Maths Uni Chat

Intending graduate maths applicant to Cambridge here...carefully studying the Tripos schedules...and IA and IB course descriptions

Could someone tell me whether IB Complex Analysis depends on IB Analysis 2?

And what bits of IA Metric & Topological Spaces are pre-required...or useful?

Thanks!
Birgitta

Reply 5543

Original post by around

I don't understand why people complain about the lack of online lecture notes: not having lecture notes makes me pay attention during the actual lectures and I find I learn the material far better this way.

Especially the QM course where I switched off after the first lecture after seeing the notes available online, and then freaked the **** out because the online notes are nigh-on unintelligible.

choose;

hungover / cold / tired / ill

It is usually advisable to have notes on-line in case of the aforementioned.

Reply 5544

Simplicity

OP

I don't physically make notes. So it's good that they are online.

Also, my handwriting is crap.

around

I don't understand why people complain about the lack of online lecture notes: not having lecture notes makes me pay attention during the actual lectures and I find I learn the material far better this way.

Lectures are useless, don't really learn anything from them. Some people do.

The logic behind lectures is when paper and books didn't exist so it made sense to give out information orally. Now that makes no sense.

Reply 5545

ForGreatJustice

13

I use online notes to read ahead, and because my handwriting is terrible. Though I still take notes even when there are printed ones, I just feel it helps memory.

Reply 5546

harr

15

I need to find a job. :frown:

Original post by around

I don't understand why people complain about the lack of online lecture notes: not having lecture notes makes me pay attention during the actual lectures and I find I learn the material far better this way.

Especially the QM course where I switched off after the first lecture after seeing the notes available online, and then freaked the **** out because the online notes are nigh-on unintelligible.

My experience of the third year is that D courses shouldn't have online notes (because if they do I don't go to the lectures) and C courses should (because I don't go to the lectures anyway).

Original post by stripy_and_nice

Intending graduate maths applicant to Cambridge here...carefully studying the Tripos schedules...and IA and IB course descriptions

Could someone tell me whether IB Complex Analysis depends on IB Analysis 2?

And what bits of IA Metric & Topological Spaces are pre-required...or useful?

Thanks!
Birgitta

You don't need to know any Met+Top. You don't need Analysis II for Complex Analysis. What's useful depends on what you want to do. Every second year course is potentially useful, but I doubt many people do all of them.

Generally it says in the schedules when any (non-first year) course is relevant.

Reply 5547

Original post by harr

You don't need to know any Met+Top. You don't need Analysis II for Complex Analysis. What's useful depends on what you want to do. Every second year course is potentially useful, but I doubt many people do all of them.

Generally it says in the schedules when any (non-first year) course is relevant.

Hi Harr and thanks for your help here. It's now sunk into my head that you don't need to do all the IB courses to get maximum marks...

The reason I wondered about Analysis 2 was that it's taught the term before CA. Would I lose anything by doing CA first and then Analysis 2 two terms later?? I'd like to get as much out of CA as possible...

As for M&T, the schedules say that "some" of it "will" prove useful for CA. The course descriptions say that the material in M&T is "very useful" for CA. They don't give similar advice for Complex Methods.

Do you know which bits of M&T they mean? The main M&T headers are

Metrics, Topology, Connectedness, Compactness

Thanks!
Birgitta

Reply 5548

Original post by stripy_and_nice

Hi Harr and thanks for your help here. It's now sunk into my head that you don't need to do all the IB courses to get maximum marks...

The reason I wondered about Analysis 2 was that it's taught the term before CA. Would I lose anything by doing CA first and then Analysis 2 two terms later?? I'd like to get as much out of CA as possible...

As for M&T, the schedules say that "some" of it "will" prove useful for CA. The course descriptions say that the material in M&T is "very useful" for CA. They don't give similar advice for Complex Methods.

Do you know which bits of M&T they mean? The main M&T headers are

Metrics, Topology, Connectedness, Compactness

Thanks!
Birgitta

Connectedness and Compactness are constantly cropping up in CA [complex analysis abbreviation, hopefully].

Metric and Topology are obviously closely related, but it is difficult to say what you should know;

Spoiler

Generally everything isn't necessarily easier if you do take topology it is just that so much is used there is found in CA in terms of balls - so you will have 'covered' the 'foundation' before.

