# Module Reviews

## Module Reviews

Year 1

Year 2

Year 3

Year 4

MA106 Linear Algebra

2017/2018

(I studied the version for maths students, but the content is the same for non-maths students taking the module too.) This module can seem very odd as you study it, and you don’t really feel like you know what you’re meant to be learning. In the past, the exams have been very lemma-proof based, but in 17/18 the exam was based on calculations, which I think suits the module a lot better. Overall a nice module with pretty good teaching, just make sure you can remember what it is you’ve already proved, or the following proofs won’t make any sense.

2020/2021

I really liked this module as it was quite calculation based in the assignments and exam. The pre-recorded videos while useful were quite lengthy occasionally but watching on 1.5x speed kind of helps with that. The lecturers were really approachable (in a virtual sense) and injected a sense of random fun into the module through the Vevox polls and who could forget the end of module surprise. A really great module

Linear algebra explores linear maps, matrices and the relationship between them. I really liked the fact that MA106 explains some things that weren’t justified back at school, so everything makes a lot more sense now. Diane’s exams appear to be more computational as opposed to proof-based. This makes a lot of sense to me and, overall, I think the module was lectured very well. The lecturers were very receptive to student feedback through the term as well.

MA117 Programming for Scientists

2017/2018

I thoroughly enjoyed the lectures for this module, but found the actual projects very stressful. There are 2 hour support classes every week, and as long as they’re not busy, you can go along to as many as you want, and the TAs are very helpful in explaining the nuances of coding that you haven’t picked up from the lectures. There was a large jump from writing little bits of code to entire programs that many people struggled with, but once you’ve got a grip on it, you’ll be fine. It’s a good module for anyone interested in coding, as it gives an introduction to a very useful language. I would recommend it to anyone who likes coursework modules and/or wants to do more coding.

2020/2021

Before this module, I’d had a bit of experience using Python and none at all in Java. I ended up really enjoying MA117 because of the interesting projects you work on, as well as it being my only 100% coursework-based module. I thought there was a good amount of support available too. However, I remember having to spend a lot of time on these projects to get the results I wanted. I actually found Project 1 to be the hardest as I was still getting used to the syntax of Java. Also, despite being advertised as accessible to all regardless of coding experience, most of my friends who had never coded before really struggled with this module. Regardless, I recommend you give it a shot if you’re on the fence about taking it.

I found the following YouTube channel incredibly helpful, especially when I struggled to understand the concepts of Java early on and beyond:

https://www.youtube.com/channel/UC_fFL5jgoCOrwAVoM_fBYwA

MA124 Maths by Computer

2017/2018

The lecturer for this module is great, and I enjoyed his lectures so much despite being a Monday 9am. His lectures were fun and interesting, and he explained very well how to use the new commands you’d need to use in that week’s assignment. That having been said, I found the size of the assignments and having them every week rather stressful, and I’d definitely recommend pairing up for this module, as it can be quite a lot of work! As long as you can put the time in though, you can get a very high mark in this module overall.

2020/2021

This was the first time Dwight taught this module with Python so there were a couple of teething problems with the length of the assignments but by the end of the module, everything was working really well. If you’ve done a little bit of programming before then that will help but I wouldn’t say it is essential. Overall a really interesting module especially as Dwight would often show how some of the stuff that we did was useful, like computer graphics and disease modelling.

MA131 Analysis

2017/2018

Term 1 Analysis is really scary. Don’t worry if you don’t see the point of the lectures – the maths department have basically decided the lectures are pointless, and you don’t need to go as long as you’re going to the classes. Make sure you revise for the January exam (and that means start more than a week before the exam!) and look over the past papers to get a feel for what the exam style is. Term 2 – this was very badly taught. I mainly studied from the lecture notes, as they were much better than the lecturing. The assignments were moderately hard, but the class teachers were very helpful so usually between the classes and talking to your friends, you should be able to complete the assignments without too much stress. The Analysis 2 exam is the biggest exam of first year which scares a lot of people – try to work out from past papers which are the “examinable proofs” and make sure you learn them, to guarantee some easy marks in the exam and to give yourself extra time to work on the other questions.

2020/2021

I found Analysis I difficult at first, but the bi-weekly support sessions, workbooks and supervisions did a great job of helping me consolidate the newly learned content each week. Siri did a brilliant job of lecturing Analysis II and provided superb lecture notes, assignments and Moodle quizzes to aid knowledge consolidation and revision. Make sure you revise well for the June exam, as it’s worth a hefty 60% of the 24 CAT module(!)

MA132 Foundations/MA138 Sets and Numbers

2020/2021

This was probably the most polarising module of the year especially after a tricky January exam. I found it accelerated until week 10 and a lot of the hardest content was squeezed into the last couple of weeks of term. I definitely would have practiced some modular arithmetic beforehand as that was a stumbling block for me. After the January exam, the module was complete, meaning we didn’t have to revise it again in the summer which was definitely appreciated!

Foundations was one of the more tricky modules for me due to the abstract nature of the proofs involved, as well as how different the January exam was compared to past papers. There are a lot of topics covered in the ten weeks, but the final weeks’ worth of content, albeit interesting, was very difficult for most to get their heads around.

MA133 Differential Equations

2020/2021

A relatively lighter module in terms of new content and the exams are fairly routine if you do enough of them when revising. The assignment sheets were fair and complemented the lectures very well. Regarding differential equations, practice makes perfect!

A great module and a great lecturer. Even though there were technical hiccups, the module was really interesting and took A-Level ideas further into understanding why they work. The application side of the module was a bit strange occasionally but again very interesting. Dave was really helpful even if some of the questions weren’t the most maths based. A great module and hope that next years’ class get a “Bug of the Day” in each of their lectures!

MA134 Geometry and Motion

2020/2021

I enjoyed this module although it was one of the most challenging core maths modules this year. This module was well organised but sometimes confusing because it was unclear if the theory was taught in lectures because it would help with intuition or whether it was examinable. This module was mainly computational however the exam set contained proofs for the first time in a few years which took us by surprise.

A challenging yet rewarding module, delving into the intricacies of parametrisations, vector calculus and a LOT of integration. Some great lectures and lecture notes to learn and revise from, though the exams are always pretty difficult.

MA136 Introduction to Abstract Algebra

2017/2018

Everybody loved this module, probably because it was taught by Samir. Don’t be put off by the huge lecture notes, there’s really not very much in this module, and it doesn’t get particularly hard. The proofs that get asked in the exam are very repetitive year on year, and the assignments are probably the easiest assignments from first year. A highly recommended module for anyone who likes algebra, but don’t expect it to be like any algebra you’ve seen before.

2020/2021

Samir and Andrew did an incredible job of lecturing this module. Intro to Abstract Algebra explores groups and rings, introducing key theorems regarding groups and expands on how to write good proofs in the realm of algebra. You should be fine if you’ve done the past papers as the exams are fairly routine.

