

     A Formula of Euler and Appreciating Calculus

4.  My Book --

1.      mybook.jpg (171654 bytes)

Ng, T.B, Calculus, An introduction,  Springer Verlag Singapore, !997 (Revised Second Printing)

Available on order to NUS Coop email:

mailing address:  Kent Ridge Post Office PO Box 1011 Singapore 911101

2.       Real Numbers?      ---- Available for download -------

5.  My Calculus web site


            Here you can access materials to introductory calculus, do assignment, seek guides and comments to the tutorial assignment, answer to questions you want to know about intermediate value theorem, extreme value theorem, mean value theorem, etc,  links to other calculus web sites, etc.

My  Dreams

How do we communicate mathematics, more precisely, how do we convey beauty in mathematics across to students of mathematics in general? I shall be undertaking a project on Mathematics in Art, Science and Technology. Below I try to explain why I begin this project.

I feel very strongly that we should try to present mathematics at the elementary levels as the mathematicians see it at the highest levels. Much too often in any undergraduate mathematics classrooms, the professor kept the aesthetic side of mathematics away from us just as we would keep secrets away from the kids. Particularly so is calculus taught this way. Generation of mathematicians has reduced the intellectual content of calculus to insignificance on the assumption that the depth and subtleties of the subject cannot be communicated. Mathematicians make mathematics and do not like to communicate and those who attempt to communicate face such adverse criticism from their ranks as G.H. Hardy foretold on page 61of his book A Mathematicianís Apology " Ö, there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds." Even Hardy has to call his book an apology for writing about mathematics. Our profession must explain more often what it is that we do. It may be that on a modest count mathematicians publish 25,000 research papers per year but no one outside of the community of research mathematicians has seen them or even heard of them. But on the rare occasion when they do as in the more recent case of Fermatís Last Theorem, few would understand what the fuss is about. In the present age of super fast computers, the need to explain and to communicate mathematics become even more urgent and compelling less those unexplained mathematics will lurk unsuspectingly behind every computer and any machine that are making decisions which we cannot comprehend and on which lies heavily the burden of the uncertainty of the correctness of the decisions.

My Concern

I would like to instill an awareness of scholarship in mathematics among our students and a tradition of scholarly pursues in creating mathematics. I have a dream of seeing our students discussing among themselves problems of mathematics, be them in mathematics or in applications in science, technology or the arts and a vibrant post graduate community who will come from among their ranks.

List of publications

Department of Mathematics
National University of Singapore
Block S17
10, Lower Kent Ridge Road
Singapore 119076


(65)  6516-2755 work_phone (office)


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Lst Modified Monday, 13 April 2015