Mathematical Sciences - University Of Oxford
Mathematical SciencesUniversity of OxfordContentsStudying Mathematics at Oxford. 2-5University Mathematics. 2The Oxford System. 3The Degree Structure. 4Libraries and Societies.5Admissions and Preparation for the Course . 6-12Admissions .6Admissions FAQs.8Information for International Students .10Preparation for the Oxford Mathematics Course.11The Mathematics Course. 13The Mathematics & Statistics Course.15The Mathematics & Philosophy Course. 17The Mathematics & Computer Science Course. 19The Mathematical & Theoretical Physics 4th Year .21Careers. 22Puzzles.23The Equations.24
Studying Mathematics at OxfordUniversity MathematicsFew people who have not studied a mathematics or science degree will have much ideawhat modern mathematics involves. Most of the arithmetic and geometry seen inschools today was known to the Ancient Greeks; the ideas of calculus and probability youmay have met at A-level were known in the 17th century. And some very neat ideas areto be found there! But mathematicians have not simply been admiring the work ofNewton and Fermat for the last three centuries; since then the patterns of mathematicshave been found more profoundly and broadly than those early mathematicians couldever have imagined. There is no denying it: mathematics is in a golden age and bothwithin and beyond this university’s ‚dreaming spires‛, mathematicians are more indemand than ever before.One great revolution in the history of mathematics was the 19th century discovery ofstrange non-Euclidean geometries where, for example, the angles of a triangle don’t addup to 180 , a discovery defying 2000 years of received wisdom. In 1931 Kurt Gödelshook the very foundations of mathematics, showing that there are true statementswhich cannot be proved, even about everyday whole numbers. A decade earlier thePolish mathematicians Banach and Tarski showed that any solid ball can be broken into asfew as five pieces and then reassembled to form two solid balls of the same size as theoriginal. To this day mathematics has continued to yield a rich array of ideas andsurprises, which shows no sign of abating.Looking through any university’s mathematics prospectus you will see course titles thatare familiar (e.g. algebra, mechanics) and some that appear thoroughly alien (e.g. GaloisTheory, Martingales, Communication Theory). These titles give an honest impression ofuniversity mathematics: some courses are continuations from school mathematics,though usually with a sharp change in style and emphasis, whilst others will bethoroughly new, often treating ideas on which you previously had thought mathematicshad nothing to say whatsoever.The clearest change of emphasis is in the need to prove things, especially in puremathematics. Much mathematics is too abstract or technical to simply rely on intuition,and so it is important that you can write clear and irrefutable arguments, which makeplain to you, and others, the soundness of your claims. But pure mathematics is morethan an insistence on rigour, arguably involving the most beautiful ideas and theorems inall of mathematics, and including whole new areas, such as topology, untouched atschool. Mathematics, though, would not be the subject it is today if it hadn’t had beenfor the impact of applied mathematics and statistics. There is much beautifulmathematics to be found here, such as in relativity or in number theory behind the RSAencryption widely used in internet security, or just in the way a wide range of techniquesfrom all reaches of mathematics might be applied to solve a difficult problem. Also withever faster computers, mathematicians can now model highly complex systems such asthe human heart, can explain why spotted animals have striped tails, and can examinenon-deterministic systems like the stock market or Brownian motion. The high technicaldemands of these models and the prevalence of computers in everyday life are makingmathematicians ever more employable after university (see Careers on page 22 formore information).Mathematical Institute,University of OxfordPage 2January 2017
The Oxford SystemStudents at Oxford are both members ofthe University and one of 29 colleges,and mathematics teaching is shared bythesetwoinstitutions.Oxford’scollegiate system makes both study, andthe day-to-day routine, a ratherdifferent experience from otheruniversities.Most of the teaching of mathematics inOxford, especially in the first two yearsof a degree, is done in tutorials. Theseare hour long lessons in college betweena tutor, who is usually a senior memberof the college, and a small group ofstudents (typically a pair). This form ofteachingisveryflexibleandpersonalized, allowing a tutor time withthe specific difficulties of the group andallowing the students opportunities toask questions. It is particularly helpfulfor first year mathematicians whonaturally begin university from a widerange of backgrounds and syllabi.College tutors follow closely theirstudents’ academic progress, guide themin their studies, discuss subject optionsand recommend textbooks, as well asbeing able to answer questions aboutOxford generally. Colleges are muchmore than just halls of residence though,each being a society in its own right, andthere will be other students studyingmathematics (and other subjects) incollege who, invariably, will prove a helpwith study and often friends duringuniversity and beyond.Mathematicians from across all thecolleges come together for lectureswhich are arranged by the University.This is usually how students first meeteach new topic of mathematics. Alecture is a 50 minutes talk, usually givenin the new Mathematical Institute, withup to 280 other students present.Unsurprisingly there is less (but, by nomeans, no) chance to ask questions asthe lecturer discusses the material, givesMathematical Institute,University of Oxfordexamples, provides slides and makenotes at the boards. The lecturer will,like your college tutors, be a member ofthe Faculty, but usually a tutor at adifferent college to your own. For moststudents the material