ST104 Statistical Laboratory

2020/2021

This module introduces the R packages as well as some basic statistical analysis techniques. The material is pretty straightforward, and if you enjoy coding this module shouldn’t be too hard. However, sometimes the lectures can be a bit dry. It is also worth pointing out that R programming is included in the exam, which is certainly strange.

ST111 Probability A

2017/2018

This module is quite odd if you’ve studied statistics at A-Level – you’re going over many things you’ve seen before, but in a very different way. It’s helpful to try to abandon what you’ve learnt in A-Level to begin with rather than try to make the links, since this module is so much more theoretical than how it is taught in school. The assignments can be confusing but if you go to the seminars and go over the exercise sheets you’ll be fine. Don’t be fooled by the applied nature of the assignments though – the exam is probably 50% bookwork so make sure you know your theorems and proofs!

2020/2021

Probability A is not an easy module. There are some interesting ideas and I liked the formalisation of the statistics that we did. We were provided plenty of examples to supplement the lecture material. However, the assignments and exam were very challenging and the timing for the exam is very tight. One hour for 30 marks may sound reasonable but there was an awful lot of text to digest in our exam.

ST112 Probability B

2017/2018

(Note: teaching for this module was heavily affected by the strike action.) I really enjoyed the content of this module and found the lectures interesting, but struggled in applying the content to the assignments. Make sure you do the exercise sheets or go to the seminars to get the answers, they help a lot when you do the assignments! The exam was very theory based, so knowing the main theorems by heart and being able to prove them is key. A very useful module for anyone, but particularly those wanting to do further statistics modules.

2020/2021

I think Giuseppe lectured this module really well, providing lots of examples and non-compulsory assignment sheets to aid understanding. Although these sheets were really tricky, I thought our final exam was the most fair of all the exams I sat. Note that Prob B is vastly different to Prob A. Prob A is more about enumeration and notation for events and outcomes, Prob B is more about applying integration skills and identifying common statistical distributions. The integration side of Prob B is what appealed to me throughout the module and some of the proofs were very satisfying.

This module has extremely difficult concepts. To put it simply, if you don’t work hard, you will fail. That being said, the material is pretty interesting if you are motivated enough. It is also a prerequisite to almost all ST modules in the future, so unless you know you hate probability, I’d recommend this module.

IB104 Mathematical Programming I

2017/2018

Would definitely recommend! This module is particularly nice if you studied D1 & D2 at A Level, as it covers topics such as linear programming, simplex etc. The hardest thing about this module is the fact that it is in term 3, so you’re having to attend lectures and complete a big assignment (worth 33% of the module) whilst revising for exams. Another frustrating aspect is there are no past papers online as the lecturer does not see the point in providing students with them. However, the module is nice (no way as much content as a 12 CAT module usually has), and the lecturer is engaging and also holds problem classes where you can get help so would recommend, if you can cope with the extra workload in term 3!

EC106 Introduction to Quantitative Economics

2017/2018

This module can be quite tough if you haven’t done A Level economics. However, I did enjoy it in the end. The first term is microeconomics and that is super boring, and you can barely understand a word that the lecturer says. However, in term 2 you study macroeconomics which is far more exciting, and with an excellent lecturer! Would recommend for anyone with a genuine interest in economics or who are aiming to go into a career like finance/actuarial where economics is really important.

2017/2018

I did not enjoy the teaching style of this module at all, finding the lecturers were boring and made everything unnecessarily complicated. The four tests throughout the year added a lot of stress, but they were reasonably formulaic and you could get a good mark just by memorising the answers from the last two years’ tests. The exam didn’t take much revising for as there was little to no theory, and the maths in the exam questions was simple. Overall a boring module, but if you’re willing to learn the content on your own (which doesn’t take very long), then a good module to get a high mark in.

2017/2018

The Micro side of this module is not lectured amazingly, particularly if you don’t sit near the front it is very hard to hear Sharun. The macro lecturer however, Dennis Novy, is really good. Would recommend this module if you are interested in economics, even if you didn’t do A level (I didn’t). There is a lot of content, and it is very theoretical, but it was definitely one of my easier modules in first year.

PH136 Logic I: Introduction to Symbolic Logic

2017/2018

A 1st year philosophy module which is relatively easy to understand and get a good grade in. I would advise looking at the style of paper as it tends to recur, and practice each type of question. In the exam you must be vigilant in checking your work as one small mistake can cost you a lot of marks.

2020/2021

If you are only looking for a module that fill up your CATS requirement, then this is the module you want to have. There is no assignments, only one exam. The material is very easy for any maths students. As long as you do the exercises they give out and go to the seminars, this module should be super chill and easy to get a first in.

An excellent module to take to help cope with the enormous work load in Term 2 of Year 1. Remember in Foundations when you spent one lecture on truth tables? They take up half of this module, just to give you an idea of how slowly you go through content. The exam is almost exclusively computational, so you will be fine as long as you regularly do the online exercises, of which there are plenty.

PX120 Electricity and Magnetism

2020/2021

This was definitely the hardest module I took this year, and the first few weeks getting to grips with 3d coordinate systems put a lot of people off. This year due to COVID the module was largely independent study from the lecture notes and exercise sheets with a couple of accompanying videos each week only on the hardest content. It took a lot of time and motivation to feel on top of the content, so I’d recommend this module only if you’re willing to put in the extra effort. However I found it very rewarding and the exam was very kind given the online circumstances. It also helped with MA134 Geometry and Motion which was a nice bonus of taking the module.

PX148 Classical Mechanics & Special Relativity

2017/2018

This module built very well on existing A Level mechanics knowledge and the lectures were therefore easy to follow. The special relativity section was very interesting as it was new knowledge, but the level was accessible to someone who hadn’t studied the topic before. The online lecture notes provided were very coherent, and I would recommend the module to anyone with a keen interest in Physics. However, the exam was a LOT more difficult than material covered in lectures, and therefore it was hard to know how to revise effectively. Overall I would only recommend this as an optional if you enjoy a challenge.

2020/2021

I really enjoyed this module. The lecturer was great and very clear and the rate of the module just right. There was quite a lot of video content, almost 3 hours a week. An advance warning however that week 6 mechanics got quite tough but as long as you learn the examples given it’ll be fine. Only downsides were that if you’re a Maths student, your problem sheets don’t get marked and you don’t get access to the MasteringPhysics textbook and so solving problems has to be self-motivated throughout.

CS137 Discrete Maths and its Applications II

2020/2021

This module covers the following topics: Big-O notation, simple sort and search algorithms, Master Theorem, graph theory (including Hall’s Theorem, bipartite graphs, matchings and vertex covers, trees, Euler walks/circuits, trees and more) and applications of graphs to discrete probability (e.g. proving statements through the use of graphs). As you can see, the module provides plenty of really interesting topics for you to learn about. However, the module was not lectured very clearly, the seminars (albeit online) were not engaging/helpful and the exam was way too difficult. Take this module at your own risk.

