Oxford University, Cambridge University and the Imperial College of Science, Technology and Medicine, London, are in close geographical proximity to each other. Yet, each one of them teaches different things in mathematics at the undergraduate level. Also, the emphasis on topics and themes varies from year to year. This allows a great flowering of ideas and activities. Similarly, the Massachusetts Institute of Technology and Harvard University are in close proximity to each other and yet again the emphasis on what they teach and how they teach undergraduate mathematics differs in content, emphasis and flavour. This makes one wonder why the UGC has chosen to micromanage the design of the mathematics undergraduate curriculum? The UGC would perhaps be better served if it stepped back a little instead of its often well-intentioned but ill-conceived attempts to help bolster academic standards through a sort of prescriptive micromanagement.
It seems that the UGC is prescribing a common syllabus for the study of undergraduate level mathematics for the entire nation. This has been necessitated by the fact that so many of our universities have abysmally low standards. However, this way of tackling the problem has the grave danger of proving to be counterproductive. All undergraduate institutions would end up teaching the same things in the same manner. One of the first casualties of such a move shall be the destruction of local urges and aspirations to teach topics and themes that could be different. The same institution may also want to teach different things to different batches. Such diversity helps build intellectual and academic enthusiasm, vigour and energy.
When the world is making advances in various realms of technology, science, medicine and other disciplines through the uses and applications of mathematics, the UGC seems to be taking a retrograde step by introducing misleading and even dubious mathematics in the name of topics such as Vedic Mathematics. Of course, some very profound mathematics was discovered in India since Vedic times, but the same discoveries have happened in other cultures, albeit a bit later. These are beautiful developments but not of much use from the perspective of giving any new insights or better ideas since so much that is new, and profound has been developed in the last 200 years in mathematics. Just look at Galois Theory, Algebraic Geometry, Functional Analysis, Function Theory and so on. The list is endless.
The UGC should really be wondering why our universities have failed woefully to use mathematically reliant subjects like neural networks, big data and such to develop even rudimentary AI platforms or why we could not use mathematics to develop something like the Google search engine.