Mathematics in Corpus

This photograph was taken (by David Williams, who designed the Corpus picture tour) during an actual tutorial. The tutor is Andrew Fowler, and the student is Richard Hall, who subsequently did the M. Sc. in Mathematical Modelling and Scientific Computation at Oxford, and then a doctorate with Chris Gilligan in the Department of Plant Sciences in Cambridge. Following that, he took up a postdoctoral research position in California.

Teaching

Tutors:	Dr Andrew Fowler Prof Colin McDiarmid
Lecturers:	Dr Florence Tsou Mr Karel Hruda (Computation)

Mathematics at Corpus is principally taught by Andrew Fowler and Colin McDiarmid, assisted primarily by Florence Tsou. Karel Hruda teaches Computer Science. Andrew Fowler is an applied mathematician, whose research interests mainly lie in various environmental applied sciences, for example, geophysics and glaciology. Colin McDiarmid's research is in a wide range of discrete mathematics, with applications in operational research and theoretical computer science. Florence Tsou is a mathematical physicist, whose research interests lie in the realm of geometry and relativity. She is currently writing a book with Roger Penrose. Karel Hruda is a graduate student in the Computing Laboratory, whose thesis is on parallel implementation of a functional language.

Admissions

We normally take six undergraduates a year. This often includes one or two in the joint schools (with Philosophy or Computer Science or Statistics). We welcome applicants for the three- and the four-year Mathematics courses. (If you are unsure about which is for you, it is best to apply initially for the four-year course.) We are happy to consider candidates for deferred entry.

All colleges like you to apply to them, because all colleges want the best range of applicants to choose from. But in reality, there is little to separate colleges in terms of how it will affect you academically, although tutors will obviously have different styles and attitudes. There is no particular advantage to be gained in applying to a larger college on the basis that there is a greater chance of getting in. This is partly because the larger colleges attract more applicants, so that the applicant/student ratio is broadly similar, and also because at entrance, the information on all candidates is available to all colleges through a database. The best way to choose a college is to come and visit on an open day.

Most Mathematics applicants take double Maths A-levels, but this is by no means obligatory. Indeed, the differing background of applicants is something we weigh up carefully. Other A-levels taken by recent successful applicants have ranged from Physics and Chemistry to English, Music and German. The main qualities we seek are commitment to mathematics and the potential to flourish.

Interviews

Applicants often get nervous about interviews, understandably. But you should think of them in a positive way. We are not trying to trick you, or catch you out, we are trying to ascertain your ability and, particularly, your potential. It is as important for you as it is for us that we make the best assessment of this. For us, because we want to admit the best students; for you, because if you are not up to the demands of the course (and it is intense), then far better that we find out at interview, rather than finding out later.

The interview is important, but it is not everything. In Corpus, you will have two separate interviews. You will have at least one other interview at another college; you may even have a third interview with us. You shouldn't leap to conclusions about your interviews. In my experience, students usually think they have done less well than they have. Why? Because of the nature of the interview. As an example, if you do very well, then the interview may have served its purpose after fifteen minutes. But if you do very badly, the same may be true. A question I sometimes ask in interview is this: can you prove that the square root of two is irrational? As with all such questions, this is some way off any A level syllabus, and it is unusual. But sometimes students have seen this, either in casual reading or through interview preparation. And if they answer correctly, they will feel good; and if not, they will feel bad. But the important point is not whether you know the answer, it is whether you can think about the problem. And if you have seen it, then what about the square root of three? Or five? Or any number? Or the m-th root of n? Or roots of any polynomial with rational coefficients? Many interview questions have a structure like this, they start somewhere and then work their way up.

Before you come up

Sometimes, for example at open days, people ask what the best preparation is for starting their degree course; or, what is the best combination of A level modules to choose. Is mechanics or statistics a useful preparation? What about other A levels; do I need Physics, for example?

The answer to this may be somewhat surprising. What is essential in preparing for a mathematics degree is to be competent in basic technical mathematics, and we are inclined to be less interested in the more exotic things you may have done. Thus, the best preparation is to know thoroughly the six modules of A level pure mathematics. Differentiation and integration need to be second nature, and you need to know about things like hyperbolic functions, because the course does not spend time catching up on these.

So why are mechanics and statistics not so necessary? Well, for example, in the first term here you do Newtonian orbital mechanics: predict the motion of planets round the sun. And to do this, you write down Newton's second law (F = ma) in the form of a vector differential equation. And then you solve this equation to produce Kepler's ellipses, and so on. The point is, the technique of mechanics lies in understanding differential equations.