MA209 Variational Principles

2017/2018

Hello! Variational principles is a term 3 module. This unfortunate fact does deter many people from taking the module. However, there are only 15 lectures and lectures happen 4 times a week. I personally found that doing this module gave me a break from revision and forced me outside (briefly!). Mathematically, this module is essentially an introduction to the calculus of variations. This calculus seeks to find functions that are extrema to a given integral, possibly subject to constraints. This sounds simple enough, but surprisingly the maths is very rich. This calculus is used in Hamiltonian mechanics, quantum mechanics, engineering and many other disciplines. In addition, I personally find the maths very beautiful! There are weekly exercise sheets but the final mark is your exam mark. There are no printed lecture notes but the lectures are very good. Make every effort to attend them (or make friends with someone who does!). To summarise, the module contains good mathematics and provides a welcome break from intense revision!

MA213 Second Year Essay

2017/2018

This module seems daunting at first – the idea of finding a topic, writing an essay and presenting it. But actually, once you’ve found a topic, it can be really interesting and become a nice break from other modules. Start thinking about your essay topic well before the deadline for the title as then you’ll have a topic you’re actually interested in. Also, try to keep on top of the work for the essay though as that’ll give you more time at Easter to focus on revision.

2020/2021

Do it early. It’s so much easier to get a solid amount of work done on your essay over summer, or over Christmas, rather than when you’ve got several other modules to keep up with too. In terms of the topic, try starting off with something quite broad (so you have enough sources to work from!) and see where it takes you. Also, you will need to write your essay in Latex. You don’t have to be amazing at Latex, but make sure you attend the course (especially if Andrew Brendonn-Penn is still leading it).

MA243 Geometry

2017/2018

Hello! If you are reading this, you are probably interested in Geometry. And so you should be — geometry is a very beautiful area of maths. If I were only allowed to use one word to describe this module, that word would be “interesting”. Indeed, as well as learning euclidean and spherical geometry, you will be introduced to hyperbolic geometry, affine geometry and projective geometry. Hyperbolic geometry is analogous to spherical geometry done on a sphere of radius i (Ahhh!!!!!) and the latter two are important in algebraic geometry (4th year!). I must emphasise that this module is NOT EASY. The content is covered faster than most second year modules; there are weekly assignments and the maths may appear abstract when first encountered. Do not take this module if you’re looking for easy marks. In addition, the recommended textbook by Miles Ried is not the best textbook in the world. The lecture notes last year was the textbook. Even though I would still recommend getting this textbook, I would also recommend getting the textbooks by Coexter (title given in webpage) and also Ratcliff’s foundation of hyperbolic manifolds (available from Warwick library online) for the hyperbolic geometry section. However, despite the previous two paragraphs, I was satisfied by studying this module. Hence, my final advice would be to take this module if you like geometry and are seeking intellectual satisfaction.

A very interesting module with a good teaching structure. People who are more algebra minded rather than analysis minded tend to like this module.

2018/2019

The lectures were fascinating and honestly worth the three 9AMs. The weekly assignments were a reasonable amount of work in term 1 and the marking was a bit weird with assignments being out of 2. The module is quite tricky and easily one of the hardest parts of the year. Moreover, the exam was absolutely horrendous and made no sense as a two hour paper.

MA244 Analysis III

2020/2021

Definition, theorem, proof, repeat… a pretty typical analysis module focusing on integration, although the second half of the module is analysis with complex numbers, which is nicer. Jose is an excellent lecturer and the notes are good, but he set a ridiculously hard open book exam with far too much unseen material. Make sure to familiarise yourself with the key definitions and theorems and practice coming up with examples and counterexamples.

The module was majorly restructured starting in 18/19. The first part of the module rigorously introduces integration via the Darboux Integral (called the Riemann integral here, as it often is! It is equivalent though), and you look at integrals of functions that are not necessarily continuous. (where the Fundamental Theorem of Calculus does not apply). You prove the various properties of the integral from scratch, including FTC. The second part of the module introduces sequences of functions, their convergence and the notion of uniform continuity. This is used to develop integration a bit further, you prove Leibniz’s rule on differentiation under the integral sign, Fubini’s theorem on changing the order of integrals, and some sufficient conditions on integrating a sum termwise and on moving limits into integrals. These are all stuff you would have basically skimmed over and taken for granted in your earlier calculus work, so I quite enjoyed looking at this and being more confident in my manipulations. There was a bit at the end on absolute continuity and bounded variation which seemed a bit out of place and underdeveloped. The third part of the module introduces Complex Analysis, which is much nicer than Real Analysis. A major point is that complex-analyticity (has a Taylor expansion) and complex differentiability are equivalent in the complex functions, whereas not all smooth real functions are analytic. Mainly you focus on line integrals in the complex plane, which have some very powerful theorems associated (including Cauchy’s integral formula, and the residue theorem, though the latter isn’t covered in this course), and can relate back to real integrals to give cool ways of integrating functions like e^(-x^2), sin(x)/x or 1/(1 + x^n) from 0 to infinity. (differentiation under the integral sign mentioned earlier gives nice ways to evaluate the first two, as well, though that isn’t as explored in this course) You prove quite a powerful theorem called Liouville’s theorem, and apply this to show that smooth complex functions satisfying certain properties must be constant or assume a certain form, say a polynomial. (again, this is enabled by complex differentiability being much stronger than real differentiability) This module was lovely, and the assignments were fairly reasonable. There were quite a few questions available to practice. However, the final exam was anything but, and most people seemed to find that it was ludicrously time pressured because the lecturer essentially filled the exam with assignment-level questions. There were very few marks that you could get quickly, as there should be. It was so bad, Dave Wood had to reassure us that it would be considerably scaled. I would imagine next year’s will be easier. (though for the first years that start in 2022, the specification is due to be changed again to add more complex analysis and some fourier analysis so may be harder yet, sorry!)

MA251 Algebra 1: Advanced Linear Algebra

2017/2018

This module follows on from Linear Algebra. The assignments were hard but not the worst of second year. I’d recommend looking at the Maths Dr. Bob videos on YouTube when trying to understand the matrix section. The last section of the course is similar to Algebra 2 content. My advice would be not to heavily rely on a Jordan matrix question in the exam as sometimes long fiddly algebra can lead to computational errors which cost marks.

2018/2019

Whilst the lectures for this module were not the most engaging or coherent, the content was comprehensible and easy to self study, despite the fact that the lecture notes were unclear in places. The exam and the assignments were very doable, making this module one of the easiest this year. As such, I would highly recommend it to everyone who enjoyed Linear Algebra in first year, as it follows from this module very well, and was overall an enjoyable and relaxed module.

2020/2021

Algebra 1 follows on from Linear Algebra in that it is all about matrices; specifically, about changing basis in such a way that the matrices we end up with look “nice”, which means slightly different things depending on the context. A lot of the theory and proofs I found difficult to follow, but most of the module is quite computational and so the hardest part is avoiding silly little errors in your working. I strongly advise practising the computational questions as much as possible; there are tons of examples/questions in the notes, assignments, past papers, etc.

