Unremarkable ventures IV

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_gcx
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#21
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#21
(Original post by SilentSolitaire)
Logic and verification looks interesting and so do the analysis modules - are you a lot happier with the courses this year? The second year essay looks really cool; I've heard a bit about the Baire Category Theorem but I haven't studied much analysis or topology so I don't know a lot (hopefully I'll get time to read up on it at some point...). I think the first part is probably not too bad though? How long is the essay supposed to be?

Also can I be tagged this year?
It wasn't really the course content itself last year, it was the lack of excitement (which is not abundant in Algebra I but I'll cope) I'll soon be able to look at third year (particularly after this term because of Algebra I) stuff which I'm very excited to look at, which is what I'm particularly looking forward to.

The essay is supposed to be like, 10-12 pages (I think they can stop reading after like 15) and when I drafted it out, for the complex analysis essay it'd have taken too long to go through the prerequisites and I remember worrying it'd be too much of a squeeze/pain. Analysis III covers disappointingly little. Idk why the full Complex Analysis is postponed to third year. I would've taken it this year but I managed to find enough second year stuff.

I admittedly don't know how the finer details will work out, I only just about know the statement of the Baire Category Theorem at the moment! (wasn't in the topology notes I used) Guess I'll find out when I come to reading. Just seems like a fun thing to do, and it actually seems to be quite standard theorems that I shouldn't have issue finding sources for.
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_gcx
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#22
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#22
Have a very strong worry that I'm rushing through the content without doing the right "enrichment"/extension (might be sufficient for preparing for the exams but I think I need to do better than that). I think I'll give myself a textbook whose exercises I'll try to work through for at least Analysis III/NMT/MV Calc. [PDEs also being on the cards depending on how much I dig it]

Probably Munkres for Topology due to its legendary reputation plus it has a few solution banks. Undecided on the text for the two analysis modules. (if anyone has any recommendations I'd be happy to hear them but I don't think any > second years actively look at this thread lol)

Might work through some stats for fun but I can't see myself doing much extension work for algebra, unless it becomes important for something else I want to do or revisiting Alg II (or doing Alg I) sparks any special interest.

Not much else to say - I'm working through stats and I'm near the end but I've found it to be a bit "example heavy". A few lectures were entirely dedicated to finding maximum likelihood estimators of the parameters for a few (well, like 7 or 8) common distributions (basically boiling down to optimisation problems), and similar now with confidence intervals. Only issue really is that the strategy each time is very similar. Doesn't feel like there's as much theory as I would've liked but I guess such is to be expected from a more application-centric course.
Last edited by _gcx; 10 months ago
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zetamcfc
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#23
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(Original post by _gcx)
Have a very strong worry that I'm rushing through the content without doing the right "enrichment"/extension (might be sufficient for preparing for the exams but I think I need to do better than that). I think I'll give myself a textbook whose exercises I'll try to work through for at least Analysis III/NMT/MV Calc. [PDEs also being on the cards depending on how much I dig it]

Probably Munkres for Topology due to its legendary reputation plus it has a few solution banks. Undecided on the text for the two analysis modules. (if anyone has any recommendations I'd be happy to hear them but I don't think any > second years actively look at this thread lol)

Might work through some stats for fun but I can't see myself doing much extension work for algebra, unless it becomes important for something else I want to do or revisiting Alg II (or doing Alg I) sparks any special interest.

Not much else to say - I'm working through stats and I'm near the end but I've found it to be a bit "example heavy". A few lectures were entirely dedicated to finding maximum likelihood estimators of the parameters for a few (well, like 7 or 8) common distributions (basically boiling down to optimisation problems), and similar now with confidence intervals. Only issue really is that the strategy each time is very similar. Doesn't feel like there's as much theory as I would've liked but I guess such is to be expected from a more application-centric course.
Never realised you did a GYG (Amazing the things you find when you literally have nothing to do lol). BCT seems an interesting choice for an essay, what kind of things were you planning on including (Apart from the proof of course)?

I think you'd be fine with Principles of Mathematical Analysis by Rudin for your analysis courses. Although it isn't the most gentle of books, you are more than capable.
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_gcx
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#24
(Original post by zetamcfc)
Never realised you did a GYG (Amazing the things you find when you literally have nothing to do lol). BCT seems an interesting choice for an essay, what kind of things were you planning on including (Apart from the proof of course)?

I think you'd be fine with Principles of Mathematical Analysis by Rudin for your analysis courses. Although it isn't the most gentle of books, you are more than capable.
The essay is pretty short - 10-12 pages and space fills up pretty quickly, I'd imagine by the time I've covered everything in the OP I'll have hardly any space. I cover an interesting but tangential application of BCT space permitting, eg.

