Girton College University of Cambridge

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Mathematics in Cambridge

Mathematics is one of the oldest subjects to be studied at Cambridge. Holders of the Lucasian Chair, perhaps the most prestigious professorship in mathematics, have included Isaac Newton, Paul Dirac, and Stephen Hawking. Today, the subject is as vibrant as ever, with exciting new developments in research and constant review of teaching methods.

Brief outline of the course

The normal undergraduate Mathematics course, leading to the B.A. degree, consists of three years of study, Part IA, IB and II.

Part IA is a broadly-based year, providing foundations in pure, applied and applicable mathematics. In the main of the two options, Pure and Applied Mathematics, there are courses, each consisting of 24 lectures, on Numbers and Sets, Groups, Vectors and Matrices, Analysis, Vector Calculus, Differential Equations, Dynamics and Relativity and Probability. The other option, which is taken by a relatively small number of students, is Mathematics with Physics; in this students take three-quarters of the mathematics lectures, but replace the courses on Numbers and Sets and Dynamics and Relativity with courses in the Natural Sciences Tripos. At the end of the first year, students studying this option have to decide whether to continue with Mathematics or move over to Natural Sciences.

In Part IB, there are further developments in Algebra, Analysis (real and complex), Geometry and Methods, and students are also introduced to Fluid Dynamics, Quantum Mechanics, Electromagnetism, Markov Chains, Numerical Analysis and Statistics. There are also short courses on Metric and Topological Spaces, Variational Principles and Optimization, and there are Computer Projects to be worked on during the year.

In what is usually the final undergraduate year, Part II, the courses are divided into two categories, C-courses which are intended to be straightforward and accessible, and D-courses which are more demanding, and it is possible to obtain more examination credit for D-courses than for C-courses. There are 10 C-courses and 26 D-courses and they cover a wide variety of topics in pure, applied and applicable (statistics etc) mathematics, ranging from Logic and Set Theory through General Relativity and Mathematical Biology to Stochastic Financial Models. There are also Computer Projects , as in Part IB.

In each year, examinations are held in late May or early June; in each case, there are four three-hour papers, usually taken on successive days. There is no programme of continuous assessment, but the marks from the Computer Projects in Part IB and II do count in the examinations. The results are announced in June.

After Part II, it is possible for students with a First, or with First Class potential, to take Part III of the Mathematical Tripos, which is an intensive year of preparation for research and leads to the degree of M.Maths. It can also be taken by students from other universities who are interested in doing research in mathematics, and in their case leads to the degree of Master of Advanced Study. There is a huge range of courses in pure, applied and applicable mathematics. The Faculty also runs an M.Phil course in Computational Biology.

For more details on the course, see the Faculty website.

Organisation of teaching

The Mathematics Faculty of the University and the Colleges share the teaching of mathematics. The Faculty organises the lectures, which are attended by students from all colleges, while the colleges are responsible for the organisation of supervisions or tutorials for their own students. The teaching terms last eight weeks in the Michaelmas and Lent terms, and four weeks in the Easter term (when lectures are followed by time for revision and then the examinations).

Typically, a student attends two lectures a day, six days a week (the Mathematics Faculty still has Saturday morning lectures!) and two supervisions a week. Each of these lasts an hour. In the first year, there are about 250 students in lectures, but by the third year, the number in each course is usually a lot smaller because of the large choice of courses. There are usually two students (and a supervisor!) in a supervision, and this provides the personal contact and individual attention which is not possible in a lecture. In a supervision, students ask questions about lectures and the supervisor will explain parts which are unclear, and perhaps initiate discussion about points of interest. The work for a supervision is usually based on example sheets given out by the lecturer every two weeks (the frequency of supervisions on a typical course). Students spend two or three days working on the sheet and hand it in before the supervision. The supervisor marks the work and then goes over it in the supervision, helping students with questions they cannot do and sometimes suggesting alternative methods for those completed.

The supervisions for Part IA and IB are done mainly by Girton Fellows and sometimes Girton research students. In the first year, they usually take place in the main college building where all first year students live. In Part II, there are so many courses that individual colleges cannot usually cover them all with their own personnel. Girton is in a group of eleven colleges which cooperate in the Part II teaching.

