how to get better at Cambridge maths

I’ve recently been asked twice by first-year Cambridge maths students how to get good at maths. While I did reply to one of them with advice specific to their situation, this is a good topic for a simple, informative post. (Definitely not meant to be my best post – it won’t be, I have covid as I write this.)

[As an aside, from my perspective having gone through the four years of the Cambridge maths system, aiming to get better at “Cambridge maths exams” is quite a narrow-minded approach and I’m sure everyone would be better off in the long run by focusing on other measures of success. But I definitely understand their situation, having been there myself in the past: it’s the “tunnel vision” that one often gets here.]

Advice

Improvement Steps

1. Work more
2. Work better
3. Work less

I think every piece of advice I’d have can be summarised in one of these three categories. I don’t know you, so I don’t know which bit is the one that would be more helpful. If you can’t really tell which is the one you need, I suggest trying first to work more, then to work better and finally to work less. And see how that goes.

The order is up to debate but, in my opinion (as a student and now supervisor), many first-year Cambridge mathmos come here thinking that their degree will be as easy as A-Levels were for them. The issue is especially aggravated by the university lifestyle, low-contact hours and little accountability mechanisms. An interesting case to watch out for are students for whom their previous study routines worked at the start of their degree until they reach a breaking point (eg in their second term).

Working more

It’s pretty self-descriptive, but a non-exhaustive list of ideas for things one should/could do (in no particular order of importance):

• Go through your notes after each lecture
• Revise your notes before each lecture
• Find extra problems in textbooks
• Try to find a second method for solving the questions in the example sheet.
• Spend longer at each question you seem unable to solve
• Do (more) past papers
• Look out for lecture notes of older versions of the course, to see if they have relevant but different content
• Do questions which appeared in past versions of the example sheets.
• Ask your supervisor for extra practice problems

Working better

This is what people often call “work smart not hard”.

• Use Anki
• Or make your own paper flashcards
• Anything from my notes on how to make the most out of supervisions
• Put your phone away!
• Turn off email (and messenger etc) notifications in your laptop (if you use it to study)
• Use pomodoros to focus
• Teach what you are learning to others
• Discuss what you are learning (or struggling to learn!) with other students
• Prioritise which questions/topics to spend time on
• Be organised (there’s so much I could say about this, that I just won’t say anything more)

working less

This is the good old “take a break!”. Working smart is tiring, and sometimes all you need is more rest.

• Rest during your pomodoro breaks
• Take Sundays off from maths
• Exercise everyday
• Do something every day/week that you find rewarding and is not maths
• Take a break from what you are learning right now, and spend X time learning about something just because it is interesting (doesnt have to be maths)
• Anything from https://www.neelnanda.io/blog/29-meaningful-rest

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Other resources:

• Notes I made for an informal revision talk and Q&A: https://docs.google.com/document/d/1RFKdoSrRLSPOECIpi6HgB6b9pKiQfSJgCGvdxfUx4KA/edit?usp=sharing
• https://www.neelnanda.io/blog/34-learning

I’m sure there are many other good resources out there. I might update the list.