Mathematics (includes Mathematics with Physics)

Cambridge is renowned for the excellence of its Mathematics graduates. Could you be one of them?

Demanding but rewarding
If you are fascinated by mathematics and relish solving difficult problems, Cambridge could be the right place for you. The Mathematical Tripos here is the most demanding undergraduate mathematics course available in Britain and correspondingly one of the most rewarding. It is also one of the largest – with an intake of about 250 students each year – and the oldest.

Our reputation as a leading international centre for mathematics dates back to the time of Sir Isaac Newton, probably the greatest mathematician and physicist of all time, who was Lucasian Professor from 1669 to 1696. Since then, mathematics in Cambridge – both research and teaching – has been enhanced by a string of brilliant mathematicians including five Nobel Prize winners and seven Fields Medallists (a Fields Medal is the mathematical equivalent of a Nobel Prize). Three centuries after Newton, Cambridge is still at the forefront of mathematical knowledge. Most of the Faculty members are leading authorities on their subjects.

Our Faculty is also closely linked with the Isaac Newton Institute in Cambridge. This research institute attracts specialists from all over the world to tackle the outstanding problems in the mathematical sciences. It was here that Andrew Wiles chose to announce his proof of Fermat’s Last Theorem.

The excitement of research at Cambridge is reflected in our teaching programme. We know that our students are among the best in the country so we provide a challenging course, aiming to ensure that they exploit the benefits of this cutting-edge environment.

We are not the only ones who value our students highly. A Mathematics degree, especially a Cambridge Mathematics degree, is versatile and very marketable. The demand for our mathematicians is high, not only in the academic world, but also in business, commerce and industry. Whether you think you might be one of the 45 per cent of our students who go on to take a higher degree, or whether you are looking for a career in the financial sector or in another field altogether, the knowledge, skills and expertise you’ll develop here will prove invaluable.

What are we looking for?
The most important requirement is a lively interest in mathematics so that you can take full advantage of all that Mathematics at Cambridge has to offer.

Although our course does not assume any knowledge of mathematics beyond the A level common core, we regard as essential an experience of mathematics equivalent to at least AS level Further Mathematics either at your school or through one of the distance learning programmes currently available.

Statistics or computing or even mechanics are not essential: you can start all these subjects from scratch when you get here. However, there is a large component of theoretical physics in the course, so you will find it helps to take mechanics modules at A level Mathematics. Physics A level is also useful.

More specific details of the entrance requirements and procedures are given in the Guide to Admissions in Mathematics fact sheet which you can obtain from our website of the Faculty of Mathematics.

From mathematical logic to black holes: a course that suits you
Two aspects of the Mathematical Tripos that our students appreciate greatly are its flexibility and the exceptionally wide range of subjects offered. An unusual feature is that the workload is not fixed. Each year you can choose the number of courses you study to suit your own work pattern. Some students like to take as many courses as they can; others like to take a smaller number and study them very thoroughly.

How you will be taught
During your first year ( Part IA), you will have 12 lectures each week and, normally, two supervisions. In the following years, the greater choice and flexibility means that the pattern of lectures and supervisions is more irregular, but the average load is roughly the same.

The Mathematical Tripos is a tough course but you will receive lots of support from members of staff, and the libraries and IT facilities are superb. Our other facilities are also excellent: the Faculty of Mathematics occupies the magnificent purpose-built Centre for Mathematical Sciences, a short walk or bike ride from the city centre.

Flexibility: a choice of course
Year 1 ( Part IA)
There are two options:

• Option (a) Pure and Applied Mathematics, for students intending to continue with Mathematics
• Option (b) Mathematics with Physics

Option (b) is intended for students with a strong interest in mathematics who may want to change to Physics after the first year. You can continue with Mathematics after taking Option (b), or change to Physics after taking Option (a), but this may involve extra work over the long vacation.

Year 2 (Part IB)
You choose from a range of courses, bearing in mind your probable third-year subjects.

Year 3 (Part II)
You choose from a very wide range of courses according to your personal interests. There are two types of course which are different in style:

• One type gives the opportunity to learn more about a subject without being held up by detailed proofs and derivations.
• The other type is more systematic and rigorous, and provides a basis for a further course in mathematics or theoretical physics, such as Part III.

Year 4 (Part III)
The optional fourth year, Part III of the Tripos, is famous throughout the mathematical world. This masters level course, leading to the Certificate of Advanced Study in Mathematics, serves as a preliminary to research in mathematics, theoretical physics, or astrophysics. Fourth-year Cambridge students are joined by a similar number of students from many countries worldwide.

Changing Tripos
About 10 per cent of students change from Mathematics each year. Many of these take the Mathematics with Physics options in their first year, with the intention of changing to Physics. Over the years, mathematicians have changed successfully to nearly every other subject taught at Cambridge. However, it is inadvisable to apply for Mathematics intending to transfer to a subject other than Physics.

Examinations
All the undergraduate courses, except for the second- and third-year computing projects are assessed by three-hour written examinations. Continuous assessment of your work is provided by your supervisors, but does not count towards your degree.

Course outline

Part I Flexibility: a choice of subjects In the first two years you concentrate on the basic tools you need to study mathematics at deeper levels, with a roughly equal blend of pure and applied mathematics. Part IA Year 1 The options introduce you to the fundamentals of higher mathematics. These include, for example: Pure Mathematics: algebraic systems (such as groups) and rigorous analysis Applied Mathematics: mathematical methods such as vector calculus, and Newtonian dynamics and Special Relativity Those taking Mathematics with Physics will also cover, for example, kinetic theory; fourier analysis; and electromagnetism. Part IB Year 2 The topics become broader and deeper, and are classified as pure, applied or applicable, although there are strong links between the different areas. For example: The pure side is divided into Algebra and Analysis. Algebra here does not mean tedious manipulation of letters of the alphabet (though facility with this sort of algebra is important). It is the study of systems of objects such as groups which obey certain rules. These rules describe the symmetries which underlie most areas of mathematics and physics. In Analysis, the foundations of calculus are examined, including the beautiful theory of functions of a complex variable (calculus on the Argand plane). The applied side consists of Mathematical Methods and Theoretical Physics. The aim of the Methods courses is to set out techniques for solving a range of problems without too much emphasis on rigorous justification. The Theoretical Physics courses introduce you to the pillars of modern physics: electromagnetism, relativity and quantum mechanics. There is also a course on Fluid Dynamics, which is studied not just for its physical importance but also its mathematic elegance. Applicable mathematics involves Statistics and Optimisation (choosing the best route through a network, for example). The basic ideas of data analysis are introduced, and there is a course in Optimisation, which, because of its neat mathematical treatment of familiar problems, is one of the most popular subjects. There is an optional Computational Projects course, in which computers are used as tools for solving mathematical problems. Part II Year 3 The third year gives you the opportunity to explore your mathematical interests in detail, and use the skills you’ve acquired. There is a very wide choice including topics such as: Coding and Cryptography, Logic and Set Theory, Algebraic Topology, Number Theory, Cosmology, Principles of Quantum Mechanics, Stochastic Financial Models, Waves. There is an optional Computational Projects course. Part III Year 4 Students who decide to stay for the fourth year (Part III) have over 80 courses to choose from, covering all areas of mathematics and theoretical physics and are encouraged (but not required) to complete a mathematical essay or project chosen from a similarly broad range of topics.