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Cambridge Maths Students and Applicants

Personally, I think lecture notes are sufficient. For courses in the first term you don't actually get lecture notes, but I found my own notes were fine either way. There are topics from time to time that I needed to consult an extra source to properly understand, but really that's about it. I generally find I don't have the time to spent time doing exercises from books anyway, you get plenty of practice with example sheets.

That said, your mileage may vary. You may find to useful to consult books for alternative explanations, additional examples and exercises, etc. I generally find myself googling things I don't understand, but going to the library to get a relevant book isn't a bad idea either. This is something that you'll probably figure out for yourself very quickly though, so I'd just recommend trying out various things and see how they turn out.

Of course, if you're thinking on self-studying a topic on your own, then that's a different story altogether.

Well im on my gapyear atm so Id have to be selfstudying the courses. What do you think then?

Btw did you manage to transfer to straight maths?

Reply 4381

ctrls

9

Original post by newblood

Well im on my gapyear atm so Id have to be selfstudying the courses. What do you think then?

Btw did you manage to transfer to straight maths?

I'm tempted to say a book would be more useful in that case. Lecture notes are useful because they are catered specifically for the course, but otherwise you might as well use a well-known book which presents the material nicely, contains its own exercises, etc.

I find this is especially the case for the first year Maths tripos, where everything is specifically organized under the assumption that you are doing all the courses. As an example, Numbers and Sets introduces basic notions of analysis and Differential equations covers partial differentiation and sketching multi-variable functions. And then there's vectors and matrices, which consists of a bunch of semi-related topics thrown together into a single course.

And no, my DoS convinced me to try both for a year and see what happens. Though as it stands, I'm learning towards switching next year.

Reply 4382

newblood

19

Original post by ctrls

I'm tempted to say a book would be more useful in that case. Lecture notes are useful because they are catered specifically for the course, but otherwise you might as well use a well-known book which presents the material nicely, contains its own exercises, etc.

I find this is especially the case for the first year Maths tripos, where everything is specifically organized under the assumption that you are doing all the courses. As an example, Numbers and Sets introduces basic notions of analysis and Differential equations covers partial differentiation and sketching multi-variable functions. And then there's vectors and matrices, which consists of a bunch of semi-related topics thrown together into a single course.

And no, my DoS convinced me to try both for a year and see what happens. Though as it stands, I'm learning towards switching next year.

Well im going to start Part IA in October, so the courses im working through are the Cambridge ones. So the lecture notes being prescribed for IA isnt really an issue. I think as im going slow-paced through the material as I only do a little bit I might aswell use books and lecture notes, to complement each other.

Good luck on the maths front then

Reply 4383

Blutooth

16

Original post by Many-Faced God

I appreciate that.If you read my previous post you will see that I am reading "real" category theory along with other "real" mathematics(like algebra,analysis and recently I have started diff. geometry).In fact I have been doing so for quite a while.I dont blame you for not reading them though they are far too long.
Thanks for the link.

I dont even know why category theory came up.My point was

If you love math and are curious about comp. sci. you should start with haskell.I think you disagree?
Although I am not sure anymore.

Could you specify what exactly you recommend?

I think you are a theoretical computer scientist on the types and languages side. However, there are plenty of other flavours of theoretical scientists. You could be really into algorithms, which encompass integer programming, self-adjusting trees, cryptography, etc. YOu might also like to dip into the foundations of machine learning -VC dimension and all that stuff. Then there's also database systems implementation and concurrency, which can be studied at quite a theoretical level. You could also go into bioinformatics or quantum computation (ok taht requires category theory).

If I could recommend something that would really get someone into computer science, I'd recommend 4 courses:

Algorithms and data structures, Models of computation, functional programming, perhaps deductive logic. That's probably more balanced for someone who is into maths. I also really enjoyed machine learning theory, but that's not really bread and butter CS.

(edited 9 years ago)

Reply 4384

grid

Original post by around

Computer scientists need to know about boolean algebra in the same way that athletes need to know about grass biology. I mean, seriously, why would you bother.

Really, around! Why would you "bother"? Because you've got an insatiable interest in what's going on and you're not just doing something as a job? Bothering doesn't only have to come from 'needing' in some impoverished sense of that term; it can come from needing in the sense of being driven, fascinated, always finding new angles and connected fields to explore and understand. You're lucky you're not an athlete with me as your trainer! :smile:

Reply 4385

SimonM

18

Because if you take that attitude you'll never get anything done. Sure, study whatever interests you, but don't feel like you have to study everything your field depends on, otherwise you'll never get to study what you're interested in.

Reply 4386

grid

Original post by harr

Lectures should have everything you need, and your college library is likely to have some relevant books if you want extra questions or alternative explanations.

Any student who is wondering whether they can go to university and, when they're there, get away with not reading any books or material on their subject other than their lecture notes might be well advised either to change their attitude or to consider doing something else instead of going to university.

Reply 4387

grid

Original post by SimonM

Because if you take that attitude you'll never get anything done. Sure, study whatever interests you, but don't feel like you have to study everything your field depends on, otherwise you'll never get to study what you're interested in.

I didn't say "everything". I was responding to the view that says "why would you bother" studying anything related to what's in front of you if you don't "need" to?

