BA/MMath in Mathematics & Philosophy Handbook (2025-26 Entry)
B Recommended Patterns of Teaching 2025-26
Prelims (Year 1)
Course structure: The table summarises the courses taken for Prelims.
| Paper | Term | Department | College | Comments | ||
|---|---|---|---|---|---|---|
| Lectures | Classes | Tutorials | Classes | |||
| Introduction to University Mathematics (MI) | MT | 8 | 2 | Weeks 1-2 | ||
| Introduction to Complex Numbers (MII) | MT | 2 | 0 | Week 1 only | ||
| Linear Algebra I (MI) | MT | 14 | 4 | |||
| Analysis I (MII) | MT | 15 | 4 | |||
| Introductory Calculus (MIII(P)) | MT | 16 | 4 | |||
| Probability (MIII(P)) | MT | 16 | 4 | Lectured by Dept. of Statistics. | ||
| Linear Algebra II (MI) | HT | 8 | 2 | |||
| Groups and Group Actions (MI) | HT | 8 | 2 | |||
| TT | 8 | 2 | ||||
| Analysis II (MII) | HT | 16 | 4 | |||
| Analysis III (MII) | TT | 8 | 2 | |||
| Introduction to Logic | MT | 8 | ||||
| Philosophical Topics in Logic and Probability | HT | 8 | ||||
| General Philosophy | MT | 8 | ||||
| Frege, Foundations of Arithmetic | TT | 8 | ||||
Notes:
All first year lecture courses are supported by tutorials organised by colleges. The normal expectation is that a 16-hour lecture course is supported by 4 one-hour tutorials or the equivalent in small classes. It may be the case that a tutorial or class addresses several lecture courses, rather than being solely dedicated to a single lecture course.
Part A (Year 2)
Course structure: There are 2 compulsory core courses (A0 and A2), 5 options courses (A3-A5, A8 and ASO) from which students choose 2. ASO comprises 6 short options from which students usually study 3 courses. These are studied alongside the Philosophy papers discussed in 3.6.
| Paper | Term | Department | College | Comments | ||
|---|---|---|---|---|---|---|
| Lectures | Classes | Tutorials | Classes | |||
| A0 Linear Algebra | MT | 16 | 4 | |||
| A2 Metric Spaces and Complex Analysis | MT | 32 | 8 | |||
| A3 Rings and Modules | HT | 16 | 4 | |||
| A4 Integration | HT | 16 | 4 | |||
| A5 Topology | HT | 16 | 4 | |||
| A8 Probability | MT | 16 | 4 | Lectured by Dept. of Statistics. | ||
| A13 Geometry | HT | 16 | 4 | |||
| ASO Number Theory | TT | 8 | 2 | Weeks 1-3 | ||
| ASO Group Theory | TT | 8 | 2 | Weeks 1-3 | ||
| ASO Integral Transforms | HT | 8 | 2 | Weeks 1-4 | ||
| ASO Graph Theory | TT | 8 | 2 | Weeks 1-3 | ||
| ASO Calculus of Variations | TT | 8 | 2 | Weeks 1-3 | ||
| ASO Mathematical Modelling in Biology | TT | 8 | 2 | Weeks 1-3 | ||
Notes: All second year lecture courses are supported by tutorials organised by colleges. The normal expectation is that a 16-hour lecture courses is supported by 4 one-hour tutorials or the equivalent in small classes.
Part B (Year 3)
Course structure: Students take 4 units of Mathematics from Schedule 1, two of which shall be B1.1 Logic and B1.2 Set Theory, 3 papers in Philosophy and either 2 further units in mathematics from schedules 1 and 2 combined or 1 further paper in Philosophy. The 3 or 4 Philosophy papers are studied during both second and third year.
