Unremarkable ventures IV

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?

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.

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)

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.

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?

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?🤔

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.

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'' , 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/staffintranet/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.

@_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.