loop quantum gravity said:
i want to know, is the restriction on choosing nine lecture courses obligatory?
i mean if you want to take more than the nine, is it possible, or very unlikely
You can offer a maximum of nineteen units (which roughly translates to six "major" courses, not nine) for examination. While a lot of people go to more courses than that just to obtain a flavour of some areas which may be outside their primary area of interest, it's really not in your interest to spend too much time outside of your main courses. If you want to obtain a distinction in the tripos, concentrate on six subjects and do as well as you can in them.
For what it's worth, I think Part III is *way* overrated. The structure of the course, and the peculiarities of the lecturing system at Cambridge in particular, are heavily weighted in favour of people who have already been at Cambridge as undergrads. More particularly, you will be expected to memorise vast amounts of material if you are to be successful in the tripos examinations, an approach which puts many of the outsiders to significant disadvantage. I did it because I was already here as an undergrad and wanted to do a postgrad here also, but if I'm honest, I don't see Part III as being of terribly great value, especially to outsiders. You won't actually learn a great deal about physics; you'll learn how to memorise things.
My advice to people who want to come to do Part III is this: acknowledge that the odds are stacked against you and ask yourself why you really want to do the course. If you're interested in graduate study, identify the area in which you are interested and find out which institutions are leaders in that field, and then apply to those places. *Do not* come to Cambridge simply because you want to see what it's like, or because Hawking is here (he'll be retiring in eighteen months to two years anyway, but I digress). Finally, if you don't have excellent results from your undergrad degree, there's probably a large chance that you won't be successful during the tripos exams: they're significantly more difficult than anything you will have seen before.