If f \in C^\infty [0,1] and for each x \in [0,1] there exists n \in \mathbb N such that f^{(n)} (x) = 0, then f is a (restriction of some) polynomial.
If f : \mathbb R^+ \to \mathbb R^+ is continuous and for all x \in \mathbb R^+ we have \lim_{n \to \infty} f(nx) = 0 (in the sense of a discrete limit) we have \lim_{x \to \infty} f(x) = 0. (in the sense of a continuous limit)
as a kind of dessert, idk. (motivated by looking around at other applications of BCT, certainly is versatile)

Yeah Baby Rudin definitely caught my eye, it definitely covers the things I need and doesn't look overly intimidating. Chapter 9 seems to cover what I need in terms of Multivariable Calculus but I will need to check. In terms of complex I'm unsure whether to go back to Gamelin (I used it ages ago but have been told it's comparatively very computational) or try another.
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zetamcfc
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#25
(Original post by _gcx)
Yeah Baby Rudin definitely caught my eye, it definitely covers the things I need and doesn't look overly intimidating. Chapter 9 seems to cover what I need in terms of Multivariable Calculus but I will need to check. In terms of complex I'm unsure whether to go back to Gamelin (I used it ages ago but have been told it's comparatively very computational) or try another.
As an intro I like Priestley's Complex Analysis, also the book that introduced me to complex analysis which was the Springer book by Howie. But there are so many out there you wouldn't go wrong with any text really.
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_gcx
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#26
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#26
(Original post by zetamcfc)
As an intro I like Priestley's Complex Analysis, also the book that introduced me to complex analysis which was the Springer book by Howie. But there are so many out there you wouldn't go wrong with any text really.
This'd mainly be for the exercises rather than a first course, but I'll keep these in mind!
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_gcx
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#27
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#27
Back to uni in 2 weeks, should really work more consistently. Pretty happy with how much I finished this summer though.

Topology exercises can be pretty frustrating, in that you can sometimes tell it's a simple question with a simple answer but it can take a little bit of thinking to get it down on paper and ironed out. (or think of a counterexample that works) Find this the case with topology more so than other areas. Worked through the first two exercise sections (in the topological spaces section) of Munkres and odd exercises from some other sections. I looked at Munkres' other book "Analysis on Manifolds" and I think ch. 2-4 covers everything I need for MV calc, which I'll keep in mind because I quite like his topology book. I do very much look forward to ch5 and beyond where the actual manifold-y stuff comes in. Apparently Steen and Seebach's "Counterexamples in Topology" is good for building intuition and coming up with counterexamples to things, might look at it.

I think I'm basically done with the content of stats, I know the rest of the inferential stuff from FS1 (power functions, type I/type II errors, etc.) and I really don't care to go through it again because nothing more interesting is really done with it, it isn't really expanded upon except stated slightly more formally. (I was aware of these formulations anyway because I didn't like A-levels way of presenting things) Definitely prefer more abstract courses. (of course you need examples but imo it should be more examples interspersing the theory rather than theory interspersing the examples) Will work through a few of the extension questions. The exam literally just looks like distributional stuff, which I'm glad about because that's the stuff in stats I like but it doesn't really feel like a lot is covered.
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_gcx
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Already coronavirus cases at Warwick even though only international students have moved in. (supposed to be self-isolating for 2 weeks but partying instead) yikes
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Synergy~
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#29
(Original post by _gcx)
Already coronavirus cases at Warwick even though only international students have moved in. (supposed to be self-isolating for 2 weeks but partying instead) yikes
Oh no 🤦*♀️ Did the university comment on the situation and/or the possible consequences?
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_gcx
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#30
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#30
(Original post by Synergy~)
Oh no 🤦*♀️ Did the university comment on the situation and/or the possible consequences?
not really: https://theboar.org/2020/09/student-...vid-19-rootes/
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neko no basu
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(Original post by _gcx)
Already coronavirus cases at Warwick even though only international students have moved in. (supposed to be self-isolating for 2 weeks but partying instead) yikes
oh, ofc that "unauthorised gathering" last week 🤦
I'm surprised it wasn't broken up though, are there no campus security...or do they not really care?🤔
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_gcx
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#32
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(Original post by neko no basu)
oh, ofc that "unauthorised gathering" last week 🤦
I'm surprised it wasn't broken up though, are there no campus security...or do they not really care?🤔
Boar says it was dispersed.