MA249 Algebra 2: Groups and Rings

2017/2018

This module is very different from Algebra 1. If you liked Abstract Algebra, then this module follows on from that. The lecturer wasn’t very good so I relied heavily on the lecture notes and online resources to understand content. Also, the assignments were hard to understand so working with others was useful. The exam was VERY hard, but everyone found it hard (so don’t panic too much!). The content overlaps with Number Theory at times, which was helpful as it meant I’d seen some of the content before.

2018/2019

Algebra 2 is an amazing module although it’s quite different from Algebra 1. The very beginning follows from Introduction to Abstract Algebra ,although the kinds of things you deal with end up being quite different. The module has a lot of content but, especially in the ring theory section, it’s all contained in fairly brief sections. There is a decent amount of overlap in the ring theory section with Introduction to Number Theory but it’s taught slightly differently and one definition actually changed. The lecturer for our year was outstanding and the lectures were an absolute joy to attend. The assignments were all fairly straightforward – although they were marked rather harshly – and as long as you kept on top of all the different definitions and concepts, the module isn’t too hard to follow. Moreover, the exam wasn’t very difficult in our year and was very similar to assignment questions with a few of the more important pieces of bookwork thrown in. Overall, this was certainly one of the most interesting parts of second year and had the most entertaining lectures I’ve had so far.

I really enjoyed Algebra 2, which follows on from Abstract Algebra rather than Algebra 1 (so no matrices here!). The groups section equips you with more tools to investigate and classify the structure of groups, while the rings section has a bit more of a theorem-proof style to it. The assignments are good practice and the lecture notes are extremely good.

MA254 Theory of Ordinary Differential Equations

2017/2018

I really enjoyed this module. The content was hard to understand at first, but once you get your head around it, the module isn’t too bad. The lecturer was really good and set a nice paper. I’d recommend going to the revision lecture as that was useful. This module is good for anyone interested in dynamical systems and anyone taking Intro to Maths Bio as there is some overlap. The exam is pretty standard and I’d recommend learning the diagrams for the specific examples given in lectures, as they are important.

2020/2021

This module revisits some of the material covered in ODES in first year, but with more rigour. Don’t judge it solely on the first 2 weeks, because it gets much more interesting after that! You’re introduced to a wide variety of tools to help you investigate features of ODEs, with the ultimate aim tending to be sketching a phase portrait, which when you get it right, is very satisfying. The exam questions tend to be a mix of ODEs from the notes and slight variations of them, and there are only so many things you can be asked to do, so it’s not too hard. The lecturer is very good, and there are lots of exercises to revise from. Overall, a very well-taught and interesting module.

MA256 Introduction to Systems Biology

2017/2018

I loved this module. There is an overlap with the theory content from Theory of ODEs so if you’re interested in dynamical systems and applications, then this is a good module. This was a term 3 module but the content wasn’t too taxing. I found the section on biological systems hard to get my head around initially, but that quickly fell into place. I would recommend doing the example sheets and attending the support class.

2020/2021

3/5 Fairly cool module – interesting and not too hard, but not brilliantly taught. Basically, if you like ODEs then you’ll LOVE this module- and if you take Theory of ODEs then take this for a nice easy 6 CATs. It’s a term 3 module which isn’t ideal but it does save having to actually revise it! In terms of content it’s a highlights tour of results in ODEs applied to biology, which in all honesty was quite fun. BUT (and this may be highly specific to 20/21) it wasn’t particularly well taught. There were no notes, only 2 very short examples sheets and some fairly unhelpful support classes. Due to the short (3 week) delivery of this module the lecturer wasn’t able to elaborate on any results or examples*. Personally, this module drove me mad because of this, but once you get your head around how to apply the results it’s not too bad. *He is actually involved with COVID modelling so he’s a complete legend, and I think in a normal year this module would’ve been a lot better. – Recommended if you like Differential Equations

MA257 Introduction to Number Theory

2018/2019

Number theory is a beautiful area of maths, and I would recommend this module to anyone interested in number theory/algebra. The content is not always straightforward and some of the proofs are very complicated, but the exam set this year was very fair and most people did really well. There’s also a significant overlap between MA257 Number Theory and MA249 Algebra 2; taking Number Theory will significantly help with the ring theory content in Algebra 2, which I found to be very beneficial.

2019/2020

This module is essentially a whistle-stop tour of number theory, with the main tool being commutative rings and their ideals (hence there is a significant overlap with rings section of Algebra II.) It starts a bit abstractly, looking at different types of rings (mostly integral domains) but then you will apply the developed algebra to number theory problems, such as Pythagorean triples, sums of two/four squares, modular arithmetic and quadratic reciprocity.

This was by far the hardest 2nd year module I did. Some of the proofs are extremely difficult, and the assignments almost more so. The exams that the lecturer (Adam Harper) sets are very repetitive however and are essentially a list of proofs from the lectures with some standard calculations thrown in (e.g. a Chinese Remainder Theorem calculation or calculating a Legendre symbol). It is therefore imperative that you learn the lecture notes and bookwork proofs; it is not sufficient to only do the past papers and redo the assignment sheets just before the exam like you may have done in first year. In fact, this is a key lesson for most second year modules and beyond; past paper/assignment sheet revision may get you a first in first year, but it won’t even get you a 2.2 in second year and above.

In short, this module was really painful (in fact it was harder than nearly all of my third year modules), but if you learn the lecture notes you can still get a very high mark. The lecturer kind of just reiterated the lecture notes. You will prove some famous number theory results (Lagrange’s four square theorem, when can an integer be written as two squares etc.) but I didn’t find them very interesting.

2020/2021

5/5 stars – awesome module, with some really beautiful results. Hands down my favourite module in second year. Number theory is a great area of maths, and studying some seemingly simple questions with a range of tools is very rewarding. I found this module to be well-paced, with a range of interesting results and often nice proofs. There is a fair crossover of content from the latter half of Algebra 2 which is always nice. Adam did a better job than most lecturers of adapting the content to online learning – with very clear and easy to follow notes and thorough online (asynchronous) videos. Assignments aren’t always easy but have some satisfying questions. Recommended if you like Abstract Algebra

MA260 Norms, Metrics and Topologies

2018/2019

This module was amazing. The lecturer was excellent and made the fairly abstract concepts seem intuitive and comprehensible. As such, the lectures were really engaging and absolutely worth going to. The content is lots of small, fairly straightforward proofs which fall together very cohesively. The exam was fair and followed the pattern set by assignment sheets and the metric spaces papers from previous years. Overall, this module was one of the most fascinating, and enjoyable parts of my degree so far and I would definitely recommend it for anyone for whom this module isn’t core.

2020/2021

A huge analysis-flavoured module packed to the brim with definitions, theorems and proofs. In a way, it is easier than previous analysis modules, since a lot of the content generalises what has been seen before, so there are sometimes patterns you can spot in the proofs. There is a LOT of content though. Practice coming up with examples and counterexamples as this sort of thing featured heavily in the exam. There are no assignments, but you should do the exercise sheets at some point to check your understanding, and also as practice for unseen proofs.

