Cambridge Maths Students and Applicants

Original post by Pyoro

While I was in Churchill (2013–16), it was unheard of. I spoke to someone at an open day (summer 2012) who was moving from part II maths to part III astro/physics, from Christ's to Pembroke. But I don't remember why, or know if it's always possible.

The why is easy; why wouldn't anyone move to Pembroke given the opportunity?

The how is harder to answer. At minimum I know this is possible to do between Part III and PhD, as you get to give collegiate preferences on the application form. Whilst I have asked to stay at the same college if the department gives me an offer, I do have a friend from Queens' who currently has a conditional PhD offer at Corpus.

Reply 6363

Original post by aem157

How are the courses in IA roughly ordered in terms of difficulty?

I would order them as follows based on the idea that "methods" courses are easier than applied courses which are easier than pure, but only knowing a level maths this is probably slightly inaccurate:
differential equations
vector calculus
dynamics and relativity
probability
numbers and sets
vectors and matrices
groups
analysis I

I don't think there's a sensible ranking. It all depends on an individuals particular strength and what you're basing difficulty off: exam question difficulty, course material difficulty (how to measure that?), example sheet difficulty (differs from year to year), etc...

For example, if we were to go off on only the material covered, Numbers and Sets would be a lot higher in than list, it's very elementary. Yet, some of the exam/example sheet questions can be made hard. So where to place it?

Someone who prefers pure would place Dynamics and Relativity a lot lower than you have, and analysis and groups a lot higher. You see the conundrum?

(edited 7 years ago)

Reply 6364

https://www.maths.cam.ac.uk/undergrad/course/schedules.pdf ?

Original post by aem157

tl;dr: Could someone please post a list of courses in the maths tripos and the prerequisites for each one?

Reply 6365

shamika

Original post by aem157

Can't work out the prerequisites on my own unfortunately.

I'm not sure how Zacken (or anyone else) can help if you can't (or won't) read through the details of what's in each course.

If you're not at uni yet, to get into Cambridge you need to do A-Level maths (and at least AS Further Maths) or equivalent in IB, Scottish highers or whatever the exams are in the country of your choice. You'll also need to be able to pass STEP. That's enough to get you through the first term courses. After that you'll need some stuff they teach you in the first term in the second, first year stuff for second year and so on. If you have a specific question I'm sure someone will try to answer it but it's hard to understand what you're actually after.

Reply 6366

username937760

Original post by aem157

Thank you for your reply. That definitely makes sense, yes, but I probably should have made myself clearer and used the word "complexity" instead of "difficulty" as that is closer to what I meant. I believe that branches of maths can certainly be classified in terms of complexity based on their prerequisites. So for example elementary number theory (of the type found in numbers and sets say) would be more "complex" than elementary algebra, which it assumes. (This is why I placed methods lowest.) In short, I am trying to ignore the actual structure of the courses (example sheets, exams, etc) and focus on the material itself.

tl;dr: Could someone please post a list of courses in the maths tripos and the prerequisites for each one?

For such a list of prerequisites, unless you plan on invoking buzzwords like elementary (which loses all meaning when everything is elementary according to 99% of professors), you're after a detailed list of necessary lemmas, theorems, concepts and so on which would take an age to compile - simply saying e.g. "Number Theory is required" is not specific enough to get something you can compare by.

Even assuming someone were going to compile this list, it's meaningless unless you understand everything on said list. Certain theorems with little to no prerequisites require some pretty deep insight whereas others are just plugging in about 5 previous preliminary results.

tl;dr no.

Reply 6367

Ben385

10

Original post by aem157

I'm trying to understand how higher maths is classified because there are so many different branches that I'm afraid that doing a degree might feel a bit like navigating through a maze (I haven't been to uni yet). There's always the "just blindly solve the problem sheets and don't try to understand anything" route but that is worse than the blindest faith - for a mathematician. I believe it is important to have some idea at least of what mathematics "is". One thing I tried is to divide maths into discrete and continuous. All the analysis/continuity stuff would go in the latter and the more discrete/algebraic material in the former but I must admit that this is very vague. Also, it is hard to believe that no one has written a "classification of the branches of mathematics" somewhere, so if anyone knows where I can find that particular piece of research please do let me know.