of a lecture ispresented too intensely to take in all atonce, and so it falls to a student toreview their lecture notes and othertextbooks, determine which elementsare still causing difficulty, and try towork through these. To help, thelecturer, or a college tutor, will setexercises on the lecture and theseproblems will typically form the basis ofthe next tutorial in college.By the third and fourth years the subjectoptions become much more specializedand are taught in intercollegiate classesorganized by the University. These aregiven by a class tutor (usually a memberof Faculty or senior graduate who hastakenandpassedteachingqualifications) and a teaching assistant.They range in size – typically there are8-10 students – and there is againplenty of chance to ask questions anddiscuss ideas with the tutors.College tutors mark their students’tutorial work each week, commenting onprogress being made and, at the end of aterm, your various tutors will writereports on that term’s work and discussthese with you. Most college tutors alsoset college exams, called collections, atthe start of each term, to checkprogress and as practice for lateruniversity examinations. The results ofcollections will not count towards thedegree classifications, awarded at theend of the third and fourth /studyhere/undergraduate-study/whichcollegefor links to the colleges’webpages.Page 3January 2017
examinations, known as the PreliminaryExamination (or ‚Prelims‛). Studentstaking the examination are awarded aDistinction, Pass or Fail.The vastmajority of students pass Prelims at thefirst attempt. Those who do not passPrelims in the first instance in June mayresit one or more of the examinations inSeptember. Successful students maythen continue their degree.The Andrew Wiles BuildingThe Mathematics Department has nowsettled in to the Andrew Wiles Buildingon Woodstock Road as part of the newRadcliffe Observatory Quarter. You canfind more information and pictures y/why-oxfordThe Degree StructureThere are three and four year degrees inMathematics (BA/MMath) and also inthe various joint courses: MathematicsandStatistics(BA/MMath),Mathematics and Computer Science(BA/MMathCompSci) and Mathematicsand Philosophy (BA/ MMathPhil). Thereis also now a fourth year stream –Mathematics and Theoretical Physics –whereby students study for anMMathPhys. See page 21 for details.All of these mathematics degrees have astrong reputation, academically andamongst employers. The joint degreeswith Philosophy and with ComputerScience contain, roughly speaking, thepuremathematicsoptions.TheMathematics and Statistics degrees havethe same first year as the Mathematicsdegrees, before the emphasis in optionsincreasingly moves towards probabilityand statistics. Each degree boasts a widerange of options, available from thesecond year onwards. They will train youto think carefully, critically andcreatively about a wide range ofmathematicaltopics,andaboutarguments generally, with a clear andanalytical approach.Decisions regarding continuation to thefourth year do not have to made untilthe third year. In the third and fourthyears there are again a large number ofoptions available, including the chance towrite a dissertation and other optionswhich include practical work or projects.Some of these options build on materialfrom earlier courses, whilst othersintroduce entirely new topics. Somethird year courses, and almost all thefourth year courses, bring you close totopics of current research. You maychoose a varied selection of options or amore specialized grouping reflectingThe degree structures and theassessment of these degrees have muchin common. (See later sections for moreon the specifics of each degree.) Thefirst year mathematical content of eachdegree contains core material, coveringideas and techniques fundamental to thelater years. At the end of the academicyear, in June, there are five universityMathematical Institute,University of OxfordThe first term of the second yearinvolves the last of the core, compulsorycourses (Linear Algebra, Metric Spaces,ComplexAnalysis,DifferentialEquations) and some options. From thesecond term onwards a wide range ofoptions becomes available. Typically astudent takes five or six of nine ‚longoptions‛ in the first two terms and threeof nine ‚short options‛ in the third term.These vary from pure topics like numbertheory, algebra and geometry, throughto applied areas such as fluid dynamics,special relativity and quantum theory.Other options are also available in thejoint degrees which reflect the nature ofthe speciality. Students can choosemainly pure, mainly applied, or a mixtureof topics.There are universityexaminations at the end of the year; noclassification is made at that stagethough the marks achieved counttowards the classification awarded in thethird year.Page 4January 2017
your future academic or careerintentions. There are again universityexaminations at the end of third year,some of which may be replaced withequivalent project work.The Invariants also publishes a termlymagazine and runs a puzzle competition.The Mirzakhani SocietyYou will receive a classification (First,Upper Second, Lower Second, Third,Pass, Fail) based on the assessment ofyour examinations, practicals andprojects from the second year and thirdyears (i.e. not counting your Prelimsresults), and a further separateclassification similarly assessed on yourfourth year (if applicable).MURC and JCCUTheMathematicsUndergraduateRepresentative Committee (informallyknown as MURC) – is a student bodyrepresenting the interests of students inmathematics and the joint degrees. Itconsists of a representative from eachcollege, elected by the undergraduatemathematicians of the college. Thiscommittee passes its views on syllabusand examination changes and generalmatters such as the timing of lectures.LibrariesStudents normally buy a certain numberof basic textbooks, but typically findthat libraries cover other more specialistneeds. Each college has its own libraryfrom which its undergraduates mayborrow books. These libraries usuallyhave copies of all