- The following topics are missing.
- "Discrete" Mathematics / Non-numerical Computations.
The idea of the courses should be to maintain contact with different areas of mathematics. For example, if we do not teach students probability for two years then whatever they have learnt about it in school will be "lost". The same applies to other things like "permutations and combinations" and their connections with finite groups, graphs and (non-numeric) algorithms.
In school, all mathematics subjects are taught together. In college, the teaching is separated into "subjects". To some extent this is inevitable. However, we should try to avoid a situation where they feel "Algebra, Analysis, Geometry, Probability, ..." are separate subjects.
One counter-balance to (2) and (3) above is that we should not try to teach them too much!
Another counter-balance to (2), (3) and (4) above is that we should not be too shallow/superficial in what we teach.
Achieving the correct balance would be the trick!
I personally feel that the IIT-B syllabus (and indeed most IIT mathematics syllabi) have been too heavily loaded with Analysis and so go against the spirit of (2) and to some extent (3).