BA/MMath in Mathematics Handbook (2025-26 Entry)
7. Teaching and Learning
7.1 The Department and the Colleges
Oxford University is a collegiate university. All undergraduates are members of both a college and the University. Courses, syllabi, lectures and examinations are organised and delivered by the University. Colleges deliver tutorial and class teaching, and are generally responsible for the academic and personal well-being of their students.
In a college there will usually be two or more subject tutors to select students, deliver tutorials and class teaching and generally guide students through their studies. Usually at the beginning of each term, a student will meet their subject tutor(s) to discuss selection of options and to make and receive information on teaching arrangements, etc. Your subject tutor(s) will monitor your academic progression through each term and will receive reports from other tutors who will teach you through Moodle.
The Mathematical Institute contains lecture theatres and seminar rooms in which undergraduate lectures and intercollegiate classes are given. Most matters concerned with the administration of the Mathematics courses are dealt with in the Institute - for example the setting of synopses, lecture timetables and lecture notes. If you have comments relating to departmental provision or any issues with teaching or supervision, please raise these as soon as possible with the relevant contact in Appendix E.
7.2 An Average Week
Students are responsible for their own academic progress. Typically, your tutors will be expecting you to work around 40 hours per week during term time. This may vary a little from week-to-week, depending on how you are finding the material. You are advised to read the University's guidance on undertaking paid work at https://www.ox.ac.uk/students/life/experience.
Of these 40 or so hours, around 10 will be lectures, and 2-3 will be tutorials or classes. This means the remaining 25+ is unassigned, to be filled by your own independent study. A table setting out the recommended patterns of teaching for each year of the course is included in Appendix B.
You should seek advice from your tutor if you find it impossible to complete your academic work without spending significantly longer than 48 hours per week on a regular basis.
It is important that you quickly get into a mode of learning that suits you. In an effort to help structure this independent study, the first year lecturers produce five weekly exercise sheets (one per two lectures) that will form the basis of tutorials. This means that roughly 5 hours should be assigned to each sheet. From the second year onwards there will be one sheet per four lectures, so you should be spending closer to 10 hours per sheet.
Success on the course is not simply a matter of completing these sheets. The exercises will be chosen as a guide to what you need to know and to demonstrate how the material hangs together; these are their aims. Some of the exercises you may find routine and quickly solve; others will take longer to crack, perhaps only on your third or fourth attempt. Do not be surprised if some of the final questions prove too difficult to complete, but you should have attempted everything. Ultimately the problems you have had will be addressed in the next tutorial.
The main ingredient for success in mathematics at university is committed independent study. It is the breaking down of subtle analytical problems yourself, the appreciation of how method and theory connect, the necessary organisation and perseverance that the course requires, which ultimately makes our students successful both during their time at Oxford, as well as after graduation.
7.3 Vacations
You should expect to spend some time in the vacations consolidating and revising the material covered in the preceding term. You may also have one or two problem sheets to complete during the vacation or some pre-reading or work in preparation for the next term. In some vacations you will need to revise for examinations (which may be college collections or University examinations).
7.4 Lectures and how to get the best out of them
All official lectures are advertised in the termly lecture timetable (see section 1.2). Lectures are usually timetabled to last an hour but there is a convention for undergraduate lectures to commence a few minutes after the hour and likewise finish a few minutes before the hour to allow for students to move in and out of the room.
All lecture livestreams and recordings will be available via the course materials page (video capture) at the following link: https://courses.maths.ox.ac.uk/
When we think of traditional university teaching, we think of lectures. They are an integral part of learning at university, but initially they will prove to be an unfamiliar and perhaps alien means of communicating mathematics. You will need to be disciplined, motivated and committed in order to get the best out of them. For mathematics, they are an important and effective way of conveying information. Most mathematicians find it easier to learn from lectures rather than books.
It is inevitable that you will not be able to take in everything all at once in a lecture, so you should revisit the lecture material using the lecture recordings or other materials provided by the lecturer in your own time to improve your knowledge and understanding.
Unsurprisingly, different lecturers will have different styles, and topics in mathematics may warrant slightly different ways of teaching. Some lecturers will provide lecture notes, posted online, but it is a good idea to take your own notes, so you stay attentive during a lecture and understand how a calculation or argument follows from another. Note-taking is a valuable, transferrable skill. It is sensible to keep your lecture notes together with tutorial notes, problem sheets, and mark solutions etc. so that they can be easily referenced afterwards for further study and revision.
Try not to fall behind with a topic: if a course has not gone well during the term, spend some extra time over the vacation catching up. The mathematics you meet in your first year, complicated though it may seem now, will appear rather routine a year later (probably in less time than that) and it is only by repeatedly familiarising yourself with its ways and patterns that this will become so.
If you have missed a number of lectures through illness or other reasons, please consult with your College Tutor for advice on catching up missed work.
