The Oxbridge Interview Book: Perplexing Problems in Maths, Physics and Engineering, with Solutions

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9781780746029: The Oxbridge Interview Book: Perplexing Problems in Maths, Physics and Engineering, with Solutions
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In The Oxbridge Interview Book, Thomas Povey shares 109 of his favourite problems in the mathematical sciences, guiding us through the wonderful, fascinating and quirky questions that have become synonymous with the Oxbridge interview.

Whether you are an aspiring scientist or an old-hand, you can now pit yourself against these uncompromisingly challenging problems, developed in time honoured tradition to test an interviewee’s ability to think. Detailed answers are provided, with a refreshing blend of scientific history, application and personal anecdote.

In this delightful and idiosyncratic romp through pre-university maths and physics, the author shows us that behind every single one of these questions lies a new way of thinking about subjects we felt we had understood. He argues that engaging with the unfamiliar is key to forming deeper insights and developing intellectual independence. The Oxbridge Interview Book is a manifesto that science should be playful, and that we should celebrate the curious.

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About the Author:

Thomas Povey studied Physics at St Catherine’s College, Oxford, and went on to complete a Doctor Philosophy in the Turbomachinery Group; he was subsequently appointed as the Rolls Royce Industrial Fellow before taking up his current post as Tutorial Fellow at University College in 2004. He lives in Oxford, U.K.

Excerpt. Reprinted by permission. All rights reserved.:


A short introduction:

I love Oxbridge interview questions. I always have. I'm not talking about the ones you read in the newspapers every year though. They are made up to sell stories. snippets from bruised candidates, mangled then garnished, and served up as a supposed expose of off-the-wall questions dons like to humiliate hapless students with. They are, I am afraid, a fiction. Designed to appeal to those who prefer sensation to reality. If you are looking only for entertainment, I suspect this book is not for you. but that is not to say this book is without entertainment, because it is true that the real Oxbridge interview questions do tend to be somewhat quirky. they are also - almost always - difficult. But they are never flippancies. They may sometimes sound ridiculous, but the purpose is always series. They are designed with only one object in mind - to distinguish from the many brilliant candidates we see each year those with the very greatest potential.

Some schools prepare their students for Oxbridge interviews. That is to say, they give their students extra classes, and even mock interviews. To do this, it is necessary for these schools to collect Oxbridge interview questions. The questions are put into files, and those files are pulled out around October every year, in the period leading up to the admissions process, to give the students some practice before they go up to interview. When the students return in December, they are debriefed, and the files are replenished with the latest crop of questions. It would be hard to say that there was anything sinister or wrong about this, but it is certainly the case that only some schools offer specialised help of this kind.

There are many schools which rarely send students to Oxbridge, and for quite a few of them our interview process is somewhat opaque. I know this because almost every time I meet a teacher or a headteacher, the moment they find out I am involved in admissions, they say "So what sort of questions do you ask at interview?" For applicants, and by extension the worried parents of applicants, it often feels as though our process must - from the outside - be entirely opaque. It is very common to meet applicants at open days who ask questions like, "Given that I go to a school that doesn't send many students to Oxbridge, should I apply and do I have any chance of getting in?" This happens to be a very easy question to answer. I explain that there are two very simple tests. One - are you likely to meet the standard offer in your chosen subject? Two - do you have a genuine passion for the subject? If the answer to both questions is unreservedly yes, then I can advise the candidate that if they apply their chance of getting in will be better than average, and if they don't apply, their chance of getting in will be exactly zero. "And what sort of thing do you ask at interview?" is invariably the follow up question.

I happened to go to a comprehensive school. It was a very good school, though at that time not very used to sending students to Oxbridge. Certainly the impression was not given that students should be prepared. for the interview. It might have been felt that the few students applying to Oxbridge were going to get into a good university anyway, and that limited resource might better be focussed on the students who needed more help. It is an argument with two sides. Whatever the reason, the three of us who applied that year (two to Cambridge, one to Oxford) really had very little idea what to expect. We took it seriously, and brushed up on our respective subjects, but we didn't have much concept of the type of questions that would be asked. In retrospect it would have been helpful to have more of an idea.

