Part B Mathematics and Philosophy 2020-21

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This Supplement to the Course Handbook specifies the Mathematics courses available for Part B in Mathematics & Philosophy in the 2021 examination. It should be read in conjunction with the Handbook for Mathematics & Philosophy for the academic year 2020-2021, to be issued in Michaelmas Term. The Handbook contains in particular information on the format and rubrics for written examination papers in Mathematics, and the classification rules applicable to Part B.

See the current edition of the Examination Regulations ( for the full regulations governing the examinations.

Part B of the Honour School of Mathematics & Philosophy

The following is reproduced from the Examination Regulations applicable to the 2021 examinations.

The examination for Part B shall consist of units in Mathematics and subjects in Philosophy. The schedule of units in Mathematics shall be published on the Mathematical Institute website by the beginning of the Michaelmas Full Term in the academic year of the examination concerned, after consultation with the Mathematics Teaching Committee. The schedule shall be in two parts: Schedule 1 (standard units) and Schedule 2 (additional units). In Philosophy the subjects shall be subjects from the list given in Special Regulations for All Honour Schools Including Philosophy.

Each candidate shall offer:

    (i) Four units of Mathematics from Schedule 1, two of which shall be B1.1 Logic and B1.2 Set Theory ,
    (ii) three subjects in Philosophy from
    101-116, 120, 122, 124, 125, 127-129, 137-139 and 198 of which two must be 122 and either 101 or 102, and
    (iii) either two further units in Mathematics drawn from Schedules 1 and 2 combined or one further subject in Philosophy from subjects 101-116, 120, 124, 125, 127-129, 137-139, 198 and 199: Thesis.

Note that the units listed under Schedule 2 are not available to those who wish to offer a total of four Philosophy subjects.

The Schedules of Mathematics units for Mathematics & Philosophy

All units in Mathematics are drawn from the list of options for Mathematics Part B.

Schedule 1 comprises those Mathematics Department courses for which the core and options in Mathematics & Philosophy Part A provide the requisite background.

Schedule 2 contains an Extended Essay option and certain further courses from Mathematics Part B appropriate for the Joint School.

In addition you may apply for special approval to be examined in Mathematics Department units not included under Schedule 1; any such subject approved will be treated as falling under Schedule 2. For the procedure for seeking approval, see below.

For the 2021 examination, the Schedules are as follows. (N.B. All topics listed are units unless otherwise stated).

Schedule 1

  • B1.1 Logic [Compulsory] (MT)
  • B1.2 Set Theory [Compulsory] (HT)
  • B2.1 Introduction to Representation Theory (MT)
  • B2.2 Commutative Algebra (HT)
  • B3.1 Galois Theory (MT)
  • B3.2 Geometry of Surfaces (MT)
  • B3.3 Algebraic Curves (HT)
  • B3.4 Algebraic Number Theory (HT)
  • B3.5 Topology and Groups (MT)
  • B4.1 Functional Analysis I (MT)
  • B4.2 Functional Analysis II (HT)
  • B4.3 Distribution Theory and Analysis of PDEs (MT)
  • B4.4 Fourier Analysis and PDEs (HT)
  • B8.1 Probability, Measure and Martingales (MT)
  • B8.2 Continuous Martingales and Stochastic Calculus (HT)
  • B8.4 Information Theory (MT)
  • B8.5 Graph Theory (MT)
  • SB3.1 Applied Probability (HT)

  • Schedule 2 (additional units)

  • BEE "Mathematical" Extended Essay [double unit] (MT/HT)
  • BO1.1 History of Mathematics [double unit] (MT/HT)
  • BOE "Other Mathematical" Extended Essay [double unit] (MT/HT)
  • OCS1 Lambda Calculus and Types (HT)
  • OCS2 Computational Complexity (HT)
  • OCS3 Knowledge Representation and Reasoning (HT)
  • OCS4 Computer-aided Formal Verification (MT)
  • Any other unit course from the list of Mathematics Department units in Part B for which special approval has been granted.

    Procedure for seeking approval of additional options where this is required

    You may, if you have the support of your Mathematics tutor, apply to the Chairman of the Joint Committee for Mathematics and Philosophy for approval of one or more other options from the list of Mathematics Department units for Part B, including the Statistics and Computer Science options. This list can be found in the schedule of units for Mathematics Part B.

    Applications for special approval must be made through the candidate's college and sent to the Chair of the Joint Committee for Mathematics and Philosophy, c/o Elicia Styler, Mathematical Institute, to arrive by Friday of Week 5 of Michaelmas Term. Be sure to consult your college tutors if you are considering asking for approval to offer one of these additional options.

    Given that each of these additional options, which are all in applied mathematics, presume facility with some or other results and techniques covered in first, second or third year Mathematics courses not taken by Mathematics & Philosophy candidates, such applications will be exceptional.

    You should also be aware that there may be a clash of lectures for specially approved options and those listed in Schedules 1 and 2 and with lectures in Philosophy.

    Registration for Part B Mathematics courses 2020-21

    Students will be asked to register for the options they intend to take by the end of week 10, Trinity Term 2020. It is helpful if their registration is as accurate as possible as the data is used to make teaching resource arrangements. Towards the start of the academic year students will be given the opportunity to make edits to their course registration. Students will then be asked to sign up for classes at the start of Michaelmas Term 2020. Further information about this will be sent via email before the start of term.

    Students who register for a course or courses for which there is a quota should consider registering for an additional course (by way of a "reserve choice") in case they do not receive a place on the course with the quota. They may also have to give the reasons why they wish to take a course which has a quota, and provide the name of a tutor who can provide a supporting statement for them should the quota be exceeded. Where this is necessary students will be contacted by email after they have registered. In the event that the quota for a course is exceeded, the Mathematics Teaching Committee will decide who may have a place on the course on the basis of the supporting statements from the student and tutor, and all relevant students will be notified of the decision by email. In the case of the "Undergraduate Ambassadors' Scheme" students will have to attend a short interview in Week 0, Michaelmas Term.