Reply 5549

Original post by DeanK22

Connectedness and Compactness are constantly cropping up in CA [complex analysis abbreviation, hopefully].

Metric and Topology are obviously closely related, but it is difficult to say what you should know;

e.g. you don't need to know what a topology actually is in complex analysis and could just work with balls and their complements [balls are just sets of complex numbers that are a disc around some point, i.e. { z : |z-a| < r} is a ball centred at a with radius r]. Compactness is just a bounded set that is closed - i.e.e a square with its edge, a disc with its boundary.

Connectedness can also be given just by standard definitions in terms of balls [roughly, you also require some other definitions which on the surface do not appear to need such concepts].

Generally everything isn't necessarily easier if you do take topology it is just that so much is used there is found in CA in terms of balls - so you will have 'covered' the 'foundation' before.

Thanks Dean. Unfortunately I don't think I'll be able to fit in the whole of M&T before doing CA. Do you think it would be sufficient to study, say, the 3 chapters on Connectedness and Compactness in Wilson Sutherland's Introduction to Metric and Topological Spaces?

Also, would you envisage any problems with not having done any of Analysis 2 before I do CA?

Birgitta

(edited 13 years ago)

Reply 5550

Original post by stripy_and_nice

Thanks Dean. Unfortunately I don't think I'll be able to fit in the whole of M&T before doing CA. Do you think it would be sufficient to study, say, the 3 chapters on Connectedness and Compactness in Wilson Sutherland's Introduction to Metric and Topological Spaces?

Also, would you envisage any problems with not having done any of Analysis 2 before I do CA?

Birgitta

You shouldn't get worked up about not having covered anything. Everything will be proved in notes / during the course.

It is just the small stuff really; not small in the sense of depth or scope but simply such things as;

Let B be a closed and bounded (compact) subset of the complex numbers (C) and let f: B -> C be continuous. It follows f(B) is compact.

In the topology course you would have the result:

Let f : X --> Y be continuous and X be compact. Then f(X) is compact.

The results are pretty much the same - the method of proof would also be very likely to be the same.

Or let E be a connected subset of the complex numbers, then f(E) is connected.

Similarly we have let f : X -> Y be continuous and E a subset of X that is connected. Then f(E) is connected.

Yes that is an excellent book.

Good luck!

* obviously it is beneficial to know all this stuff before but it certainly is not necessary (I do not have access to the file though I recall looking at some Analysis 2 notes a long time ago and it just seemed to comprise of a collection of results extended to R^n) though the course might have changed as these were old, old notes.

(edited 13 years ago)

Reply 5551

Original post by Hashshashin

Original post by tommm

Out of curiosity, what's the par for number of questions completed on an examples sheet?

That early in first year? Probably ~75%.

Does it go up or down as time goes on?

Reply 5552

around

13

I definitely didn't do 75% towards the end of IA.

Reply 5553

qgujxj39

I only did 3 questions properly on groups 3. :smile:

Reply 5554

At Cambridge, how does it work if you are publicly funded and want to stay publicly funded for 4 years to get the MMath? Do you:

a) collect BA at end of 3rd year and then collect MMath at end of 4th?
b) turn down BA at end of 3rd, and collect only the MMath at end of 4th?
c) turn down BA at end of 3rd, and collect both BA and MMath at end of 4th?

Thanks!
Mary

Reply 5555

Original post by tommm

I only did 3 questions properly on groups 3. :smile:

I take it Simplicity's advice was close to your heart.

Reply 5556

Slumpy

16

Original post by stripy_and_nice

At Cambridge, how does it work if you are publicly funded and want to stay publicly funded for 4 years to get the MMath? Do you:

a) collect BA at end of 3rd year and then collect MMath at end of 4th?
b) turn down BA at end of 3rd, and collect only the MMath at end of 4th?
c) turn down BA at end of 3rd, and collect both BA and MMath at end of 4th?

Thanks!
Mary

I think if you stay on, you don't graduate in third year, you just do it in 4th year(and I think it happens automatically to an extent). Don't know which you collect.

Reply 5557

QED

11

does anybody have a possibly suspect source for perhaps questionable maths related textbook pdfs?

Reply 5558

Jake22

18

Original post by QED

does anybody have a possibly suspect source for perhaps questionable maths related textbook pdfs?

yes. google [textnamehere].djvu and then google seperately for a .djvu to .pdf converter.

Reply 5559

Simplicity

OP