Reply 4388

newblood

19

Original post by grid

Any student who is wondering whether they can go to university and, when they're there, get away with not reading any books or material on their subject other than their lecture notes might be well advised either to change their attitude or to consider doing something else instead of going to university.

Why? I know many mathmos at a range of top unis incl. cambridge and warwick who have all told me they only used lecture notes throughout their time and i wont need anything more than that as all the material is covered there, and theyve all done well.

Sure you can look at books aswell if you want/need to for interest or clarification. But it appears to me that the majority dont, for lack of want or for lack of time. People dont just go to uni to study. 24/7...

Reply 4389

harr

15

Original post by grid

Any student who is wondering whether they can go to university and, when they're there, get away with not reading any books or material on their subject other than their lecture notes might be well advised either to change their attitude or to consider doing something else instead of going to university.

The question was specifically about books recommended in the schedules. My advice was not to *buy* more than a couple of the recommended books in advance. I even said that "working through some books before you arrive is likely to be very helpful." (My post in context.)

If you are going to read around the subject to get a broader understanding (and you should), books that have been specifically chosen to match what you're already studying might not be the best time investment. Books that aren't on the schedules are worth considering, as are "blogs, expository papers, MO, math.SE..."

But depending on your aims, you might not want to do this. Many people just go to university to have a bit of fun and get a good job at the end of it. If you're just looking to get a 2i without too much work then focusing on the lecture notes makes sense. (I would guess that if your aim is just to maximise your mark then the best approach is to combine lecture notes, example sheets, past papers and textbook exercises, regardless of whether you're aiming to pass or to be Senior Wrangler, though I haven't got any data.) You might argue about whether working for three years to get a positional good is a sensible use of society's resources, but from the individual's perspective it makes perfect sense to go to university. Everyone is well advised to consider doing something else instead of going to university -- it's a big decision -- but I reckon most Cambridge students benefit from their choice.

(edited 9 years ago)

Reply 4390

around

13

Original post by grid

I didn't say "everything". I was responding to the view that says "why would you bother" studying anything related to what's in front of you if you don't "need" to?

Because Boolean algebra has very very very little to do with TCS (or modern maths - Stone duality is much more important), and there are far more worthwhile things to be studying instead. As much as I hate economics, marginal utility is a useful concept sometimes.

Reply 4391

gsckmom

6

Original post by marers

A while ago, many top students seem to have completed Part III after 3 years as undergraduates.

Also the Maths Faculty website refers to an "accelerated Tripos" consisting of Parts IB, II, and III.

How common is this, or something similar, nowadays?

Original post by around

It's possible.

Is this still possible?

Reply 4392

ddhurst

7

Out of curiosity, if a student were to apply to a Cambridge college having already sat STEP and achieved SSS, would their prior academic record be rendered irrelevant?

Can you foresee a circumstance in which any applicant who had SSS in STEP would be rejected?

Also, is age largely irrelevant for maths applicants as well? For example, would a 24 year old be able to get into any college (not just mature ones) to study maths if he demonstrated that he had the ability?

Reply 4393

username1162972

18

Original post by ddhurst

Out of curiosity, if a student were to apply to a Cambridge college having already sat STEP and achieved SSS, would their prior academic record be rendered irrelevant?

Can you foresee a circumstance in which any applicant who had SSS in STEP would be rejected?

Also, is age largely irrelevant for maths applicants as well? For example, would a 24 year old be able to get into any college (not just mature ones) to study maths if he demonstrated that he had the ability?

I know breaks from maths/ gap years are frowned upon from most colleges from the Cambridge Maths guide.

Posted from TSR Mobile

Reply 4394

ddhurst

7

Original post by physicsmaths

I know breaks from maths/ gap years are frowned upon from most colleges from the Cambridge Maths guide.

Posted from TSR Mobile

The reason being because they fear applicants will have forgotten/fallen-behind with all the M/FM/STEP material. But if you proved to them that you were well on top of it by securing top marks in the STEP papers, I don't think they'd have any reason to believe you weren't on top of things...

Reply 4395

around

13

Original post by ddhurst

Out of curiosity, if a student were to apply to a Cambridge college having already sat STEP and achieved SSS, would their prior academic record be rendered irrelevant?

Can you foresee a circumstance in which any applicant who had SSS in STEP would be rejected?

Also, is age largely irrelevant for maths applicants as well? For example, would a 24 year old be able to get into any college (not just mature ones) to study maths if he demonstrated that he had the ability?

I'm fairly sure that a maths grad from a reasonable uni could get SSS in STEP, but probably would never get an offer to sit another undergraduate degree in maths.

You're going to have to be more specific about your situaton.

Reply 4396

ddhurst

7

Original post by around

I'm fairly sure that a maths grad from a reasonable uni could get SSS in STEP, but probably would never get an offer to sit another undergraduate degree in maths.

You're going to have to be more specific about your situaton.

I, the 24 year old, would have never done an undergraduate mathematics degree before. I would be applying as a mature student who had been working since leaving high-school at 18. Nonetheless I would be applying having achieved SSS the previous year (aged 23).

Reply 4397

username1162972

18

Original post by ddhurst

The reason being because they fear applicants will have forgotten/fallen-behind with all the M/FM/STEP material. But if you proved to them that you were well on top of it by securing top marks in the STEP papers, I don't think they'd have any reason to believe you weren't on top of things...