As well as having a number of supervisors, each student has a Director of Studies, who is responsible for the academic side of the student’s life. The Director of Studies will have been involved in Admissions, and will then have the role of guiding the student about which courses to take, arranging supervisions, writing references and dealing with many other work-related aspects of life at Girton. The Director of Studies is available much of the time to answer students' queries by email and to see them when necessary.

The Centre for Mathematical Sciences (CMS)

The Mathematics Faculty, which consists of two departments, Applied Mathematics and Theoretical Physics (DAMTP) and Pure Mathematics and Mathematical Statistics (DPMMS), is housed in an exciting new purpose-built complex of buildings in Clarkson Road, next to Wolfson Court, which is Girton’s second site. CMS consists of seven pavilions, containing seminar rooms and office space for the faculty members, and a central core, with a large cafeteria/common room and a number of lecture rooms. The Part II and Part III students attend lectures there, while the Parts IA and IB students have lectures in large rooms in the centre of town (the Cockcroft Lecture Theatre and the Mill Lane Lecture Rooms). CMS is also the site of the Isaac Newton Institute, a leading national research institute in mathematical sciences, and the new Moore Library for the Mathematical Sciences, which has the University’s main collection of books and journals in mathematics and related areas.

The Girton Mathematics Department

At present, there are two teaching fellows in Mathematics at Girton. Dr. Ross Lawther is a pure mathematician, who covers much of the supervision in pure mathematics in the first two years at Girton. He does research on finite groups. Dr. Ruth Williams is a Reader in Mathematical Physics at DAMTP and currently lectures on General Relativity. She supervises much of the applied mathematics in the first two years at Girton and also covers some of the Part II Theoretical Physics courses. She has written a semi-popular book, jointly with G.F.R. Ellis, on relativity, entitled “Flat and Curved Spacetimes”. She is also Director of Studies in Mathematics at Girton.

Our previous pure mathematics teaching fellow, Dr. Dennis Barden, although officially retired, is still very active in Girton mathematics, supervising and running ‘surgeries’ for first and second year students. He does research on differential topology and differential manifolds and has recently coauthored two books, “Shape and Shape Theory” (with K. Carne, D. Kendall and H. Le) and “An Introduction to Differential Manifolds” (with C. Thomas).

Girton currently has a total of nine research students, in both pure and applied mathematics. They are a tremendous asset to the College, particularly as supervisors, and are very popular with the undergraduates. 

We aim to take about 10 undergraduates a year to do mathematics at Girton, so there are usually about 30 mathematics undergraduates in residence, plus about half a dozen doing Part III.

Distinguished Girton mathematicians

Until the 1970s, Girton was a women’s college, so the eminent Girton mathematicians from before that were all women. There was a particularly remarkable group of three who all lived for most of the twentieth century. Dame Mary Cartwright was an analyst and one of the first women Fellows of the Royal Society. Her work on differential equations was the basis of the very important modern theories of dynamical systems and chaos. After finishing her D.Phil in Oxford under the supervision of G.H Hardy, she was associated with Girton for the rest of her long life. She not only taught mathematics at Girton, but was also Mistress (the head of the College) from 1949 to 1969. Bertha Swirles, Lady Jeffreys. was a student at Girton; after a brief spell as lecturer at several other universities, she returned to Girton as a Teaching Fellow and was Director of Studies in Mathematics from 1949 to 1969. She did important research in quantum theory in the exciting early days of its development, but she is perhaps even more well-known for the book she wrote with her husband, Sir Harold Jeffreys, entitled “Methods of Mathematical Physics”. This is a classic which has influenced (and still influences) many generations of mathematicians. The third of the group, Olga Taussky-Todd, was born in what is now the Czech Republic, was educated in Vienna and came to Girton as a Research Fellow in the 1930s. She went on to become a Professor at California Institute of Technology, the first woman full professor there, and did outstanding research in number theory and matrix theory. She was ‘Woman of the Year’ for the Los Angeles Times in 1963!

More recent distinguished Girton mathematicians include Professor Dusa McDuff, a geometer at Barnard College, Columbia University, in New York, and a Fellow of the Royal Society; and Dr. David Hobson, a Reader at the University of Bath, who recently won Cambridge University’s prestigious Adams Prize for his contributing essay on financial mathematics.