ST202 Stochastic Processes

2017/2018

I actually enjoyed this module. I’d heard people say it was awful, but I found it interesting and not too difficult. However, the exam was horrendous. But don’t let that put you off as everyone found it hard! This module is useful if you’re interested in stats and links nicely with some applications (e.g. maths biology). I’d recommend taking Intro to Math Stats before taking this module so that you can have a solid understanding of distributions (which is necessary). Overall, despite the awful exam, I am glad I took this module.

ST220 Introduction to Mathematical Statistics

2017/2018

I enjoyed this module. If you’re interested in stats or some applied areas (e.g. maths biology), then I’d recommend taking this. This module follows on from Probability A and B, explaining some of the content from first year in better detail, and then moves on to hypothesis testing. The hypothesis testing section is hard to get your head around (as it is more theoretical and it had been a while since I’d done hypothesis tests!), so I’d recommend working through the examples given in the lectures. The lecturer was good and explained things well. There are optional assignments which I’d recommend doing as they are useful when trying to understand some of the content. The support classes are also worth attending, even if only to get the assignment solutions!

EC220 Mathematical Economics 1A

2018/2019

This module is all about game theory and, despite ‘mathematical’ being in the title, the maths involved is very basic. It also contains very few economics examples, and differs completely from EC106! The content itself is not too difficult, and is delivered by a fantastic lecturer. However, the exam set this year was absolutely horrendous (although an incredible amount of scaling was applied). I’d recommend taking this module if you would like a break from maths and are interested in game theory and/or economics itself. Also, completing the exercises in the recommended textbook will help you in the exam.

2020/2021

The content, all about game theory, I found extremely interesting. The maths involved is quite basic (and if EC106 is still listed as a prerequisite, then it shouldn’t be). However, there are no proper notes and minimal example sheet questions, so when the lecturer tells you that the Steven Tadelis textbook is absolutely essential, you should believe him. (This is the only maths textbook I have ever bought so far for uni and it was definitely worth it.)

MA359 Measure Theory

2018/2019

Nice module, good lecturer, easy assignments, hard exam. This module is a must do for anyone willing to do some more Analysis or interested in probability/stats. It certainly falls under the category of “if you want to do more maths in the future then you gotta know something about this”. It is important to note it is a prerequisite for many other analysis modules. It essentially establishes basic material that will be fundamental for many other modules (e.g. ergodic theory, probability theory, etc…).

2018/2019

I disliked measure theory a lot. That could be a surprising reaction given I quite enjoyed Functional Analysis 1, which has some crossover. Most of the proofs felt like they used random tricks pulled out of nowhere, which made it difficult to learn ways of proving things in the module. Beyond this, we got quite unlucky with the way the module was examined. If you revised off the notes made in lectures, you were at a significant disadvantage to those who revised using the recommended textbook. The exam paper was entirely example based and in the lectures, we didn’t cover many examples at all so I feel the exam was an unfair reflection on the course that was taught. I would suggest that there is no need to take the module if you’re on the BSc but maybe you’ll like it, who knows? You don’t have to listen to me, I’m not your mum.

MA3A6 Algebraic Number Theory

2019/2020

Algebraic Number Theory is the most enjoyable module I have taken during my degree. It is a very wide field of Maths so the course content tends to vary year on year, but I found that it was taught coherently with each chapter building on/linking to the previous one. This does mean that it is important to keep up with the lectures as it is not a module you can easily dip in and out of.

The lecturer was extremely clear with good pace, and the lecture notes had a fair balance of proofs and examples. The exercise sheets were of a sensible difficulty which enabled us to consolidate the lectured material, and they were a similar style to the exam questions and therefore acted as good preparation.

Unfortunately, the exam this year was much harder than the past papers as questions were worth fewer marks than expected, and many bookwork proofs and examples were given a twist which increased the difficulty significantly. However, I would still recommend this module to anyone interested in this field of Maths as it was incredibly interesting and enjoyable. It is worth noting that there is lots of overlap between Algebraic Number Theory and Galois Theory, so it is worth taking the two alongside each other.

2017/2018

Out of all the modules I studied at Warwick, Algebraic Number Theory (ANT) was my favourite module by far. The module explored some really interesting results – for example, the Noetherian property and the Unique Factorisation of Prime Ideals. We also learnt some fascinating applications, such as how to compute the integral basis of a ring of algebraic integers. ANT also built upon previous ideas introduced in Algebra II and Intro to Number Theory – the perfect fusion of algebra and number theory! My favourite part of this module was learning how to solve Diophantine Equations! The lecture notes were very thorough and well put together – another credit to the brilliant lecturer. I would recommend the module to anyone who has an interest in algebra and/or number theory.

MA3D1 Fluid Dynamics

2019/2020

Fluid Dynamics is a good choice for anyone with a grasp of differential equations. A strong knowledge of spherical and polar coordinates is also incredibly useful. The lecture notes were exemplary, and the lectures were good for anyone requiring a detailed discussion of aspects they didn’t understand; the lecturer gave incredibly clear explanations, although the pace was often slow.

There were no assessed example sheets for this module although I would recommend completing the exercise sheets before the exam as these provide good practice for exam style questions. The exam tends to be very similar year on year (with some questions copied and pasted) so past papers are an essential revision resource.

It is worth noting that the second year Physics module ‘Physics of Fluids’, whilst not at all essential as a prerequisite for Fluid Dynamics, covers very similar content. Therefore, this module may seem fairly dry for anyone who has taken Physics of Fluids.

Overall I would recommend this module to anyone with an interest in applied Maths as it was fairly interesting and didn’t add stress to the term.

MA3D4 Fractal Geometry

2017/2018

This module would appeal to students with an interest in both geometry and analysis, in my opinion. Personally, I found it difficult to connect different components of the module together.

MA3D5 Galois Theory

2018/2019

Galois theory was born when Galois realised why the general quintic polynomial is not soluble in radicals. Basically, he realised that there exists quintic polynomials for which the permutation group of their roots was ”not correct” for the polynomial to be soluble in radicals. Galois theory builds up the algebraic machinery necessary to make sense of what I wrote above. Additionally, using this machinery, you prove other interesting results such as the impossibility of certain ruler and compass constructions and the classification of finite fields. I personally found the constructions laborious at first, but eventually the machine “starts to work” and you obtain very beautiful theorems and proofs. Understanding this machinery is not too hard, but will require some work. This is made easier by Samir’s awesome lecture notes (and Ian Stewart’s book on Galois theory for anyone interested to learn more). Clearly, this module has a lot of algebra. If you really hated Algebra 2, this module is not for you. However, if you are considering doing any number theory or algebraic geometry (or any serious algebra for that matter) in the future, you have to learn Galois theory at some point. This module therefore will be important for you to learn.

