Unremarkable ventures IV

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Logic and Verification - Not going to lie, I did gravitate towards this as an "easy" option. Did not want to cop out and take the piss-easy Logic I module offered by philosophy though. I've done propositional logic in two modules so far (Sets and Numbers and ST116), so this'll be my third time covering it so a lot will be familiar. That said, there's bits that are totally new to me, (disjunctive/connective normal form, annotating resolution/deduction proofs) so the logic part should be interesting. The second part of the module uses Prolog and is about formal verification of software systems. Know nothing about it yet, sounds fun. It's 25% coursework so it should be cushiony.

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Algebra II - I think I've actually finished this module before but that was ages ago when I thought I'd go into algebra. I ended up enjoying it up to the bit on ring theory when it all got very dense and very dry. Now looking back I doubt I'll get into it. Especially since Algebra I was more or less the most bored I've ever been doing maths. Hopefully I'll be able to jog my memory for the most part - I managed to do most of the first two assignments without much looking back on my notes. Will definitely have to re-cover the clunkier proofs. People say Algebra II is a hard low-performing exam and not representative of lectures but honestly looking at past papers I don't think so, it seems to be very bookwork heavy/relatively straightforward proofs/computations, found that very strange. I think if I knuckle down I should be able to get a decent result out of it. The first part of the module speedruns the first year algebra module, pretty much rendering it redundant (idk why), with a few bits about classifying groups along the way. Then you go onto isomorphism theorems, group actions, then ring theory (bunch of first year recap, ideals, domains and polynomial rings). Doesn't sound dense, but certainly is.

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Partial Differential Equations - Apart from knowing how to compute Fourier series, I don't really know what to expect out of this module. Hoping not too computational. A lot of analysis in research is of PDEs (there are 2 sequels to this module, theory of PDEs in third year and advanced PDEs in fourth), and hopefully this module will let me decide whether I'll want to take PDEs/analysis generally further. Really not familiar with any of it but it looks like we cover a few solution techniques (which includes fourier series) to solve four classes of PDE. (transport, wave, heat, Laplace, all physicsy)

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Introduction to Number Theory - I did about half of this course last [academic] year but gave up in like March or April. Hoping I'll get into it more this time around, and that everything I've already done will come back to me reasonably quickly. First chapter covers a lot of elementary theory (divisibility and such), ring theory, moving onto linear congruences in the second chapter (with stuff like Legendre symbols, Chinese remainder theorem). Third chapter is all on quadratic reciprocity (bit of a shorter one, only 5 or so pages), fourth chapter looks at geometry of numbers, theorems on representing numbers as sums of squares, Legendre's equation, FLT for n = 4. Idk if the fifth chapter is examinable (would guess ont) but it covers RSA, the Miller-Rabin primality test and a statement of the prime number theorem. Analytic number theory is still on my "maybe" list for fourth year since it ties in extremely closely with complex analysis. I don't think I like algebra enough to do algebraic number theory in third year and the course looked fairly dry.

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Norms, Metrics and Topologies - Reasonably confident with most of this (my second year essay uses it heavily) but still room for improvement via textbook exercises. The exercises set last year as part of the course were a) optional and unmarked b) extremely uninspired (in an almost limitless topic with so many interesting ideas to explore !!) so I think looking elsewhere is the way to go. Not sure whether I'll go back to Munkres or find another text. Oddly the exam is 3 hours despite being no different in format (that I know of) to other 2nd year exams so hopefully this'll be a good one. Course introduces topological spaces, and covers continuity, compactness, connectedness, completeness. (the idea of topology is to generalise work done in real analysis to more general spaces) No quotient spaces for some reason which is fine with me since they're a bit tricky conceptually. Can't remember if BCT stuff is in there or not.

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Geometry - Never learnt a lot of this module properly. The content seemed very very skinny. A whole week of lectures was dedicated to proving Cauchy-Swartz for time like and space like vectors in hyperbolic space. No projective geometry. Planning on starting to go through this soon.

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Analysis III, Statistics - no issues.

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Multivariable Calculus - need to go over bookwork and the Hessian.

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Algebra I - recap bookwork, actually get to learning classification of finite abelian groups.

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PDEs - it's as computational and applied as I feared, rip. Hoping it'll be ok regardless.

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Algebra II, Number Theory - So far very familiar from learning them last year so should be able to crunch through these in not too long.

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NMT - no issues, might need refreshing on bookwork.

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Logic and Verification - just working through it as I'm going along, pretty decent so far.