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GUIDE TO ADMISSIONS IN MATHEMATICS 1 Cambridge Mathematics The Cambridge underg

GUIDE TO ADMISSIONS IN MATHEMATICS 1 Cambridge Mathematics The Cambridge undergraduate mathematics course, known as the Mathematical Tripos, is widely recog- nised as one of the most rewarding - and correspondingly demanding - undergraduate mathematics courses available. You will have to work hard, but will enjoy the opportunity to explore an exceptional range of interesting and beautiful mathematics, and to interact with other enthusiastic and talented mathematicians. Two other aspects of the course that our students greatly appreciate are its ﬂexibility and the breadth of subjects offered. 2 Why Mathematics? Here are some reasons often given for studying Mathematics at university. • You ﬁnd mathematics interesting. This is an excellent reason. • You are good at mathematics. This is a necessary, but not sufﬁcient, condition (as mathematicians would say). You may be ﬁnding the mathematics you are doing now quite straight- forward, so that you hardly have to work at it. When you study mathematics at higher levels it is not so straightforward, so you have to be prepared to work hard at it. And remember that this work will be a major part of your daily life. • The job prospects are excellent. This is a true statement: employers love mathematicians because mathematics is all about the vital skill of problem solving, but it’s not on its own sufﬁcient reason. You should choose to study mathematics because you enjoy it! There are other ways of getting good jobs than spending three or four years studying something that you don’t enjoy. “I ﬁrst developed an enthusiasm for maths when I was studying it at GCSE level. I had always been very good at maths but I’d always just seen it as necessary and functional. I hadn’t realised the breadth of its applications, and it had certainly never occurred to me how fun and rewarding maths could be." Naomi, Murray Edwards College 3 Why Cambridge Mathematics? Here are some reasons for studying Mathematics at Cambridge. • Cambridge is, according to all major surveys, one of the top universities in the world. • The Cambridge mathematics course is one of the very best mathematics courses in the UK. • The fourth year of our mathematics course (called Part III) is world famous and a breeding ground for future leaders in mathematical research. • Cambridge Colleges offer a level of academic, pastoral and ﬁnancial support that is unsurpassed by any UK university. • Cambridge mathematicians are possibly the most sought- after mathematics graduates in the UK, and go on to high- level jobs in many diverse and very fulﬁlling careers. • Cambridge is a beautiful, ancient and vibrant city. “The two supervisions per week, where you discuss examples from the lectures in pairs with an academic, are an amazing chance to talk to someone who is extremely knowledgeable in that area." Shona, Clare College “Being able to speak to your supervisor and say "I don’t know this" is incredibly reassuring, ... the system is in place for us to succeed with support." Clement, Jesus College 4 Our course Introduction Cambridge has enjoyed a reputation for excellence in Mathemat- ics since the time of Isaac Newton, over 300 years ago. Over the years, some of the world’s leading mathematicians have taught in the Faculty, including Fields Medallists (a Fields Medal is the math- ematical equivalent of a Nobel Prize), and even Nobel Prize win- ners (although there is no Nobel Prize for mathematics). Probably the most well-known member of the Faculty currently is Professor Stephen Hawking, the distinguished theoretical physicist. The Mathematics course in Cambridge is known as the Mathemat- ical Tripos, comprising the 3 years of the undergraduate course (Parts IA, IB and II) plus the optional one-year Masters course (Part III). The course dates back to the time of Newton, whose pioneering work in mathematics and physics was a strong inﬂuence for many years. The name Tripos comes from the word for the three-legged stool used by the ‘Ould Bachilour’ of the University who conducted the University examinations in medieval times. The examination then took the form of a debate or wrangle and concentrated on Grammar, Logic and Rhetoric. Although the Mathematical Tripos has changed much over the centuries, some traditions remain: the students in the ﬁrst class are still called Wranglers. 2 Features of the course The main distinguishing features of the Cambridge Mathematics course are: • It covers the whole range of mathematics: from number theory, logic, geometry and group theory on the pure side, to ﬂuid dynamics, math- ematical biology, quantum mechanics and cosmology on the applied side, and includes subjects such as probability, statistics, numerical analysis, ﬁnancial models and computing. • It has an upside-down pyramid structure, with a set of compulsory courses in the ﬁrst year, but a very wide choice in the third year and fourth year. This means that you will not be tied down to a specialised choice before experiencing university maths, but you will get a thor- ough grounding which leaves all options open. Later, you will have freedom to choose a specialization with true knowledge of your math- ematical abilities and preferences. • The examinations in the ﬁrst three years are non-modular in structure: it is not the case that each examination paper is devoted to an individual lecture course. Instead, there are four three-hour papers at the end of each year. In the ﬁrst year, two topics are examined on each paper and in the second and third years the examination papers are cross-sectional, meaning that instead of each lecture course having a dedicated examination paper, each examination paper has questions on many lecture courses. The ﬂexibility that this allows is regarded as one of the great strengths of the Tripos: this allows you to choose how many courses you wish to revise for the examination and therefore to work at your own pace, which is important in mathematics. The examinations in the fourth year are modular, but you have some ﬂexibility in the number of exams taken. • Lecture courses in the ﬁrst three years are supplemented by supervisions. Supervision is the Cambridge term used to describe teaching in a small group of students (usually two). The su- pervisor, who is normally a member of the teaching staff or a research student, sets work for the students to prepare and then goes over it in the supervision. Usually the work takes the form of examples sheets (sometimes called problem sheets) prepared by the lecturer to illustrate the ma- terial covered in the lectures. A great strength of the supervision system is that it gives students an opportunity to discuss their individual work and particular problems. Lecture courses in the fourth year are supplemented by examples classes, where the set work in examples sheets is discussed, and you can ask questions about material that you found difﬁcult or complicated. Lecture courses in Mathematics are organised by the Faculty of Mathematics for students from all Colleges in the University. Attendance at lectures is not compulsory but few students manage to cover the material adequately by themselves even when good textbooks are available. Each lecture lasts approximately 50 min- utes and there are on average two lectures per day from Monday to Saturday, in the mornings only. Lectures are given for eight weeks in each of the Michaelmas and Lent terms and for four weeks in the Easter term, ﬁnishing about ten days before the examinations. There are no lectures in the Easter term in the third year. Supervisions on the various courses are arranged by the Colleges rather than by the Faculty and stu- dents receive on average two supervisions per week, each lasting about an hour, which usually take place in the afternoon during weekdays. Examples classes in the fourth year last about one to two hours, and their number depends on the courses you are taking. 3 Aims of the course Our Mathematics course aims to: • provide a challenging course in mathematics and its applications for a range of students that includes the best in the country; • provide a course that is suitable both for students aiming to pursue research and for students going into other careers; • provide an integrated system of teaching which can be tailored to the needs of individual students; • develop in students the capacity for learning and for clear logical thinking; • continue to attract and select students of outstanding quality; • produce the high-calibre graduates in mathematics sought by employers in universities, the pro- fessions and the public services, many of whom will become world leaders in their chosen ﬁelds; • provide a Masters course (Part III) suitable for students wishing to embark on a research career in the mathematical sciences. Facilities and Resources As a mathematics undergraduate at Cambridge you will have many resources to support your learning and opportunities to broaden your experience. • Library facilities are outstanding, which means you will not need to buy any textbooks: ◦Every College has a library which contains the standard books recommended uploads/Litterature/ admissions-guide 1 .pdf