A lot of people are put off this module because of the Algebra 2 prerequisite but I would recommend this module to everyone. The necessary algebra content is revisited at the start of the module and doesn’t stretch much beyond definitions of rings, homomorphisms and ideals. This module was easily my favourite of the year. The content was a really nice balance of proofs and calculations and it was delivered by an enthusiastic and engaging lecturer. The module is accompanied by printed lecture notes written by Samir Siksek and a book by Ian Stewart so you will never be short of revision material. People who enjoy this module should definitely consider doing Algebraic Number Theory in the following term.

2020/2021

This module is basically field theory. You will use the theory of field extensions to answer number theory problems; the motivating examples include the insolubility of a quintic and the impossibility of squaring the circle, but you will mainly be applying it to irreducibility of polynomials. This module never fully engaged me. The theory is very abstract but the assignment sheets are quite concrete and rely only on a few key results, hence most of the theory is useless for the assignment sheets. Furthermore, the lecturer (Gavin Brown) went through a small amount of the notes in the lectures, mostly just the key results and worked examples. This meant that much of the theory just went by me and I put little time into the module, only enough to do the assignment sheets. The end result was that the module was a bit unsatisfying. The upside to this was that the assignment sheets were quite fun, and you may find that they’re a bit more “A-Level” (i.e. using results to solve problems) than other modules. I think this module will massively benefit from returning to normal, where traditional lectures will make you fully engage with the content. The exam was, for me, the perfect open-book exam. The questions were tough, but with the notes you could fight your way through them. This module is suitable for any algebraist since there are no non-Core prerequisites (Algebra II only). The ideas overlap significantly with Algebraic Number Theory (although you solve the problems with different machinery), so it may be interesting to do both of them together.

MA3F1 Introduction to Topology

2018/2019

Probably one of my favourite modules so far. The lecturer was really clear with his explanations and open to questions. His website was very helpful. Both TAs were great as well. So on the “logistic” point of view, this module was really well run. As for the content, as you may have guessed this module is about topology, so if you enjoyed metric spaces it’s a good one to take. You will also need some bits from Algebra II (quotient groups, equivalence relations), but nothing too complicated, so you can still take this module even if you didn’t like Algebra II. The content gets harder and more abstract in the last weeks, but again the lecturer is always happy to answer questions and the recommended book (Introduction to Topology by Hatcher) provides a lot of useful examples. Overall, I really enjoyed this module and I hope I have convinced some of you to try it.

I found this module to be one of the hardest that I studied at Warwick. The concepts took a long time for me to grasp and the lecturer relied a lot on ‘intuition’ which I certainly did not have during the lectures. I found there was a real clash between the lecture and support classes to whether topology was all about rigour or intuition. However, once you start to get your head around the topic, this module contains some interesting results. Overall, I would take this module if you are genuinely interested in the subject and want to take it further but you should be prepared to battle with some new ideas and methods of working.

2019/2020

The lectures for this module were fairly straightforward and the lecturer gave very clear explanations and drew lots of useful pictures. The content itself isn’t particularly challenging and the weekly assessed assignments are without a doubt the easiest ones I’ve seen in my degree to the point where they don’t really help teach the content so doing the optional ones is certainly a good idea. However, the exam this year was unreasonably long and made absolutely no sense as a paper. Actually finishing the exam was quite challenging as the questions gave incredibly few marks for a great deal of work. Some of the definitions asked were never properly stated in lectures or in the notes. Overall, the module is fairly interesting, and could make a nice addition to any selection of modules, but the exam could be quite the deterrent and if you’re not interested in topology may be too off-putting. It’s worth noting that, if you’re taking this module as a prerequisite to algebraic topology, some of the material on lifting properties of covering spaces is never taught and is only in the textbook.

2020/2021

Colin Sparrow lectured this module. The module was not lectured amazingly. However, the content was very interesting and would’ve been easy if the module was lectured better. This module is essential for a geometer / topologist. The key topics are:

Fundamental groups: of S^1, homotopy invariance, induced homomorphisms (and a bit of category theory)

Brouwer fixed point theorem

Borsuk-Ulam Theorem

Seifert-Van Kampen Theorem: wedge product, möbius strip and projective space, CW complexes

Generators and relations of groups, topological spaces whose fundamental group is isomorphic to a given group

The exam was quite easy.

MA3F2 Knot Theory

2018/2019

As an advocate for quirkier mathematical concepts, I was really intrigued by the many properties and calculations which we can attribute to knots and links. It would help to have a basic understanding of Algebra 1 and maybe (but not required) Introduction to Topology, but otherwise not much else is needed. Though this module usually gets a bad reputation for its choice of lecturer, this year the lecturer was replaced, in which the new lecturer was very enthusiastic and encouraging, which was a massive help. Even if our lecturer hadn’t been replaced, I reckon the exams are usually pretty straightforward, especially in our year of knot theory. Unless you disagree with the content of the module, I’d definitely recommend!

MA3G6 Commutative Algebra

2018/2019

An oversimplified description of Commutative Algebra would be that it is the study of commutative rings and algebraic structures associated with these rings. However, Commutative Algebra is VERY big and there are many open question that remain within the subject. The lecturer for my year was okay and his lecture notes were okay as well. The subject itself is quite deep with many hard problems. However, I think it is not too difficult to get started and understand most of the content in the module. In my year, we had 5 assignments for the module. Each assignment had a maximum of 3 marks; every correct answer received 0.5 marks and the final mark was rounded to the nearest integer. The assignments were not ridiculously hard, but they were not easy either. It was also important to attend the support classes (or get notes from someone who did!) as some assignment questions depended on the material covered in the support class. Moreover the lecturer we had is not a big fan of hard exams — the exam we had was almost entirely bookwork. This module is an essential prerequisite for anyone wanting to study algebraic geometry in the future (indeed, the course is designed by algebraic geometers) and is also important for any future number theorists and general algebraists. To those who are interested in studying the subject deeper, I recommend the book ”Undergraduate Commutative Algebra” by Miles Reid. It contains most of the course; many exercises and is very clearly written. (A lot of people recommend Atiyah’s book on commutative algebra, but I think that book is terrible).

2019/2020

Commutative Algebra is essential for anyone intending to study further algebra, in particular Algebraic Geometry. The content of this module was fairly interesting and easy to grasp despite an often unclear delivery from the lecturer. The notes were generally good although they did not always correspond to lectures since the order of teaching was different.

The exercise sheets were a reasonable difficulty and indicative of exam style questions, and the lecturer uploaded clear solutions which was very useful. The exam, whilst harder than previous years, was still very fair with a good balance of seen and unseen content.

Overall, for anyone interested in algebra, this module is a fine choice in term 2.

This module is “ideal” if you love algebra but don’t want to faff around with commutativity. However, there are a lot of methods and practice you need to do in order to get the gist of the questions. This isn’t just a copy-the-bookwork module, you need to understand and gain an intuition to the concepts taught, so that you can solve the homework and exam problems. If it’s the same lecturer, he’s not very keen on definitions, so the intuition is crucial.