Similarly, statistics is heavily based on probability theory; and much of the probability you do involves advanced calculus (for example, how do you solve Buffon's needle problem?). So it is maybe nice to see these applications of mathematics early, but when you do them, dare I say, properly, then you will need all the technical machinery of calculus and differential equations.

The same applies to an A level like Physics. A long time ago, I was coerced to do Physics at A level, rather than the French I wanted to, on the basis that it would be more useful in my application to Oxford. I don't believe that it was. One of the things I didn't like in the subject was electricity and magnetism. The magnetic field B was measured in flux lines per unit area. Where were these flux lines? The poor teacher was flustered. It's not surprising. You do electromagnetism properly when you study Maxwell's (partial differential) equations, and this happens in a third year course at Oxford.

Mathematics at Oxford

One of the things you will find on starting Maths at University is that there is a change in style and emphasis from what (I suppose) you do at school. Firstly, school students usually equate applied mathematics with mechanics and statistics, and while these subjects indeed form part of the degree course (and are indeed applied), in a sense they are not central to the concept of applied mathematics. Rather, what you find is that pure mathematics at University introduces new and more abstract ideas in courses on algebra and analysis; you encounter the importance of proof, even of apparently obvious statements. And then, a subject like differential equations becomes more applied, essentially because the problems of mechanics are framed in their terms. (Indeed, the study of many parts of mathematics was first couched in terms of applications to physical problems.)

For example, the small amplitude motion of a simple pendulum or of a linear spring is described by the equation of simple harmonic motion, y'' + y = 0, whose solutions are the trigonometric functions. Of course, one thinks of sin and cos as geometric ratios, but equally they can be defined as solutions of the differential equation. And this way of looking at these functions generalises naturally in applications which you can study at Oxford. As an example, the differential equations which describe the ripples which spread when you throw a stone into a pond have solutions which can be written in terms of solutions of the differential equation y'' + y/x + y = 0, and these functions are called Bessel functions.

The Oxford syllabus

In the first year you do Moderations, which culminates in a series of four exams at the end of Trinity (summer) Term. There is no choice available, the aim being to give you a broad grounding in the basics of the subject. The subjects you study are grouped under the general headings of algebra, analysis, physical applied mathematics, non-physical applied mathematics and mathematical methods and models.

In the second and third year you start to specialise. At this point students have usually developed some preferences, and their mathematical style is beginning to emerge; so you become an analyst, or an algebraist, or a probabilist, or whatever. Tutorials on your courses occur each week; you will normally have one pure and one applied tutorial in your first year, and thereafter the frequency is at about the same level, but is driven by course choice.

Mathematics and Philosophy

Typical applicants have a mixture of A levels, often double Maths with at least one Arts subject, and they are committed to mathematics but are interested in philosophy (and often other arts subjects as well), and want to retain some balance. You need to be particularly good at both subjects to do this. The other comment worth making is that inevitably, you will not gain the perspective on mathematics that the straight mathematicians do. You cannot in fact do most of the applied subjects, and the mathematics you do will be quite analytical, similar in style to the more formal parts of philosophy (such as logic).

Mathematics and Computer Science

Some of the same comments apply to applicants in MCS as in Maths and Philosophy, although the subjects are perhaps less far apart.

Mathematics and Statistics

This is a more recent course, so there is little of experience to say at this point. Because Statistics is so closely aligned with Mathematics, it is plausible that this joint degree will stretch (literally) the student less than the other two joint degrees. The first year of this course is the same as the mathematics course.

Three year or four year?

There is some spin on the distinction between the two courses, but basically (as is obvious) the four year course enables you to go further. There is also some spin on who does which, but also (again obviously) one expects the more mathematically capable students (as indicated by Mods results) to be the more natural four year students, and that those who are more interested in a general education to opt for the three year course. For some parts of the subject, the fourth year is akin to a first graduate year (or an M. Sc.), and the ratio of 3 to 4 years students is about 2 to 1. So the three year course is the norm, but unless you are very firm in your intentions, it is better to apply for the four year course from the point of view of funding, just in case.

A complication arises for students of physical applied mathematics, where there is a long standing and successful M. Sc. course in Mathematical Modelling and Scientific Computation, whose purpose is, in effect, to supply a fourth year in applied mathematical subjects. Applied students wishing to do a fourth year can do it this way, although the undergraduate syllabus also caters for applied mathematicians in its fourth year.

Beyond the degree

Many students stay on to do a postgraduate year on one of several M. Sc. courses. Some stay on to do research towards the D. Phil. Many leave for jobs, often these days in finance, for example in banking, accountancy, or as an actuary. Mathematicians are fairly employable, and it is certainly a good subject from that point of view.

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