# Schedule of Units (2022-23)

In Part C candidate take the equivalent of 8 unit sat Part C, with the option to take an additional 1-2 units of mathematics if they wish to do so. Each candidate shall offer one of the following:

(i) Eight to ten units in Mathematics; or

(ii) Six to seven units in Mathematics and one unit in Philosophy; or

(iii) Three to four units in Mathematics and two units in Philosophy; or

(iv) Three units in Philosophy; or

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 101-118, 120, 124, 125, 127, and 128, 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.

All units in the Mathematics Schedule 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.

*Mathematics*

The following are single units unless otherwise stated.

C1.1 Model Theory

C1.2 Godel's Incompleteness Theorems

C1.3 Analytic Topology

C1.4 Axiomatic Set Theory

C2.1 Lie Algebras

C2.2 Homological Algebra

C2.3 Representation Theory of Semisimple Lie Algebras

C2.4 Infinite Groups

C2.5 Non-Commutative Rings

C2.6 Introduction to Schemes

C2.7 Category Theory

C3.1 Algebraic Topology

C3.2 Geometric Group Theory

C3.3 Differentiable Manifolds

C3.4 Algebraic Geometry

C3.5 Lie Groups

C3.7 Elliptic Curves

C3.8 Analytic Number Theory

C3.9 Computational Algebraic Topology

C3.10 Additive and Combinatorial Number Theory

C4.1 Further Functional Analysis

C4.8 Complex Analysis: Conformal Maps and Geometry

C8.1 Stochastic Differential Equations

C8.3 Combinatorics

C8.4 Probabilistic Combinatorics

CCD Dissertations on a Mathematical Topic (double unit)

CCS2 Quantum Processes and Computation

COD Dissertations on the History of Mathematics (double unit)

And also:

Any other unit or double unit course from the list of Mathematics Department units for which special approval has been granted.

*Philosophy*

As for Part B, except for

- the exclusion of Subject 122;

- the substitution of an M-level Thesis for Subject 199.