2020/2021

This module is a whistle-stop tour of many areas of commutative algebra (the study of commutative rings). Topics include prime/primary/maximal ideals, primary decompositions, modules, ring extensions, ideals and varieties, and rings of fractions. This is very useful for any algebraist, especially those interested in algebraic curves, algebraic geometry or algebraic number theory. The ideas you use in Commutative Algebra will come up again in these modules. This is quite a difficult area of maths, and the content is hard despite being so broad. The proofs are very involved and complicated, but this isn’t a big problem since the lecturer (Chunyi Li) avoids bookwork in his assignment sheets and exam. However, he sets hard assignment sheets and exam papers, and is a big fan of “true or false” and “give a (counter)example” questions in the exam. He goes through a lot of this in seminars, so you’ll need to attend all of them and have in store all sorts of examples and counterexamples. He also leaves a lot to intuition and brief justifications, so you really need to understand the concepts, not just learn them. The lecturer is very good at explaining things and often went through some of the assignment questions in seminars, so don’t be afraid to speak to him. In previous years, people complained about the lecturer being hard to understand due to his heavy accent. It wasn’t so bad this year since he didn’t need to shout across a lecture hall, only speak into his mic, but it may be a problem again in future years.

MA3G7 Functional Analysis 1

2018/2019

This module revisits a lot of concepts developed in second year such as normed and complete spaces, compactness and inner products. It then starts to tackle ideas like separability, adjoint operators and spectral theory. A perfect follow on module to Metric Spaces (and probably Norms, Metrics and Topologies?) and a good module to take alongside Measure Theory. A pretty typical Warwick analysis module.

2020/2021

This module is a mix of analysis and infinite-dimensional linear algebra, and the content follows on nicely from Analysis III, Multivariable Calculus, Algebra I and Norms, Metrics and Topologies. You will study many different types of vector spaces (nearly all of which are normed spaces) and the maps you can put on/between them (e.g. norms, inner products, and linear operators). This module is completely accessible to any 3rd Year mathematician, including those who are less interested in analysis, and the content is fairly interesting and quite easy to grasp. The worst thing about the module this year was the exam, which was one of the most insanely hard exams I have ever taken. Even with it being open-book I couldn’t figure out how to apply the results from the lecture notes to the questions and I couldn’t begin to attempt multiple questions. Hopefully Vassili will tone things down from next year onwards. One final hint is that there hasn’t been a exam question yet on the measure theory section or the Sturm-Liouville problem. Whether you take that to mean they have to appear soon or are ignored by the lecturer is up to you.

MA3G8 Functional Analysis 2

2018/2019

This module does what it says on the tin. It’s a follow on module from Functional Analysis 1, pushing most of the concepts you have already learned that little bit further. I found the module to be quite dry and very bookwork heavy but the lecturer was always clear, provided excellent lecture notes and relevant example sheets. If you like analysis, this module is for you.

MA3H2 Markov Processes and Percolation Theory

2017/2018

Pretty fun, decent lecturer, really hard assignments, quite difficult exam. Much easier if you’ve done Stochastic Processes.

MA3H3 Set Theory

2018/2019

Axiomatic set theory is integral to everything you have studied so far. This module is a great stand alone module for analysis and algebra lovers alike. Throughout the module you will explore the axioms upon which our understanding is built, understand cardinalities and finally define the natural numbers, integers, rationals and reals. Working with concepts such as induction, transitivity and recursion, you will reach the axiom of choice and Zorn’s lemma. This module is very accessible and provides an insight in to the foundations of mathematics.

2019/2020

Set Theory is confusing to start with, but once you get a hang of what’s going on, it turns out to be a very straightforward module. You need to make it click, and when it does, it’s quite a nice module to do! The lecturer was awful though, I did well enough ignoring everything he said and just worked from the old notes. Definitely a module for self-teaching!

MA3H5 Manifolds

2018/2019

Manifolds was probably the hardest module I studied in my third year. In short, the course is about smooth manifolds. The theory of smooth manifolds is very rich: you will study vector bundles; differential forms; the generalised Stoke’s theorem and many more interesting topics during the module. However, you will soon realise that these concepts are not easy to digest. Hard work is necessary! This is why I only recommend Manifolds to people genuinely interested in the subject and not looking for easy marks. The lecturer for my year was not good and his lecture notes were terrible. This is why I recommend Lee’s “Introduction to Smooth Manifolds” to anyone intending to take the module in the future. It’s an awesome book, covering all of the module and containing important prerequisites for the differential geometry module in the 4th year.

2019/2020

The lectures for manifolds weren’t the clearest. The lecturer tends to mumble and his handwriting isn’t always legible. The module does have lecture notes and many good textbooks. The lecture notes can be unclear in places but for the purpose of getting used to definitions they get the job done and they have many examples. Be prepared for some very challenging content if you take this module; you’ll likely need to regularly go over all the definitions and the working following them. Moreover, the exercise sheets, particularly the first couple, are very challenging. However, many questions from them regularly come up in the exam and those that do tend to be the easier ones. Despite the module’s apparent difficulty, the exam is surprisingly approachable since it consists mostly of definitions and easier proofs. If you’re interested in doing any further maths, a knowledge of manifolds will be essential so this is a good module to do. I would encourage anyone taking it to try their best to avoid being put off by the difficulty of the material during term.

MA3H6 Algebraic Topology

2018/2019

Great fun, but also one of the most intense modules I’ve ever done. Would recommend for masochists only.

2018/2019

Probably one of the hardest third year modules, but content is very interesting, and also very new (you’ve never seen anything like this before). The module is essentially an introduction to homology theory, and is a nice continuation of Introduction to Topology. This module will require you to get familiar with a lot of new concepts, some of which can seem unnatural and counter-intuitive at first, but eventually everything makes sense. The assignments are also quite hard. There is one per week with about 10-12 questions (of which 3-4 are assessed) and it is important to attempt all of them as some of the results they provide do come up later in the course. For all of these reasons you should expect to spend about twice as much time on this module as for any module (consider it a 30 CATS module).

2020/2021

A very challenging but reasonably rewarding module. Tbf I relied mostly on the book and youtube lectures. Chris Lazda is a lovely guy and all but I don’t think he made the content as interesting to learn as he could’ve. Certainly a lot of time was spent understanding the topics but Im glad I did!

MA3J2 Combinatorics II

2018/2019

This module has 7 chapters, each of which heavily differ from each other, so there is a wide range of content covered, most of which has some pretty satisfying results. If you didn’t enjoy the enumerative side of MA241 Combinatorics, it doesn’t appear much at all, so don’t worry about having to delve into those results much more. The lecturer was quite slow to go through content, but was absolutely lovely and explained things very well. The exam set was also pretty manageable with no particularly difficult questions. If you learn the content well and have a solid understanding, the exam should be quite straightforward. The module is lectured using powerpoint slides, so that might put some people off, but not worth not taking if you enjoy the content.