Fair enough, didn't know it would be this complicated haha.

I would not say that it feels like navigating through a maze. Rather, it feels like the more maths you learn, the more maths you realise there really is out there, and you are also able to appreciate better the differences between different areas. It is impossible really to do this with only A-Level (or even first year knowledge). I feel like this year (I'm doing part II right now), I am starting to understand the spectrum of maths. But then again, I know PhD students blending these things together (Topological Statistics, for example).

The categorization on the Part III courses webpage could give you some insight, https://www.maths.cam.ac.uk/partiiiguide

Reply 6368

sweeneyrod

15

Original post by aem157

Thank you for your reply. That definitely makes sense, yes, but I probably should have made myself clearer and used the word "complexity" instead of "difficulty" as that is closer to what I meant. I believe that branches of maths can certainly be classified in terms of complexity based on their prerequisites. So for example elementary number theory (of the type found in numbers and sets say) would be more "complex" than elementary algebra, which it assumes. (This is why I placed methods lowest.) In short, I am trying to ignore the actual structure of the courses (example sheets, exams, etc) and focus on the material itself.

tl;dr: Could someone please post a list of courses in the maths tripos and the prerequisites for each one?

Here is a (slightly outdated) summary of first year courses. It seems mostly accurate to me (but I don't do all the courses), except that sadly Gowers no longer lectures Analysis and I wouldn't describe Probability as "widely enjoyed".

Reply 6369

shamika

Original post by aem157

Can't work out the prerequisites on my own unfortunately.

You might also like https://www.maths.cam.ac.uk/sites/www.maths.cam.ac.uk/files/coursesia.pdf which explains what's in each course as simply as possible. As Ben says, maths isn't neatly packaged into chunks like 'algebra' or 'differential equations'. A lot of active research is about linking two areas or using results from a different part of maths to solve a hard problem.

@Ben: now looking up topological statistics, had no idea that's a "thing"!

Reply 6370

Pyoro

8

Original post by aem157

...

Classifying maths is like classifying music – the more you know, the more easily you're able to trash your classification criteria and the more you stop pigeonholing bits of maths and start to instead see them as comprising various flavours of their precursors (the more-elementary maths you've learnt).

But, as with music, that's not to say people haven't tried:
https://en.wikipedia.org/wiki/Mathematics_Subject_Classification
This is admittedly with a practical purpose.

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Pyoro

8

Original post by aem157

...

Yo, your posts keep getting deleted. Didn't see your reply. Have you been swearing or sth?

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Original post by Pyoro

Yo, your posts keep getting deleted. Didn't see your reply. Have you been swearing or sth?

I think he's deleting them himself...

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Doones

21

Original post by aem157

Edit: My previous post is awaiting moderation for some reason.

It's because you are a new user posting an external link. Its standard TSR policy, nothing personal.

Posted from TSR Mobile

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FanaticEV

12

Whats a good mark in CATAM.

Or whats the average mark people tend to get, 10/20, 15/20 or something else?

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username937760

Original post by FanaticEV

Whats a good mark in CATAM.

Or whats the average mark people tend to get, 10/20, 15/20 or something else?

Lowest marks I remember anyone in my year averaged around 10 or 11, so I doubt the average is 10/20. They (alongside the Part III essay) I think tend to score fairly high on average, though rarely achieve very high marks.

Reply 6376

IGU

6

Original post by DJMayes

Lowest marks I remember anyone in my year averaged around 10 or 11, so I doubt the average is 10/20.

Are you counting 0's in the average? Any idea how many just don't bother to do CATAM for one reason or another?

Reply 6377