# Part A Mathematics & Philosophy 2019-20

The confirmed synopses for Part B 2020-21 will be available on the course management portal https://courses.maths.ox.ac.uk/ before the start of Michaelmas Term 2020.

**Three or Four Year Course**

All students who complete Parts A and B will be classified. Those who have achieved honours and who wish to graduate at this point may supplicate for a BA.

Students wishing to take the four-year course should register to do so at the beginning of their third year, and will be permitted to do so on the basis of an upper second class performance, or better, in the third year classification. They will take Part C in their fourth year, be awarded a separate classification and, if successful, may supplicate for an MMath.

The syllabus details below are those referred to in the *Examination Regulations* and have been approved by the Mathematics Teaching Committee for examination in Trinity Term 2020. Please see the current edition of the *Examination Regulations* (https://www.admin.ox.ac.uk/examregs/) for the full regulations governing these examinations. Examination Conventions can be found at: https://www.maths.ox.ac.uk/members/students/undergraduate-courses/examin....

The Part A examination **syllabus** is the mathematical material of the synopses, as separately detailed by paper below. The course synopses on the course webpages also give additional detail to the syllabus (for example, showing how the material is split by lectures) and are also accompanied by lists of recommended reading.

**Honour School of Mathematics and Philosophy - Part A**

In Part A each candidate shall be required to offer four written papers in Mathematics from the schedule of papers for Part A (given below).

These papers must include:

- A0 - Linear Algebra (1.5 hours)
- A2 - Metric Spaces and Complex Analysis (3 hours)

and two of the following papers (each 1.5 hours long).

- A3 Rings and Modules
- A4 Integration
- A5 Topology
- A8 Probability
- ASO Short Options

Paper ASO will examine the nine Short Options (Number Theory, Group Theory, Projective Geometry, Introduction to Manifolds, Integral Transforms, Calculus of Variations, Graph Theory, Special Relativity, and Mathematical Modelling in Biology). Students taking ASO are recommended to take three of these Short Options.

Part A shall be taken on one occasion only (there will be no resits). At the end of the Part A examination a candidate will be awarded a `University Standardised Mark' (USM) for each Mathematics paper in Part A. A weighted average of these USMs will be carried forward into the classification awarded at the end of the third year. In the calculation of any averages used to arrive at the final classification, USMs for A2 will have twice the weight of the USMs awarded for A0, the Long Options and Paper ASO.

**Core Material**

The examination syllabi of the two core papers A0 and A2 shall be the mathematical content of the synopses for the courses

- Linear Algebra,
- Metric Spaces and Complex Analysis.

**Options**

The examination syllabi of the four papers of options, A3, A4, A5 and A8, shall be the mathematical content of the synopses for the courses

- Rings and Modules,
- Integration,
- Topology,
- Probability,

and such other options from Mathematics Part A as are approved by the Joint Committee of Mathematics and Philosophy.

**Short Options**

The examination syllabi of the short options paper ASO shall be the mathematical content of the synopses for the courses

- Number Theory,
- Group Theory,
- Projective Geometry,
- Introduction to Manifolds,
- Integral Transforms,
- Calculus of Variations,
- Graph Theory,
- Special Relativity,
- Mathematical Modelling in Biology.

Candidates may also, with the support of their college tutors, apply to the Joint Committee for Mathematics and Philosophy for approval of other Optional Subjects as listed for Part A of the Honour School of Mathematics.

**Procedure for seeking approval of other 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 options for Part A. This list can be found in the schedule of units for Part A Mathematics 2019-20.

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 Nia Roderick, Mathematical Institute, to arrive by **Monday of Week 2 of Hilary Term**. Be sure to consult your college tutors if you are considering asking for approval to offer one of these other options.

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