7.5 Problem Sheets
All lectures in Mathematics are supported by problem sheets compiled by the lecturers. They are available for downloading from the Mathematical Institute website. Many college tutors use these problems for their tutorials; others prefer to make up their own problem sheets. In Part B, problem sheets will be used for the intercollegiate classes run in conjunction with the lectures.
Many of the books recommended in the reading lists contain exercises and worked examples; past papers and specimen papers are another source of such material, useful for revision.
7.6 Tutorials (Prelims and Part A)
To support lectures in the first and second years, colleges arrange tutorials and classes for their students. How these are organised vary from college to college. For example, you might have two (one-hour) tutorials each week, with one or two other students. Consequently, it is a highly individual and flexible way of teaching and tutorial groups are usually arranged to include students that work well together, and perhaps, who are progressing academically at the same rate.
You will be set some work for each tutorial and in the tutorial you will discuss the work and be able to ask about any difficulties you have experienced. In order to get the best out of a tutorial, it is important that you are well prepared and also that you see the tutorial as an opportunity to get resolved all the problems you encountered that week. A tutorial is, after all, an hour with an expert in that area. Your tutor is highly unlikely to give up the answer to your question immediately and may respond with hints or questions of their own, but this is all towards improving your understanding of the material and showing you how you might have made further progress with the problem yourself.
7.7 Classes (Part B)
Each 16-hour lecture unit in Part B will be supported by classes run under the Intercollegiate Class Scheme. Students generally attend four 1.5 hour classes (or equivalent) for each Part B unit. In Michaelmas term 2025-26, all classes will run face-to-face. Each class usually has between five and twelve students (although classes for more popular subjects may contain up to thirty students) from a number of different colleges and is run by a class tutor and a teaching assistant. The course lecturer provides problem sheets, and also specimen solutions for the class tutors and teaching assistants. Students hand in their solutions in advance and these are marked by the teaching assistants; at each class, some of the problems are discussed in detail, and there is an opportunity to ask the class tutor and teaching assistant about any particular difficulties. The class tutors report to colleges through the intercollegiate class database on your performance throughout the term. If you are ill and unable to attend the class, please inform the class tutor in advance of the class.
Consultation sessions to help with revision are run during Trinity term.
7.8 Undergraduate Projects
Projects give students the opportunity to develop valuable skills - collecting material, explaining it, expounding it clearly and persuasively, and using citations. Projects are also an opportunity to pursue a topic of particular interest and allow students to show their mathematical understanding and progress via a sustained piece of exposition.
7.8.1 Projects in the Undergraduate Course
You can choose to undertake project work as one or more of the optional courses studied in Part B. These options cover the whole spectrum of mathematics and include topics related to mathematics, such as the history of mathematics and mathematics education. Information on the different options can be found at https://www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/part-b-students/projects. In 2025-26, all submitted assessments such as projects will be submitted online via Inspera by the relevant deadline. Full information is provided here: https://www.ox.ac.uk/students/academic/exams/submission.
7.8.2 Extracurricular Projects
There are also opportunities to undertake extracurricular projects, such as summer projects, during your studies. These projects are an excellent opportunity to gain experience of mathematical research.
Various bursaries become available each year supporting undergraduates in project work during the long vacation in Oxford. These are usually aimed at students at the end of their second or third years. What is offered varies from year to year; usually the department's Academic Administration team will circulate details of these opportunities by email.
Further details about extracurricular projects can be found at: https://www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/projects/extracurricular-projects
7.9 Practicals
For some of the units there is a component of compulsory practical work. Arrangements will be explained by the course lecturer; your college tutor will also advise. Those who run the practical sessions will also give advice on how the work is to be written up.
7.10 History of Mathematics
You are encouraged to read around your subject, and it can be very beneficial to look through texts, other than the main recommended text(s), to see a treatment of the material other than your lecturer's and your tutor's. College libraries will usually have such texts.
It can also help to have a sense of the subject's history and development. There is a History of Mathematics option in the third year, but otherwise you will find (because of time constraints) that lecturers largely focus on teaching the current syllabus and have little time to comment on historical sidelines. We include here a short list of books recommended by tutors, for you to dip into.
H Dorrie, 100 Great Problems of Elementary Mathematics Dover (1965)
J Fauvel, R Flood & R Wilson, Oxford figures: 800 years of the mathematical sciences OUP (2000)
E M Fellmann, Leonhard Euler Birkhauser (2007)
M Kline, Mathematics in Western Culture Penguin (1972)
M Kline, Mathematical Thought from Ancient to Modern Times OUP (1972)
V Katz, A History of Mathematics: An Introduction Second Edition, Addison-Wesley (1998)
J Stillwell, Mathematics and Its History Third Edition, Springer (2010)
D Struik, A Concise History of Mathematics Dover Paperback (1946)