Mathematics at Cambridge

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The Mathematical Tripos is Cambridge's oldest Tripos (degree course), dating back to the 18th Century. It is split into four Parts (IA, IB, II, III), described below, where the first three Parts give you a B.A., and Part III gives you an M.Math. if you continue from the B.A., or an M.A.St. if you study it as a stand-alone graduate course. The course covers a wide range of topics in mathematics, and the non-modular examination system allows students to do as many or as few options as they like.

Admissions

Admission to the Mathematical Tripos usually requires A*AA (incl Maths and Further Maths) at A-level, or equivalent, and STEP, usually papers II and III with grade 1 in each, but this varies based on college and the applicants' level of study of Maths. STEP ('Sixth Term Examination Paper') is a challenging exam used by Cambridge, Warwick, Imperial and some other universities, for which preparation is designed to bring a student up to the level of mathematical maturity required to do a Maths degree at these institutions. As such, a significant proportion of offer holders fail to meet their offer, so early and thorough preparation is a must.

The style of interviews varies from college to college, but as a general rule, they will usually involve a lot of guided problem-solving, and not much time will be spent discussing the personal statement, books read, and so on. It is often advised that you should treat interviews as if they were supervisions: you are not expected to be able to do the questions you are given, but you are expected to reach the answer with a few pokes in the right direction from the interviewer where necessary.

The course

The Mathematical Tripos is split into Part IA (1st year), Part IB (2nd year), Part II (3rd year) and Part III (4th year). Upon completion of Part II, a student is eligible for the Bachelor of Arts degree. Students who achieve a 1st in Part II, or show potential to achieve a 1st, may advance to Part III, which is a graduate-level course that is also available as a stand-alone masters course to students outside of Cambridge.

Course content

Part IA

There are eight examinable lecture courses in Part IA:

• Michaelmas Term: Vectors and Matrices, Differential Equations, Groups, Numbers and Sets;
• Lent Term: Analysis I, Vector Calculus, Probability, Dynamics and Relativity.

These are usually regarded as compulsory, and are intended to provide a solid grounding in a wide range of areas of maths. Some of the courses follow on from content that appears at A-level (e.g. Vectors and Matrices), whereas some introduce completely new material (e.g. Vector Calculus).

There is also a non-examinable lecture course in Mechanics in Michaelmas Term, which is useful for people who have not done much Mechanics. (Usually it's a good idea to go if you did less than three Mechanics modules, or if you didn't do A-level and your Maths course didn't contain much Mechanics).

Additionally, there is a non-examinable course in the History of Mathematics, open to all Maths students (not just first-years). These lectures are usually very interesting, casual and entertaining; notes are not taken, and food and drink (alcoholic or otherwise) is encouraged. In Easter Term, students get the opportunity to give lectures of their own in this series.

First-year students normally go to Part IB lectures in Easter Term (see below) so that they can work on the content over the summer and so that their second-year Easter Term can be spent revising.

Part IB

In Part IB, there is a wider selection of courses, and students normally decide to specialise slightly. Most students choose courses from the whole spectrum of pure, applicable and applied maths, with preference towards a particular one. Courses on offer are:

• Michaelmas Term: Linear Algebra, Analysis II, Methods, Quantum Mechanics, Markov Chains;
• Lent Term: Complex Analysis, Complex Methods, Geometry, Numerical Analysis, Fluid Dynamics, Electromagnetism, Groups Rings and Modules, Statistics;
• Easter Term: Metric and Topological Spaces, Variational Principles, Optimisation.

Note that the Easter Term lectures are usually attended in the first year, despite being examined in Part IB.

Part II

Part II presents students with the ability to specialise further and put the mathematical tools they have obtained in Parts IA and IB to real use. Courses on offer in the 2011/12 academic year are:

• Pure: Algebraic Geometry, Algebraic Topology, Coding and Cryptography, Differential Geometry, Galois Theory, Geometry and Groups, Graph Theory, Linear Analysis, Logic and Set Theory, Number Fields, Number Theory, Probability and Measure, Representation Theory, Riemann Surfaces, Topics in Analysis;
• Applicable: Applied Probability, Optimisation and Control, Principles of Statistics, Statistical Modelling, Stochastic Financial Models;
• Applied: Asymptotic Methods, Applications of Quantum Mechanics, Classical Dynamics, Cosmology, Dynamical Systems, Electrodynamics, Fluid Dynamics, Further Complex Methods, General Relativity, Integrable Systems, Mathematical Biology, Numerical Analysis, Partial Differential Equations, Principles of Quantum Mechanics, Statistical Physics, Waves.

Courses are split into 'C courses' and 'D courses' (it should be noted that courses in Part IA and Part IB are A courses and B courses, respectively). C courses are intended to be straightfoward, and each C course gives rise to four Section I and two Section II questions in the exams. D courses are intended to be more challenging, and the 24-lecture and 16-lecture D courses give rise to four and three Section II questions, respectively, with no Section I questions. Thus one can gain four betas and two alphas from a C course, and either three or four alphas from a D course. (For more information on 'alphas' and 'betas', see below.)

