# Mathematics and Mathematics with Physics

Cambridge Mathematics is a varied and rewarding high-level course which allows you to follow your interests to the full, and also become engaged in mathematical fields you never knew existed. Our maths students perform well, and also participate fully in the life of the College. In addition, they are eventually equipped to choose from a huge range of rewarding careers,

**Please note that for applicants applying for Maths from autumn 2018 onwards, the entry requriements at all Cambridge colleges will change - see the 'What we look for' tab for details.**

St Catharine’s accepts students for both the Mathematics course and the Mathematics with Physics course. University mathematics is not at all like school mathematics. While it does involve quantities of long calculations, it also involves understanding how the ideas behind these long calculations fit together, how they work, how they may be extended, and when they fail. A degree in mathematics can be enormous intellectual fun: an opportunity to think about the toughest problems facing the modern world, and a structure to guide our search for answers.

**Course structure**

Students should apply for the **full four-year course** although the majority will graduate after three years. Students may choose to study either Mathematics or Mathematics with Physics in their first year.

At the end of the first year students who take the **Mathematics with Physics option** must choose between the Mathematics Tripos and the Natural Science Tripos for the later years of their degree. The Mathematics with Physics course may involve a higher workload for those students who make their second year course choice quite late in the year. The Mathematics with Physics course caters for students who wish to study physics as a part of the Natural Science Tripos in their second year but also take more mathematics in their first year. It also caters for students who are unsure whether they wish to continue as mathematicians or as physicists. These students take three of the four mathematics papers and an additional physics paper in their summer exams. At St Catharine’s they have a Director of Studies in Mathematics, who is responsible for arranging their preparation for the mathematics papers, and a Director of Studies in Physics who organises their physics teaching.

The Mathematics course provides all students with a solid foundation before they choose to specialise in pure, applied or other areas. It also caters extremely well for students with an interest in mathematical physics. In their **first-year** students study compulsory courses for four mathematics exam papers sat at the end of that year. The Mathematics first-year courses create common ground so students speak the same mathematical language and have the same level of knowledge in a broad range of topics drawn from algebra, analysis, geometry, number theory, probability, differential equations, dynamics and calculus. Students are also encouraged to attend extra courses in the first year, which will be examined in the second year.

The **second year** begins with more core material in both pure and applied topics in the first term. These include topology, analysis, Markov chains, quantum theory and linear algebra. In the second term, the students begin to specialise - most students do not attend all the available courses and revise only a subset of the material for their exams. The end-of-year exams consist of four compulsory papers each comprising a mixture of questions on different topics. There is also an optional computing component which is assessed during the year. At the end of the second year a small number of students may choose to switch to another subject - popular choices of alternative final year subjects include Astrophysics and Management Studies.

In the **third year** there is an enormous variety of specialist topics available for study. There are approximately forty courses, so students can choose a timetable which suits their interests and strengths. This is an opportunity for students to indulge themselves and devote the year to their favourite topics. Most students study fewer than ten of the available topics and may prepare eight for the exams. The course is examined at the end of the year in four papers, each containng a mixture of different topics. Once again, there is an optional computing component.

Students who achieve a 1st or 2.1 class in their third-year exams may be accepted into the **fourth year**, or 'Part 3' of the Mathematical Tripos. Students from Cambridge who take this route receive both a BA (Bachelor of Arts, Honours) degree and a MMath (Master of Mathematics) degree. Part 3 Mathematics is also open as a one-year course to students with Class 1 Honours degree in appropriate subjects from other top universities. Students from outside Cambridge obtain a MASt (Master of Advanced Study) degree. Part 3 is intended as a preparation for research and consists of a large number of specialist courses from which students may choose. The exams consist of individual subject papers at the end of the year. There is also an optional assessed essay component. The course has a reputation as one of the most demanding mathematics courses in the world.

Mathematics teaching at Cambridge consists of **lectures and supervisions**. Lectures are run by the University and are attended by mathematics students at all the Cambridge colleges. Lecture courses vary but, for example, a course of 24 lectures may be accompanied by 4 problem sets issued by the lecturer. Supervisions are hour-long small group teaching sessions run by a member of the teaching staff or a graduate student, usually with two undergraduate students, and are arranged by individual colleges. The supervisions are an essential opportunity for us to monitor your progress and, more importantly, the best way for undergraduates to get help in particular areas.

**Faculty website:** http://www.maths.cam.ac.uk/

In a typical year, about eight to ten students come to St Catharine's to read Mathematics. This is a similar number to many other colleges and is intended to form a supportive year group. The number of fourth-year Part 3 students can vary considerably but about five is typical, so the total number of undergraduate students reading Mathematics at St Catharine's is therefore usually about thirty. Our mathematicians usually form a friendly and cohesive social group and the college expects our students to demonstrate a willingness to work together and help each other in their studies. There is no such thing as a typical mathematician, and our students have a wide variety of interests, both mathematical and recreational, and we encouraged them to make the most of all the intellectual and cultural enrichment opportunities which St Catharine’s has to offer.