Campus security does patrol, but I'm not sure if they have the manpower to check every flat in the uni consistently every night. And then they'll just start gathering in rooms which will be impossible to spot without noise. They are generally chill but probably not in this sort of time.
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_gcx
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#33
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#33
Got assigned Miles Reid (of Undergraduate Algebraic Geometry/Commutative Algebra fame) as a personal tutor.

It's going to be intimidating having such an accomplished mathematician as a tutor.
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zetamcfc
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#34
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(Original post by _gcx)
Got assigned Miles Reid (of Undergraduate Algebraic Geometry/Commutative Algebra fame) as a personal tutor.

It's going to be intimidating having such an accomplished mathematician as a tutor.
You should enjoy the experience and try to get the most out of it.
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_gcx
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#35
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(Original post by zetamcfc)
You should enjoy the experience and try to get the most out of it.
It's nice to have a famous reference writer. Plus seeing as he's an expert in AG he should be able to suggest a DG-y URSS or point me towards staff that would take me on. So, very exciting. Too bad I don't really like algebra that much otherwise I'd be in heaven lol.
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zetamcfc
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(Original post by _gcx)
It's nice to have a famous reference writer. Plus seeing as he's an expert in AG he should be able to suggest a DG-y URSS or point me towards staff that would take me on. So, very exciting. Too bad I don't really like algebra that much otherwise I'd be in heaven lol.
I'm guessing DG is differential geometry, what is URSS? (Sorry if it's obvious i just can't see it)

''Too bad I don't really like algebra that much'' :cry:, What are the areas you are interested in?
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_gcx
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#37
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(Original post by zetamcfc)
I'm guessing DG is differential geometry, what is URSS? (Sorry if it's obvious i just can't see it)

''Too bad I don't really like algebra that much'' :cry:, What are the areas you are interested in?
Yeah I'm definitely digging the look of differential geometry right now. It leads pretty naturally on from the topics in maths I like. (complex analysis especially) Warwick has two modules in Differential Geometry, one that's an introduction to manifolds (which I feel like I'd really enjoy - goes very far) and another that's very very computational (looked an exam paper and it's literally just kinda dry calculations with curves/surfaces) that I don't think I'll do. URSS is an undergraduate research scheme that I intend to do this summer. (well more specifically - it's a funding scheme but ygm) https://warwick.ac.uk/services/aro/s...et/apr20/urss/

Maybe it's just the way it's taught, I've found it a bit dry. Linear algebra, especially. (might seem weird considering the interest above) But I guess that's because the way it's taught is often reduced to "do these computations with these matrices".

I like analysis (especially complex, favourite part of maths) and topology. Have a passing interest in stats and probability.
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zetamcfc
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(Original post by _gcx)
Yeah I'm definitely digging the look of differential geometry right now. It leads pretty naturally on from the topics in maths I like. (complex analysis especially) Warwick has two modules in Differential Geometry, one that's an introduction to manifolds (which I feel like I'd really enjoy - goes very far) and another that's very very computational (looked an exam paper and it's literally just kinda dry calculations with curves/surfaces) that I don't think I'll do. URSS is an undergraduate research scheme that I intend to do this summer. (well more specifically - it's a funding scheme but ygm) https://warwick.ac.uk/services/aro/s...et/apr20/urss/

Maybe it's just the way it's taught, I've found it a bit dry. Linear algebra, especially. (might seem weird considering the interest above) But I guess that's because the way it's taught is often reduced to "do these computations with these matrices".

I like analysis (especially complex, favourite part of maths) and topology. Have a passing interest in stats and probability.
Ah brilliant, that should be a great experience and a good look at some interesting maths.

Hmmm.... Hopefully you will enjoy your groups and rings module this year.
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Rohan77642
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_gcx do you have any good book recommendations or resources to learn complex analysis from? I have complex analysis this term and wanted a good reference book apart from the lecture notes.
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_gcx
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(Original post by zetamcfc)
Ah brilliant, that should be a great experience and a good look at some interesting maths.

Hmmm.... Hopefully you will enjoy your groups and rings module this year.
Already did a runthrough of the module and that's the reason I don't think I'm a massive fan! I liked it in the beginning but it didn't stay exciting for me.

(Original post by Rohan77642)
_gcx do you have any good book recommendations or resources to learn complex analysis from? I have complex analysis this term and wanted a good reference book apart from the lecture notes.
To learn I used Gamelin. It's probably a fairly computation-focused book but I found it very good nonetheless. Haven't learnt off any others (mainly odd lecture notes) so can't really give any other recommendations.
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