Part III

Students who achieve first-class honours in Part II can continue to Part III; students who get a 2:1 in Part II can apply for entry, subject to permission from the Faculty Board (whose website says that those who are not in the top 40% of the year for both Part IB and Part II are unlikely to be let in). Students who have graduated from other universities can also study Part III as a stand-alone graduate course.

The number of courses on offer in Part III is phenomenal, with 76 on offer in 2011.

Lectures, supervisions and classes

Parts IA, IB and II

Courses in the first three Parts of the Tripos are either 12, 16 or 24 lectures in length. 12-lecture courses entail two lectures per week for six weeks, 16-lecture courses entail two per week for eight weeks, and 24-lecture courses entail three per week for eight weeks.

Lectures are an hour long and take place between 9am and 1pm. In Part IA, students attend two lectures per day, six days per week (Monday-Saturday). In Part IB, lectures run from Monday to Friday, and the number of lectures on each day depends on the lecture courses attended. In Part II, lectures are six days per week, with the number of courses dependent on the lecture courses attended.

In supervisions, students go over answers to example sheets, of which there are 2 per 12-lecture course, 3 per 16-lecture course and 4 per 24-lecture course.

Part III

Courses in Part III of the Tripos are worth either 2 or 3 units. Courses worth 2 units usually consist of 16 lectures, and courses worth 3 units consist of 24 lectures. As with the first three Parts of the Tripos, example sheets are given out, but instead of supervisions, students usually attend examples classes. These are mini-lectures, where the lecturer goes through the problems on the sheet and answers any quick questions that students have.

Examinations

Parts IA, IB and II

In each of Parts IA, IB and II, students sit four exams in late May or early June. All students sit the same exams, and answer questions on whichever lecture courses they have chosen to go to. (This is different from most other universities in the UK, where you must sign up for modules and sit separate exams for each module.)

Each exam is split into Section I ('short questions') and Section II ('long questions'). Questions in Section I are marked out of 10 and questions in Section II are marked out of 20. Quality marks are given for good answers. Namely:

• An 'alpha' is awarded for each Section II question that scores 15-20 raw marks;
• A 'beta' is awarded for each Section I question that scores 8-10 raw marks, or for each Section II question that scores 10-14 marks.

The 'merit mark' takes into account both raw marks and quality marks, and is used to rank candidates and give classifications (1st, 2:1, 2:2, 3rd or fail). Each beta is worth 5 extra marks, the first eight alphas are worth 15 marks each, and each alpha thereafter is worth 30 extra marks. This can be summarised in the following formula: where is the merit mark, is the number of raw marks, is the number of alphas and is the number of betas.

Candidates who achieve a 1st in Part II are called 'Wranglers' (the top 1st is called the 'Senior Wrangler'), candidates who achieve 2:1s and 2:2s are called 'Senior Optimes' (pronounced /ˈɒptɪˌmiː/, 'OP-tim-ee') and candidates who achieve 3rds are called 'Junior Optimes'. The candidate with the lowest merit mark who achieves honours (usually a 3rd) is called the 'Wooden Spoon', for entertaining historical reasons involving spoons.

Part III

In Part III each option has its own paper, and unlike Parts IA, IB and II, quality marks are assigned to entire papers rather than to individual questions. The quality marks are alphas, betas and gammas, with a qualifier of + or -. So for example is the best possible quality mark, and is the worst possible quality mark, though it is possible to fail to achieve a quality mark at all. Each paper is worth 2 or 3 units, and candidates normally select 17-19 units (19 being the maximum). A 3-unit examination may be replaced by an essay, which is described as being a good preparation for further study and academic mathematical research.

CATAM

An optional part of the Tripos, which most students do nonetheless, is CATAM. This stands for Computer-Aided Teaching of All Mathematics, and refers to computational project coursework that can be undertaken in Parts IB and II of the Tripos. Projects are on a range of areas of mathematics, with a significant bias in favour of applied and applicable mathematics in Part II (probably representative of the real world).

In Part IB, students submit two 'core' projects, over which there is no choice, and two 'optional' projects out of four possible ones. 20 marks is available for each project, and the quality mark is calculated as in examinations, meaning that up to four alphas are on offer.

In Part II, there is a considerably larger choice of projects. Each project carries a certain number of units, of which up to a maximum of 30 may be submitted. (If more than 30 are submitted, the mark is scaled appropriately, rather than the best 30 units being chosen.) Each unit gives rise to a tenth of a merit mark, meaning that up to three alphas are on offer.

Links

• Faculty of Mathematics (see also: DPMMS, DAMTP, Statistical Laboratory)
• Admissions information
• Wikipedia articles on the Tripos and Part III
• TSR Cambridge Maths thread