# Part C Mathematics & Philosophy 2019-20

Foreword:

This Supplement to the Course Handbook specifies the Mathematics courses available for Part C in Mathematics & Philosophy in the 2020 examination. It should be read in conjunction with the Handbook for Mathematics & Philosophy for the academic year 2019-2020 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 C.

See the current edition of the Examination Regulations (http://www.admin.ox.ac.uk/examregs/) for the full regulations governing the examinations.

Part C of the Honour School of Mathematics & Philosophy

The following is reproduced from the Examination Regulations applicable to the 2020 examinations.

In Part C each candidate shall offer one of the following:

(i) A minimum of eight units and a maximum of ten units in Mathematics;
(ii) A minimum of six units and a maximum of ten units in Mathematics and one unit in Philosophy;
(iii) A minimum of three units and a maximum of four units in Mathematics and two units in Philosophy;
(iv) Three units in Philosophy;

from the lists for Mathematics and for 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. No unit in Mathematics, and no subject in Philosophy (apart from the thesis), may be offered in both Part B and Part C.

A unit in Philosophy consists of one of the following:

(a) One of the subjects 101-116, 120, 124, 125, 127-129, and 137-139, as specified in the Regulations for Philosophy in all Honour Schools including Philosophy. For Part C, these subjects shall be examined by a three-hour written paper together with a Part C Philosophy Essay of at most 5000 words.
(b) A Special Subject 198, as specified in the Regulations for Philosophy in all Honour Schools including Philosophy.
(c) A Part C Philosophy Thesis.
(d) A Special Subject in Philosophy as approved by the Joint Committee for Mathematics and Philosophy by regulations published in the University Gazette and communicated to college tutors by the end of the fifth week of Trinity Term in the year before the Part C examination in which it will be examined. No candidate may offer more than one Special Subject in Philosophy in Part C. In approving a Special Subject in Philosophy for Part C, the Joint Committee for Mathematics and Philosophy may specify that candidates will not be permitted to offer certain Special Subjects in combination with certain other subjects, or will be permitted to do so only on condition that in the papers on the other subjects they will not be permitted to answer certain questions. Subject to these qualifications, any candidate may offer any approved Special Subject.

The Schedule of Mathematics units for Mathematics & Philosophy

All units in the Schedule below are drawn from the list of Mathematics Department units and "Other" units available in Mathematics Part C.

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

For the 2020 examination, the Schedule is as follows. (N.B. All topics listed are units unless otherwise stated).

Schedule

• C1.1 Model Theory (MT)
• C1.2 Gödel's Incompleteness Theorems (HT)
• C1.3 Analytic Topology (MT)
• C1.4 Axiomatic Set Theory (HT)
• C2.1 Lie Algebras (MT)
• C2.2 Homological Algebra (MT)
• C2.3 Representation Theory of Semisimple Lie Algebras (HT)
• C2.4 Infinite Groups (MT)
• C2.5 Non-Commutative Rings (HT)
• C2.6 Introduction to Schemes (HT)
• C2.7 Category Theory (MT)
• C3.1 Algebraic Topology (MT)
• C3.2 Geometric Group Theory (HT)
• C3.3 Differentiable Manifolds (MT)
• C3.4 Algebraic Geometry (MT)
• C3.5 Lie Groups (HT)
• C3.7 Elliptic Curves (HT)
• C3.8 Analytic Number Theory (MT)
• C3.9 Computational Algebraic Topology (HT)
• C3.10 Additive and Combinatorial Number Theory (HT)
• C4.1 Further Functional Analysis (MT)
• C4.8 Complex Analysis: Conformal Maps and Geometry (MT)
• C8.1 Stochastic Differential Equations (MT)
• C8.3 Combinatorics (MT)
• C8.4 Probabilistic Combinatorics (HT)
• CCD Dissertations on a Mathematical Topic [double unit] (MT/HT)
• CCS1 Categories, Proofs and Processes (MT)
• CCS2 Quantum Computer Science (MT)
• CCS3 Automata, Logic and Games (HT)
• CCS4 Computational Learning Theory (MT) (The listed pre-requisites for this course are intended as useful, rather than strict requirements. Students uncertain about the background required for the course should email the lecturer.)
• COD Dissertations on the History of Mathematics [double unit] (MT/HT)
• $\mbox{}$
And also any other unit course from the list of Mathematics Department units 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 Chair 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 C. This list can be found in the schedule of units for Mathematics Part C.

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 Academic Administrator, 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 or second 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 the above Schedule and with lectures in Philosophy.

Registration for Part C Mathematics courses 2019-20

Students will be asked to register for the options they intend to take by the end of week 10, Trinity Term 2019. It is helpful if their registration is as accurate as possible as the data is used to make arrangements for teaching resources. 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 2019. Further information about this will be sent via email before the start of term.