Cambridge Maths Tripos Questions

Errata

Altered course names

For self-consistency, the course names of the following questions have been altered from how they appear in their original exam papers:

• 2009 Part IB 'Mathematical Methods' questions -> IB 'Methods'
• 2019, 2021 Part II 'Fluids' -> 'Fluids II'
• 2017 Part II 'Topics In Analysis' -> 'Topics in Analysis'
• 2017, 2018 Part II 'Coding & Cryptography' -> 'Coding and Cryptography'

When new questions are added to this site, be wary of the possibility of such variations in course names. (Especially for Part II Fluids).

Anomalies regarding the 2004 Tripos reform

The current Part IB courses 'Markov Chains' and 'Electromagnetism' were Part II courses prior to 2005.

Missings stars, daggers, etc.

Often (always?) these are missing from scanned equations and have to be added manually. The easiest way to do it is to use the unicode symbols: *, †, ‡ as follows:

$$
\tag{*}
T_{\pm}<\infty \Longrightarrow \limsup _{s \rightarrow T_{\pm}}|K(\gamma(\pm s))|=\infty
$$

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FAQ

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General

What is this?

An archive of questions from the Cambridge Mathematics Tripos in handy blog format.

Is this an official University project?

No.

Can you add...?

Maybe! Get in touch using one of the methods below.

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Comments

Can I use LaTeX?

Yes! Use $...$ for inline, and $$...$$ for math blocks. You can even copy and paste LaTeX from the questions and other comments.

Is there a quicker way?

Try Mathpix Snip to convert your handwritten equations into LaTeX.

Can I hide spoilers?

Yes, you do it like this:

<details>
<summary>Spoiler warning</summary>

Hidden text goes here.

</details>

Note that you have to leave a blank line after </summary>.

Why do I need a GitHub account?

The comments live on GitHub discussions and are created by a fork of the wonderful Giscus app.

Why can't I edit / delete a comment?

This is not implemented yet in Giscus, but you can click through to the comment on GitHub and edit / delete there.

Can I attach an image?

This isn't yet supported by the GitHub discussions API. If you add an image on GitHub, however, it will show up here.

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Technical

How was it made?

The original PDFs were converted to markdown / LaTeX using the Mathpix API. The blog itself is built using Eleventy and is based on the Eleventy Duo template. It's hosted on Netlify.

Can I contribute?

Yes! The code is on GitHub. You can join the discussion on new ideas, open an issue, or submit a pull request.

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Getting Started

• Install dependencies with yarn install

• Serve the site locally with yarn dev

• Use yarn build to build a production version of the site.

• You may need to use node --max-old-space-size=6000 ./node_modules/@11ty/eleventy/cmd.js to stop Node running out of memory due to the large amount of content.

• If you only wish to test a part of the site, it is advisable to remove unneeded question files from your local clone of this repository.

TODOs

• Deployment

• Add KaTeX copy-tex extension.

• Fix missing subjects

• First 2011 IB question is messed up (course list wasn't removed)

• Add descriptive <title> and og:title that can be used by Giscus

• Social media card for each question for posting on Twitter, Discord, etc.

• Update "powered by giscus" and add KaTeX message

• Add comment counts for giscus. This seems a bit harder see this PR

• Fixing images that don't need to be images because they are imperfectly converted text

• Downloading images from Mathpix CDN.

• Missing dagger in 1.II.6B (2005)

• Add "comment on" to each question in post list

• Add Google analytics

• Add tripos domain

• SEO and keywords

• Titles and descriptions meta tags still not working for question lists

• Spoiler rendering in comments