Just got time for a quickie this morning before I head up to the Big Smoke for the first meeting of the Astronomy Grants Panel of the Science and Technology Facilities Council (STFC). I had thought that the last round would be my last, but I must have misbehaved somehow and my sentence has been extended accordingly.

Anyway, I thought I’d follow up Saturday’s post with a response to a question that a few prospective Physics students asked me during our Admissions Day. Those attending these days have already applied to this University but, at this stage of the annual undergraduate admissions cycle, the applicants are still deciding which University to put as their first or firm choice. I see our job in the Admissions Days simply to make available as much information as possible to the applicants to help them make a choice. Quite a few people I spoke to on Saturday, however, said that they had already made up their minds and just wanted some advice about what to do during the summer after they have finished their A-levels to help them prepare for their undergraduate studies in Physics (and/or Astronomy).

The answer I gave was pretty simple: *practice your mathematics, especially your calculus! *

The justification for exhortation is that the big difference between Physics at A-level and Physics at undergraduate University level is that the latter is taught in a much more mathematical way than the former. This is because the physical laws that underpin our understanding of the natural world are expressed in a mathematical language; the more fluent you are in this language the easier you will find it to assimilate the physical concepts. To put it another way, you will find it difficult to understand the physical meaning of what is being taught if you are struggling with the mathematical meaning of the symbols being used or the manipulations needed to obtain useful solutions to the relevant equations.

Newton’s Second Law, for example, relates the rate of change of momentum of a body to the force exerted upon it. If you’re comfortable with calculus you don’t think twice about writing d(mv)/dt for the rate of change of momentum and then constructing a differential equation which you can (hopefully) solve. You won’t absorb the importance of laws like this unless you become so familiar with the mathematics that it ceases to occupy the part of your mind that’s needed to really think.

I think that learning to do Physics is a bit like learning to play a musical instrument. Practicing such basic mathematical procedures as integration and differentiation is analogous to the five-finger exercises you have to do when learning to play the piano. The more you practice them, the greater the extent to which they become hard-wired. Your brain can therefore concentrate on the more interesting conceptual stuff – that’s really the hard part of learning Physics. We do of course do as much as we can to help with this once you’ve got to University, but doing some preparation on your own beforehand would greatly smooth the transition.

So I’d tell any prospective physics student wondering what to do this summer to get hold of as many basic calculus exercises as they can and do them whenever they get the chance. It may not be the most exciting way to spend your post A-level holiday, but it is the single thing you can do that will best prepare you for life as a Physics student.

On the other hand, the advice I’d give to physicists rather later in their careers is to think very carefully before agreeing to be on committees or panels…

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