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STEP Support Programme

Meet the mentors!

You may have noticed that we have some new mentors replying to your posts on the forum. This thread is so that the mentors can introduce themselves so you know which stage of their studies they are at and perhaps a little about their mathematical interests.

To get the ball rolling, I am one of the staff members for the STEP Support Project. I did do STEP but it was rather a long time ago now...
I chose my username in honour of Sophie Germain, a French mathematician who lived from 1776 to 1831, whose birthday I share!

I have many favourite areas of mathematics. Here's a problem I really like that you might want to explore: Given a positive whole number, how can you work out how many ways it can be written as the sum of consecutive positive whole numbers? And which numbers cannot be written in this way?

Continuing to roll the ball....

I am one of the other staff members for the STEP Support Programme, and I also did STEP but it has was an even longer time ago. I worked on the STEP Correspondence Course previously and before that spent quite some time teaching in various schools.

I choose my username as it belonged to the first known female mathematician.

Hello
I'm a first year undergraduate at Cambridge and I am still stressed out about STEP (even though I have done it and won't need to do it again...strange). I was lucky enough to get help from the pilot of this last year. I am GaussIndahouse. I mainly choose Gauss because his name rhymes with Indahouse but he's known as the "prince of mathematics" because he worked on everything from statistics (Gaussian distribution) to Electromagnetism which I guess is also pretty cool.

Heya! I'm a first year Cambz mathmo as well; the memories of STEP are still scarred into my brain! (That said... overall, it was an enjoyable experience, as it hopefully will be for all of you!). I've been 'helping out' on other web-based STEP forums/threads for an odd two years or so now. :-)

Anyways, a fun problem (do-able with elementary methods): does there exist a function $f: \mathbb{N} \to \mathbb{N}$ such that $\displaystyle f^{f(n)} (n) = n+1?$ (here $f^k$ is $f$ applied $k$ times).

It's been a while since I did anything like this, do you have any hints on how I could get started?

Sorry, did not see this till now. Assuming such a function exists, the first steps to any problem of this sort is trying to determine the image of $f$, looking at it's nature: is it surjective? is it injective? [If it wasn't you'd have an immediate contradiction], once you've looked at the image, you'll want to see whether $f(n) = 1$ or not [another immediate contradiction presents itself], then there's still a bit of work to do from here on out, but I'll leave that for the forum to mull over! :-)

Hi there! I'm a second year maths student, and I like pure maths.

I chose Mary Cartwright because she was fundamental in founding Chaos Theory, which I got interested in after a maths talk a few weeks ago.
I first came across her when I did a question about https://en.wikipedia.org/wiki/Proof_that_π_is_irrational#Cartwright.27s_proof. It's a really cool result, and it was the first time I'd been able to understand a proof of it (only A Level maths required).

Thanks for sharing, I did not know about Mary Cartwright or this proof!

Hi y'all!
I'm very much a pure mathematician. I actually ended up taking STEP twice; I failed all my university offers the first time, but luckily Cambridge were somewhat forgiving! It's hard, but with enough work, it's definitely achievable.
I chose Bowditch as one of the most notable Welsh mathematicians, aside from Robert Recorde; most of his work, you probably won't meet for a fair while, but he solved Conway's Angel problem.
Best of luck!

Thanks for sharing - I'm sure forumites will be pleased to know that even if things go wrong the first time round it's not the end of the world. And of course, you didn't have the advantage of this forum to help you...

I had a similar experience my first time around applications. I've never come across anybody else who did too - good to know it's not just me!

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)