So one of the aims in putting this book together was to answer that most frequently asked question - what kind of questions are asked at interview? In here there are well over a hundred problems with solutions, the vast majority of which have been asked in interviews. I hope it will take some of the mystery out of the process, and give some insight to all those students, parents and teachers who, over the years, have told me that our admissions process still lacks transparency, and that they would value more guidance on what to expect. It is a collection of just some of my favourite problems, quite arbitrarily biased towards the area of maths, physics and engineering that I most enjoy. I invented most of the questions myself, but others are well-known, and a few were suggested by colleagues (from both Oxford and Cambridge) with an interest in this book. It is hard to be entirely original with interview questions, however. Even the ones I am most proud of will no doubt have been asked in numerous other forms over the years.

But the democratization of information about interview questions was not my sole aim. I also wanted, quite simply, to share the pleasure I have taken in som eof the maths and physics puzzles I have most enjoyed. It might seem impossibly nerdy, but (almost) nothing is as fun as being baffled by an apparently simple problem in an area of classical physics that I thought I understood. I hope these questions will appeal to those exceptionally-able high-school students who have mastered the basics, and feel they have room to play a little with some more unusual puzzles. It might also be of use to the teacher who wants to stretch the more able members of their class with something slightly off-beat. Here I am grateful to those teachers who allowed these problems to be piloted in their classes, and to the students who bravely attempted them. I learnt a lot from these questions, and had a lot of fun.

There was one problem I was unable to solve. It is that, in a real interview, questions are not asked and answered cold. They are discussed,/I. as part of a tutorial-style conversation, with the tutors helping the candidate along, providing hints, correcting mistakes, encouraging when things are gonig well, and so on. There is no real substitute for this kind of help when reading a book alone. A question which might seem impenetrable, can suddenly yield when a tutor provides just the right hint. And most tutors are expert at providing th rifht hint at the perfect moment to keep the problem and the conversation flowing. I would encourage you to try the problems with friends, or with subject tutors, or anyone with an interest and sound knowledge of maths and physics.

I should say a few words about the level of the problems. I can tell you that every single one of them is difficult in some way. I was asked by the publisher to use stars to indicate the relative difficulty of problems. Although I think this is quite subjective, I had to concede that it would be a shame for someone to happen to try all the most difficult problems first and feel defeated, so I have indicated how hard I found the problems the first time I tried them. If you think I have rated some of them too generously, it simply means your intuition is better than mine in that particular area. In general, those questions with one or two stars should yield to a student who is fully on top of the first year A-level (International Baccalaureate, Scottish Highers, SAT etc.) pre-university syllabus in maths and physics. Questions with three stars would generally require more substantial hints, and are in some cases only suitable as discussion problems.

I have also included a small handful of exceptionally hard four star questions, which are probably too long for most interview situations but give an opportunity to those exceptionally confident students who want a real challenge.

This book has been what I call my Saturday-project, and there are, I increasingly discover, always fewer Saturdays than I hope there will be. I have not had the luxury of someone to work with, so there will certainly be mistakes, and also errors of logic. They are all my fault. But I hope there are few enough that this book brings more enlightenment than confusion. The most challenging aspect of putting it together was striking the right balance with the level of questions - the fact is that real interview questions range from being quite straightforward to really quite hard. Here I am indebted to the many teachers, students and colleagues who were kind enough to provided detailed comments on the level of the questions. I would be delighted to receive further constructive notes and any genuinely unusual questions which could improve a future edition, and thank in advance anyone willing to provide this feedback.

There is a sensitivity that I should probably not duck. One rather unique thing about Oxbridge is its ability to attract strong views. Almost no matter what one does, when the word Oxbridge crops up, there will be those who take it upon themselves to argue that one school sector has been favoured over another, or that one type of student has been advantaged more or less. Equally loud will be those who promote the opposing view. A good tonic for political pontification, and a practical means of solving the apparent paradoxes that are set up, is a good dose of statistics, plenty of which appear in this book.

T.P. Oxford 2014

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