Mathematics at Cambridge Dr Chris Warner College Teaching Officer and Director of Studies in Mathematics Aspiration and Challenge Consultant Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

The Mathematics Tripos One of the most rewarding (and most demanding) undergraduate mathematics courses in Britain We are looking for applicants who have outstanding academic potential and will thrive at Cambridge Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

What does it take? A lively interest in mathematics Mathematics education to at least AS Further Mathematics Good organisational skills Tenacity and drive for excellence The potential for high achievement Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Maths Courses at Cambridge First year Largely compulsory courses including: rigorous mathematical analysis mathematical methods such as vector calculus Newtonian dynamics and special relativity probability and number theory Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Maths Courses at Cambridge Second year Core curriculum and more choice of courses: algebra analysis mathematical methods theoretical physics statistics optimisation computational projects Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Maths Courses at Cambridge Third year many choices with guidance from Director of Studies most students leave with BA Fourth year students with a First Class or equivalent performance may continue to MMath pre research level courses Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

How mathematics is taught at Cambridge “Intense” Lectures are few in number each course takes around 24 hours first year mathematics examination material is covered in 192 lectures Supervisions cover about 6 lectures of work in one hour There are 20 weeks of lectures in the first two years Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

How Mathematics is Taught at Cambridge Lectures no real opportunity to ask questions little participation from students Sets of questions to try for each course called “examples sheets” set at the rate of about one for every 5—7 lectures no solutions given Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Lectures Cover material so fast that it is rarely possible to fully understand it during the lecture there is a need to work on the lectured information later there is a need to concentrate hard so that as much is understood as possible at the time some parts of the course only become really clear on later revision Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

How Mathematics is Taught at Cambridge Supervisions based on the examples sheets two students in most cases one hour in duration each course has its own specialist supervisors (teachers) supervisor is a Professor, Lecturer, Postdoctoral Student or Postgraduate Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Nature of Mathematics Courses at Cambridge Different from A level / IB in that we only do things once the pure courses are much more rigorous the language of mathematics is much more compact we cover a lot of topics very quickly there are lots of totally new mathematical topics Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

A typical week for a First Year Mathematics Student minutes Mon Tue Wed Thu Fri Sat 9:00 10:00 L: VC L: A 11:00 L: P L: DR 12:00 14:00 Review 15:00 16:00 Prepare VC/DR Super VC/DR Super Analysis Super S:VC/DR Analysis 17:00 18:00 S:P Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

How Mathematics is Examined at Cambridge Four examination papers at the end of each year of study alpha quality mark for a mark of 15/20 or more on a long question beta quality mark for a mark between 10/20 and 14/20, inclusive on a long question 7/10 or more on a short question Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

How Mathematics is Examined at Cambridge First year examinations one pure and one applied course in each paper Second and third year examinations at most one long question and one short question in each paper Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

How Mathematics is Examined at Cambridge Merit marks 𝑀=30𝛼+5𝛽+𝑚−120 for 𝛼≥8 𝑀=15𝛼+5𝛽+𝑚 for 𝛼≤8 where 𝛼 is the number of alpha marks, 𝛽 is the number of beta marks and 𝑚 is the number of raw marks these are used to determine degree class in examinations Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Why are examination structure and Merit marks relevant? examinations reward largely correct answers students need to be good at working quickly and accurately students need to be outstanding at their favourite courses students do not need to reach a high standard in their least favourite courses students can attend courses and do not need to take exam questions in them Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Why are examination structure and Merit marks relevant? students can attempt questions on courses that they have not formally studied spreading yourself thinly over many courses is not a good strategy Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Admissions process Varies a little from College to College but Robinson is fairly typical and you get: A College mathematics test of 1 hour Two subject interviews and two subject interviewers Some general or tutorial questions in one interview Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

So, how to prepare? Work on independent learning ability to learn from a textbook or other resource willingness to struggle with a problem for some time before seeking help ability to write the language of mathematics grammar structure tidiness! strength of character to struggle with a problem before referring to examiner’s solution Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

So, how to prepare? Develop problem solving skills ability to do problems without “scaffolding” Teachers can really help here by stripping out “scaffolding” or sourcing questions from old A level texts which tend to have less structured questions looking for similar problems in a text book writing down thoughts that express the reasons for not being able to go further Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

So, how to prepare? Develop problem solving skills willingness to try later, sometimes several times seeking help e.g. from a friend for suggestions, not solutions checking to make sure of understanding – particularly important when a similar problem is used as a “template” Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

So, how to prepare? Learn how to work quickly and accurately try doing examinations in half the time try doing sets of problems very quickly … and still get the correct answer Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

So, how to prepare? Especially for interviews: practise skills until very fluent with their use e.g. can do integration by parts fast and accurately try solving physics problems using calculus e.g. SUVAT equations, forces and energy practise graph plotting including turning points Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org

Offers Vary a little from College to College but Robinson is fairly typical: Standard offer is A*A*A and STEP 1,1 or 1,2 in papers II and III A-level Further maths needed STEP is sat in schools in the summer (usually) after A levels Robinson College Dr Chris Warner cdw13@cam.ac.uk and chris@chriswarner.org