At St Catharine's many of the first-year and second-year **supervisions** are given by Fellows of the college. The remaining supervisions are usually given by Fellows of other colleges who have a long connection with St Catharine’s. St Catharine’s employs a College Teaching Officer who is a teaching specialist for the college. In common with most colleges, the third year supervisions are arranged by groups of colleges who share supervisors teaching specialist topics.

St Catharine’s places a high importance on the role of the mathematics course as a preparation for **later life**. As part of their development of transferable skills, the mathematics students at St Catharine's are encouraged to work together and support each other in their studies so that students can expect a high level of support from their director of studies, supervisors and peers. The students are also encouraged to consider Spring Week placements after their first year, when that is appropriate, and also longer work placements at the end of their second year. The college encourages mathematics students to take opportunities where available within their course or within the university community to develop computing, presentation and report writing skills. Those who arrive with some language skills are encouraged to maintain and develop them. Many of our mathematicians go on to further training after graduation, but many choose to go into the employment market where there is a huge variety of options from which to choose career paths. Mathematics graduates' career choices include academic careers as mathematicians, teachers, engineers, consultants, bankers and traders. Some have moved across disciplines and employed their skills in other subject areas. Employers are eager to take on Mathematics graduates because they see the degree as a guarantee of an ability reason clearly and to master difficult material quickly. It is a degree course which opens many doors and the college takes the need to prepare for a future career very seriously.

St Catharine’s, in common with other colleges, seeks the strongest young mathematicians. Our students come from a wide range of social and educational backgrounds, but they share a genuine passion for their subject, raw talent, imagination, a tenacity allowing them to attempt and complete difficult tasks, and an ability to work individually or as a part of a team. Applicants who do not find the Mathematics A-level (or equivalent) course very easy are unlikely to be able to cope with Cambridge Mathematics.

St Catharine's is looking for students who can cope with the **high workload and difficult material** in the Cambridge course. Applicants should have coped well with a workload equivalent to three full, academically demanding A-levels (or equivalent) taken *within* two years. We are of course happy to consider the many candidates who take an A-level one year early and then take another two A-levels in the following year - many students take A-level mathematics in one year and then take A-level further mathematics the following year instead of studying for the two exams concurrently,

As far as **school subject choices** are concerned, in common with all Cambridge Colleges we now require our applicants to be taking Maths *and* Further Maths at A-level. For candidates taking the IB, we would require IB Higher Level Mathematics. Many applicants will also be taking Physics and/or Chemistry, but this is certainly not the only possible combination and we welcome applicants taking other subjects. St Catharine’s also gives equal consideration to those taking International Baccalaureate, Scottish Highers or Pre-U qualifications. All Mathematics applicants should make every effort to study as much mathematics as possible within their study programme before starting their degree course. Although Cambridge now requires applicants to be take Further Maths at A-level, we will take into account whether you had to self-teach any modules - please tell us if this is the case.

Applicants are also encouraged to enhance their knowledge by making use of **free online help** such as NRICH. Students who may have a choice between mechanics and statistics modules and enjoy both subjects will probably find the mechanics more helpful in their first year in Cambridge, but no one is disadvantaged should they prefer to take statistical modules.

Almost all candidates are asked to sit two **STEP papers** 2 and 3, although they may find STEP 1 good preparation, too, often being asked for grade 1. Some candidates may be given conditional offers which require them to do some extra coursework in order to sit their STEP papers. Many students have only informal help with STEP at school, but STEP past papers, solutions and a guide to STEP-style problems called *Advanced Problems in Mathematics* are available from OCR publications, Mill Wharf, Mill St, Birmingham B6 4BU. Also, Dr S Siklos has written a book on how to do STEP questions. See also http://www.damtp.cam.ac.uk/user/stcs/STEP.html

St Catharine's is one of the colleges which will be participating the new **flexible offers scheme** for Maths, in which applicants who meet certain contextual criteria may receive an alternative conditional offer requiring higher achievement in A-levels, but a requirement for high marks in one, rather than two STEP papers. (For example they may be asked to achieve EITHER A*A*A and grades 1,1 in STEP 2 and 3, OR A*A*A* and grade 1 in either STEP 2 or 3, with both papers being taken. This scheme will probably start for late-2018 applicants and more information will be provided as soon as it is available.

As a college, Catz has a strong reputation for being friendly and sociable. Everyone is encouraging and supportive, especially maths students, where everyone has their own strengths and weaknesses. Each year group has around 8 mathematicians, so you get to know everyone really well. In addition, the college has its own maths society (the Hyperbolics) which organises various social events, so you get to know people from different years, including post-grads. Last year, we had pub trips, bowling and a garden party, as well as the inaugural Hyperbolics football match!

Unfortunately, it's quite easy to become a bit lazy at Catz, especially if you're a mathematician, since everything is so convenient! Lectures are less than a 5-minute walk away (or a 3-minute sprint!), and the majority of first year supervisions take place in college, so you never have to travel far. This also means you see your supervisors around and get to know them quite well - they're all really friendly as well. We've also got a really great library should you need any books, and the librarians are happy to order in anything extra.

Sam Burr and Matt Temple (second-year Mathematicians)