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Sun, 16 Dec 2007

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The Calculus Trap

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Has the IISER Mathematics syllabus fallen into the "Calculus Trap"

Some remarks in favour of Calculus.

  1. One should not really think of mathematics as being made of parts. Asking for only this or that part of mathematics is like seeing a cake and saying "I want only the icing!".
  2. There are reasons that Calculus has dominated the UG syllabus across the globe and some of these reasons remain true. Primarily it is something which is used in almost all other calculations in mathematics which are not "elementary".
  3. One doesn't want "shallow learning". Since UG courses start with calculus one wants to explore it to some depth before moving on to some other topic.

Having said that, I should say that I personally would like to see UGs introduced to other exciting things like Number Theory, Geometry and Topology. In the syllabus discussions at Mohali we varied a bit from the Pune/Kolkata syllabus. In essence (details are available from the Mohali web site), the core courses are:

1. Group theory and linear algebra.
2. Analysis of one variable.
3. Curves and surfaces in space. (Introductory diff. geom.)
4. Probability and statistics.

The requisite amount of calculus is actually done in the Physics courses in Mohali and course (3) above. This is still very calculus-oriented --- one wants to use gentle acceleration!

I should point out that (Professor I.B.S.) Passi taught an excellent course on (1) last term. In spite of that a number of students asked "What use is group theory in real life?" There would be even more questions of this kind with things like Combinatorics and Mathematical Logic.

I am glad that these questions are being asked. To a student who asks them I can only reply as follows:

Beyond school (at least) one should not wait to be taught --- one must learn to learn on one's own. There is a faculty and there is a library and there is internet. Use these well and you can learn much more than what is written in your syllabus! Later you can use your learning to try and get the syllabus changed. Based on first-hand experience I can tell you that it is possible.


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