| Paper | Term | Department | College | Comments | ||
|---|---|---|---|---|---|---|
| Lectures | Classes | Tutorials | Classes | |||
| Mathematical Units - Schedule 1 | ||||||
| B1.1 & B1.2 | MT/HT | 16 | 6 | Compulsory units | ||
| B2.1, B2.2, B2.3, B3.1, B3.2, B3.3, B3.4, B3.5, B4.1, B4.2, B4.3, B8.1, B8.2, B8.3, B8.4, B8.5, B8.6 | MT/HT | 16 | 6 | |||
| SB3.1 Applied Probability | MT | 16 | 6 | Taught by Dept. of Statistics | ||
| Mathematics Units - Schedule 2 | ||||||
| BO1.1 History of Mathematics * | MT | 16 | 6 | |||
| HT | 12 | Reading course consisting of 8 seminars | ||||
| BOE Other Mathematical Extended Essay | MT/HT | 2 | 6 | The balance of tutorials between MT and HT is agreed between the student and supervisor. | ||
| Computer Science Units | ||||||
| Lambda Calculus and Types | HT | 16 | 7 | Taught by Dept. of Computer Science | ||
| Computational Complexity | HT | 16 | 6 | Taught by Dept. of Computer Science | ||
| Knowledge Representation and Reasoning | HT | 16 | 6 | Taught by Dept. of Computer Science | ||
| Computer-aided Formal Verification | MT | 16 | 6 | Taught by Dept. of Computer Science | ||
Notes: In Part B, intercollegiate classes are arranged in place of college tutorials for the Mathematics, Statistics and Computer Science lecture courses. For some lecture courses, there may not be sufficient students to run an intercollegiate class and tutorials will be arranged instead. It is recommended that 4 hours of tutorials are provided for a 16-hour lecture course. Colleges may decide to opt out of the intercollegiate class scheme and teach their students in tutorials for a particular course. In addition to those classes, drop-in consultation sessions are arranged in Trinity term by way of revision for those lecture courses assessed by written examination. Please note that courses marked with * are double units.
Part C (Year 4)
Course structure: Students take equivalent of 8 units at Part C, with the option to take an additional 1-2 units of mathematics if they wish to do so. Students shall take one of the following: 8-10 units in Mathematics; or 6-7 units in Mathematics and 1 in Philosophy; or 3-4 units in Mathematics and 2 units in Philosophy; or 3 units in Philosophy
| Paper | Term | Department | College | Comments | ||
|---|---|---|---|---|---|---|
| Lectures | Classes | Tutorials | Classes | |||
| Mathematical Units | ||||||
| C1.1, C1.2, C1.3, C1.4, C2.2, C2.3, C2.4, C2.5, C2.6, C2.7, C3.1, C3.2, C3.3, C3.4, C3.5, C3.6, C3.7, C3.8, C3.9, C3.10, C3.11, C3.12, C4.1, C6.5, C7.5, C8.1, C8.3, C8.4 | MT/HT | 16 | 6 | |||
| CCD Dissertation on a Mathematical Topic * | MT/HT | 2 | 6 | The balance of tutorials between MT and HT is agreed between the student and supervisor. | ||
| COD Dissertation on the History of Mathematics * | MT/HT | 2 | 6 | The balance of tutorials between MT and HT is agreed between the student and supervisor. | ||
| Computer Science Units | ||||||
| Categories, Proofs and Processes | MT | 20 | 7 | Taught by Dept. of Computer Science | ||
| Quantum Computer Science | MT | 24 | 7 | Taught by Dept. of Computer Science | ||
| Automata, Logic and Games | HT | 24 | 7 | Taught by Dept. of Computer Science | ||
| Computational Learning Theory | MT | 24 | 4 | Taught by Dept. of Computer Science | ||
Notes: In Part C, intercollegiate classes are arranged in place of college tutorials for the Mathematics, Statistics and Computer Science lecture courses. For some lecture courses, there may not be sufficient students to run an intercollegiate class and tutorials will be arranged instead. It is recommended that 4 hours of tutorials are provided for a 16-hour lecture course. Colleges may decide to opt out of the intercollegiate class scheme and teach their students in tutorials for a particular course. In addition to those classes, drop-in consultation sessions are arranged in Trinity term by way of revision for those lecture courses assessed by written examination. Please note that courses marked with * are double units.
Please note that in the case of teaching provided by colleges, these figures are the departmental recommendations only and individual colleges may provide different amounts of types of teaching than those states above for a variety of reasons (e.g. individual student needs or differing number of contact hours depending on tutorial group size).