Cambridge Math Prep (STEP)

[junoexpress]

Hi,

Cambridge University has a placement like exam called STEP (Sixth Term
Exam Papers), and while there is a website for Cambridge with videos
and practice problems, I am wondering if anyone can tell me the basic
texts one should have under his/her belt in order to be prepared for
the exams. (In other words, should you know analysis at the level of
baby Rudin, probability at the level of Casella and Berger, Mechanics
at the level of Goldstein, etc.)

TIA,
Matt

[Stephen Montgomery-Smith]

I took the equivalent exam about 30 years ago, so take my answer with
a pinch of salt.

I think all these books are far too advanced to prepare for this
exam. In fact, we covered Rudin type material in the first year at
Cambridge, and Goldstein in the second year. I don't know the book by
Casella and Berger, but it looks like a good book that I could learn
from, and probably stuff we covered in part in the first year.

I had a really hard time downloading STEP exams, but my guess from
some of the help material I did find is that the content will be
closer to Calc 1 and 2, part of Calc 3, and parts of 1st semester ODE,
that would be covered in a typical undergraduate American university.
Probability wouldn't be anything more than knowing a few basic
distributions (normal, Poisson, that sort of thing). Only the
difficulty of the questions will be much higher.

The way I prepared was by doing a bunch of past papers.

[jftsang]

Hi Matt,

I took STEP this summer. You might like to challenge yourself and take a
look at easier example sheets questions on the Cambridge website. It
seems that they use the same sort of questions in STEP.

In the way of content, you can find the syllabus here:

http://www.admissionstests.cambridgeassessment.org.uk/adt/digitalAssets/103035_Specification.pdf

As you can see, the pure maths section doesn't want anything outside the
further maths course (though you'll want to know some for the interview,
I guess). The mechanics and statistics questions might require you to
take modules like M4 or S3. The test is more about logical reasoning
than playing around with high-powered maths.

Dr Siklos offers a few resources:

http://www.damtp.cam.ac.uk/user/stcs/STEP.html

Just keep practising, do all the past paper questions, discuss with
teachers. Do practise your A-Level stuff too, because that develops
speed - you'll want to be able to solve a question in thirty minutes.

Good luck,
Jonathan Michael Foonlan Tsang