Mathematics admissions at Girton

The majority of students applying to read mathematics at Girton will be doing A2-level Further Mathematics. We also admit students with other qualifications, such as Scottish Advanced Highers and the International Baccalaureate; in each case we would hope that the candidate would have taken as much mathematics as possible.

Our strategy is to interview essentially all candidates who apply to Girton (plus those open applicants who are assigned to the College), except those for whom it would be very difficult to travel from overseas. The candidates take a one-hour written test, the questions on which are used as the basis for discussion in two half-hour interviews, each with a mathematics Fellow (and possibly a research student), with a third interview with physicists if relevant. We aim to find out how candidates approach mathematics, how responsive they are to the type of teaching they will receive here and how strongly motivated they are to study mathematics. We also try to find out about their school background and teaching, so that we can set appropriate conditional offers. We always ask for A*AA at A2-level (or the equivalent for other types of examinations). We also almost always ask candidates to take the Sixth Term Examination Papers (STEP); this is because we find that A grades at A2-level cover a wide range of ability and we need to make finer distinctions. The advantage of the STEP papers is that they are the same for all candidates (thus doing away with differences between A-level boards etc), they are set, monitored and marked by Cambridge mathematicians and other mathematicians with experience of Cambridge admissions, and the detailed marks are available for Directors of Studies to see. This is very helpful if a candidate misses a grade by a few marks, then an informed decision can be made.

Candidates taking qualifications other than A-Levels may sometimes be asked to take STEP 1 and 2, while those doing Further Mathematics take STEP 2 and 3. Our offers vary between (1,1), and (1,3) or (2,2), depending on the circumstances of the candidate. The questions on the STEP papers are intended to test potential rather than knowledge; some are on familiar material but have an unusual twist, while others are on material which is unlikely to have been seen before, but in those cases, the candidate is presented with the background needed and is then required to develop it, as the questions leads.

We aim to attract students from all backgrounds, all types of schools and all regions of the UK, as well as from different countries – we usually have a number of overseas students, both from the European Union and from further afield. A few of our students come after a gap year; we do not actively encourage this, unless the applicant is extremely young, but we we are happy with it provded the plans for the gap year are worthwhile and include the opportunity for the student to keep up his or her mathematics. Such details are not so important – our overall concern is to admit students who will benefit from the Cambridge course and who have a genuine love of mathematics.

What does Girton Mathematics have to recommend it?

Girton is one of the larger colleges in Cambridge; as far as Mathematics is concerned, it is medium-sized. There are enough students each year to provide lots of company and stimulus, but the groups are not so large that anyone need feel lost. A lot of our teaching is done ‘in-house’, and there is a great deal of personal contact between Fellows and students. In addition to the supervisions, Dr. Barden runs weekly surgeries for the first and second years, which provide an extra opportunity for sorting out difficulties.

In the past few years, Girton has often been in the top third of the Baxter tables for mathematics (those tables compare examination performances of different colleges). In the ‘value-added’ table, Girton has been very near the top (this table shows how students’ results improve while they are in Cambridge). Although examination results as such are not of supreme importance (much more important is that each student should be enjoying the work and achieving his or her full potential), these facts indicate that our students are flourishing.

We have introduced a Careers Evening every three years or so, at which recent Girton mathematics graduates come back and tell us about their jobs and answer questions. The participants at a recent one included an environmental scientist, an internet company director, a mathematical biologist, an economist, an educational technologist, a teacher and a stockbroker, who were all very enthusiastic about what they did. The students found it very interesting and informative.

As mentioned earlier, first years at Girton live in the main college building, but in their second and third years, they may choose to live at Wolfson Court, which is right next to the Centre for Mathematical Sciences, and therefore very convenient for the Girton mathematicians!

Finally, Girton is a college which has an ideal balance between the numbers of men and women at both the student and fellowship levels. The atmosphere is friendly and informal, and the emphasis on the full development of each individual’s talents and potential.

Enquiries

If you would like more information about the College or the Mathematics course, please contact the Tutorial & Admissions Office at admissions@girton.cam.ac.uk or Ruth Williams at rmw7@damtp.cam.ac.uk. In particular, if you would like to meet some Girton mathematics students and Fellows, please come to one of our open mornings.