recommended booksfor core courses and many others. Thehugely resourced Radcliffe ScienceLibrary www.bodleian.ox.ac.uk/sciencehas both a lending-library and areference library.ITIf you’re buying a computer foruniversity, please do consider a laptopover a desktop, so that you can take thelaptop to classes. If you don’t have yourown, the department has several sparelaptops that you are welcome to use.The Invariant SocietyThe Oxford University Invariant Societywww.invariants.org.ukistheundergraduate mathematical society. Itsprimary aim is to host weekly popularmathematically-related talks by notablespeakers, on a wide variety of topics.Past speakers have included BenoitMandelbrot, Sir Roger Penrose, Marcusdu Sautoy and the author Simon Singh.Mathematical Institute,University of OxfordThe Mirzakhani Society is a society forwomen studying maths. Its aim is tosupport students through providing aspace to discuss issues that women mayencounter during their degrees. It holdsweekly ‘Sip and Solve’ meetings with teaand cake, and other events such associals and talks. It is open to bothundergraduates and postgrads, and has awide mix of people at its events.Page 5MURC operates a second-hand bookscheme whereby all mathematicians areable to buy and sell books. This schemeis particularly useful for ‘freshers’ (firstyear undergraduates) since they are ableto obtain cheaply some of theirtextbooks as soon as they arrive atOxford. The Representative Committeeappoints eleven junior members (i.e.undergraduate students) to the JointConsultativeCommitteewithUndergraduates (JCCU); the other sixmembers of the committee aremembers of the Departments andDivision. This committee meets once aterm and its discussions concern thesyllabus, teaching, library facilities, opendaysandgeneralaspectsofexaminations. It is also available forconsultation by the departments on anyof these matters and is responsible fordiscussing feedback from lecturesurveys.January 2017
Admissions and Preparation for the CourseAdmissionsThe following applies to prospectivestudents for the Mathematics degree, orfor any of the joint degrees, who areconsidering applying in October 2017for entry in 2018 or 2019. Much likeapplying for any other UK university,applications to Oxford are made throughUCAS, though the deadline is earlier, onOctober 15th. Your application mayinclude a preference for one college, ormay be an ‚open‛ application in whichcase a college is assigned to you.The Mathematical Sciences AdmissionsTest (MAT) is sat by candidates in theirschools, colleges or at a test centre. Thetest, which lasts 2½ hours, will be in thesame format as in 2007-16 and thesepast tests, and two further specimentests, are available with solutions /mathsadmissions-test . All applicants attemptthe first ten multiple-choice questions,and then four from six longer questionsdepending on their proposed degree.Instructions are in the test on whichquestions to complete. No aids,calculators,formulabookletsordictionaries are allowed. A syllabus forthe test is available at the abovewebsite; it roughly corresponds tomaterial from the A-level modules C1and C2, though the questions aredevised to test for a deeperunderstanding of, and imagination with,the syllabus’ methods and material.The distribution of the test will beadministered by the Admissions TestingService and all applicants mustseparately register with them by theapplication deadline (15th October),through their school or college orthrough a test centre. Schools canMathematical Institute,University of OxfordPage 6register with the Admissions TestingService to become test centres, butplease note that this takes a minimum of24 hours; seewww.matoxford.orgAll applicants are expected to take theAdmissions Test on the above date andmust notify the Admissions TestingService as soon as possible in the eventof any potential difficulties or scheduleclashes.Details of the date of the test can befound at: www.matoxford.org.ukApplicants will be shortlisted forinterview in Oxford on the basis of theirtest marks and UCAS form, with around3 applicants per place being shortlisted.(Currently there are around 7 applicantsper place.) During your stay (typicallybeing for 2-3 nights), meals andaccommodation are provided by thecollege you applied to, or were assignedif you made an open application. Duringthis time the college arranges for somecurrent students to be available toanswer your questions about universitymathematics and the college and to giveyou an alternative view of Oxford. In theevent of a shortlisted overseas applicantbeing unable to travel to Oxford aSkype, video or telephone interview maybe arranged.Interviews in Oxford take place in midDecember at the college with at leastone more interview guaranteed atanother college. Typically, interviewslast 20-30 minutes with one or twointerviewers, and you may have morethan one at a particular college.Applicants for the joint degrees withPhilosophy and with Computer Scienceshould expect at least one interview oneach discipline. In interview, you may beJanuary 2017
asked to look at problems of a type thatyou have never seen before. We want tosee how you tackle new ideas andmethods and how you respond to helpfulprompts, rather than simply find outwhat you have been taught. Interviewsare academic in nature, essentiallyimitating tutorials, this being how muchof Oxford’s teaching is done; feel free toask questions, do say if unsure ofsomething, and expect hints.If your application is unsuccessful withyour first college, another may makeyou an offer; around 25-30% of offersmade are not by the applicant’s firstcollege. Around 15% of all applicants arecurrently made offers, with the majoritybeing conditional of
University of Oxford Page 3 January 2017 The Oxford System Students at Oxford are both members of the University and one of 29 colleges, and mathematics teaching is shared by these two institutions. Oxford’s collegiate system makes both study, and the day-to-day routine, a rather different experience from other universities.
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