Some remarks on what can be done about mathematics courses for IISER in the year 2006.

The IISER syllabus was designed in an ambitious way with the idea that some of the designers would come forward to teach it.

At the time this was designed we also said that the syllabus should be approved of by the people who are actually going to teach the courses. It was assumed that motivated, enthusiastic and capable young people would be hired to do this.

Due to the limited time frame in which IISER has been started this year, neither (1) or (2) has been attained. It should therefore be acceptable to us all if a more "standard" course were taught at IISER until such time as (1) or (2) becomes possible.

Specifically, I would suggest that the first course with the somewhat "grandiose" title "Infinitesimal symmetry" should basically be a course on Matrices, Vectors and one variable calculus. The only departure I would make from tradition is that one variable calculus need not be limited to functions from R to R but could be from R to R^2 or R to R^3. This would allow us to introduce vector fields and describe the relation between calculus and Matrices/Vectors better.

I do not think that the plan as outlined above diverges very radically from what was originally proposed.