MA3J3 Bifurcations, Catastrophes and Symmetry

2016/2017

I really enjoyed this module! It starts fairly simple and is an extension of the 1st year differential equations module (2nd theory of ODEs course is useful). Lecturer recaps everything and did a demo with a Zeeman Catastrophe machine to explain concepts. Second half of the course uses aspects from Algebra 2, so some memory of Cyclic and Dihedral is useful. Main disadvantage of this module is there is no online notes for the first half (so you have to be fairly good at note taking).

MA427 Ergodic Theory

2017/2018

Wide range of content (all of it interesting!), but requires understanding and recalling results from every other analysis module ever (I’m talking Analysis 1 to Differentiation to Fourier Analysis to Measure Theory) which I did not have, so I struggled. I’d also say that because there’s so much content, some of it is stated without proof or going into depth. Take that whichever way you want!

2019/2020

Ergodic Theory is Dynamical Systems with added Measure Theory. That’s it. That’s the entire module. So if you liked both of those, it’s a definite recommendation, since revising this is a lot of repeating DynSys definitions and examples. Plus there’s some interesting stuff on information theory near the end of it. However, if you didn’t like one or both of those (I’m guessing it’s the Measure Theory part which is more off-putting), perhaps avoid it, you don’t want to repeat that additional stress.

MA4A5 Algebraic Geometry

2017/2018

One of the most notoriously difficult modules on offer at Warwick, this took me as much time as my project and two other modules combined in term 1. Well worth the effort however, in my opinion the most interesting area of mathematics there is.

2019/2020

Algebraic Geometry is the study of Algebraic Varieties, which are basically zero sets of families of polynomials. However, despite this innocent statement, there is A LOT to learn in Algebraic Geometry. Thats what makes this course difficult : there is a lot of unfamiliar maths to cover in a short space of time. What also makes this course difficult are the biweekly assignments. These assignments are hard and will take most of your term 1.

Unfortunately, the literature for a beginner in Algebraic Geometry is not that great. The best source I know is Andreas Gathmann lecture notes on Algebraic geometry. They are basically a more detailed version of the lecture notes given at Warwick. Also, Miles Reid’s “Undergraduate Algebraic Geometry” is good to have as well.

The course is basically a subset of Joe Harris’s “Algebraic Geometry – A First Course”,with many of the problems taken from this book. However, in my opinion, that book is written very tersely. You may not want to depend solely on this book.

This module is important for anyone with an interest in Geometry, Topology and/or Number Theory.

2020/2021

Algebraic geometry is hard. Not just this module but the general consensus among mathematicians is that algebraic geometry is hard. We study zero sets of families of polynomials and develop tools to help solve problems related to these, you will spend a lot of time learning how to consider your zero sets as hyperplanes in projective space, which makes things easier. You need a good understanding of linear algebra and commutative algebra to do well here.In addition to the literature mentioned above, shafarevich 1 is good for supplementary material, Hartshorne is also brilliant if you want to study beyond the course to understand where the ideas come from.

MA4E0 Lie Groups

2019/2020

The highlight and focus of the course is on maximal tori in Lie groups which is a genuinely very interesting concept yielding a nice analogue of Sylow’s theorem for finite groups. Unfortunately, this year’s exam didn’t cover tori at all so most of everyone’s revision was probably for nothing. On the bright side the TA is great!

2020/2021

Lie groups are essentially manifolds, which are also groups, and whose tangent spaces are Lie algebras – a pretty cool concept. The lectures were awkward to follow and the notes are rather dense, however they do have everything you need to learn the course. Be warned though- don’t try it if you aren’t comfortable with manifolds knowledge.

MA4E7 Population Dynamics

2017/2018

This module brings together lots of different modelling techniques which can be used to apply maths to real-world problems (no biology background is needed). The module starts with deterministic models (which overlaps a lot with MA3J3) and then looks at adding in stochasticity (usually Gaussian), age structure (PDEs) and spatial heterogeneity (distance kernels). Familiarity with the 2nd year Stochastic Processes module will be useful. The assignments (which aren’t for credit) tend to be much harder than the exam and are full of mistakes. This module is definitely appropriate for 3rd year students who have taken modules covering aspects of continuous-time markov chains and fixed point analysis for a systems of ODEs.

MA4J3 Graph Theory

2018/2019

As a graph theory enthusiast, I really enjoyed this module. Graph Theory doesn’t quite focus on the many properties and results that many mathematicians have proved throughout the years, but focuses more on developing your techniques into understanding and proving results. If you like a lot of bookwork and factual recall, this isn’t the module for you. The lecturer likes to include many several mark questions which are heavily unseen content, even in the compulsory, which tests your ability to develop your own proofs. This isn’t an easy module, and I would only recommend it if you take the time and effort to properly understand not just the content but the general ideas on how the proofs work.

MA442 Group Theory

2019/2020

Group Theory is basically making a module solely dedicated to finding all simple groups of order less than 500. If you like groups and manipulating them using a variety of techniques, this is a fun module, though it’s difficult to visualize some of the concepts introduced. The last chapter is pretty much using every technique in the previous 6 chapters in order to find some sort of counterexample, and no doubt you’ll be asked to use exactly the same techniques to counter a simple group of order >500. As you’d expect, if you like groups, you’ll find this fun.

2020/2021

The module basically takes the group theory section of Algebra II and extends it to a full module. After a review of Algebra II, the new content includes nilpotent and soluble groups, blocks, matrix groups and the transfer homomorphism. The end goal is to classify the simple groups of order up to 500 using this machinery. The lecturer this year was Inna Capdeboscq, but the lecture notes and assignment sheets were originally written by Derek Holt. Inna was a very good lecturer, but I found the proofs to be very unintuitive which made them difficult to learn. Furthermore, the assignment sheets were extremely hard and tedious with even Inna admitting they “make you want to pull your hair out”. The worst thing is that the content itself was just bland with nothing really standing out. The section on matrix groups is absolutely awful, it goes on and on for ages and it’s pointless, but the section on nilpotent and soluble groups was quite nice once you get past all the definitions. Inna decided to set a fairly easy exam this year, but past papers (probably set by Derek) look much harder. It’s hard to say what future exams will be like. In my opinion, this module is only worth it as a 4th year CATS filler or for avid group theorists. But be warned: when people say, “Group Theory is an easy 4th year module”, they mean it’s easy relative to some other 4th year modules. No 4th year module is easy, and Group Theory was certainly harder than all the 3rd year modules I took this year.

MA426 Elliptic Curves

2019/2020

Elliptic Curves has a heap of content, but a lot of it seems like waffle, when really you should be sifting through to find what you need to understand to solve the problems (here’s a hint, the complex chapter is useless). However, once you know the techniques, applying them is quite fun, and I’d suggest that this module is certainly closer to A-Level calculation-based maths rather than your boring repetitive bookwork nonsense. Also, there’s not really any need for prerequisites, and it pairs well with a Maths in Action project on cryptocurrencies, which at least 9 people figured out.

MA424 Dynamical Systems

2019/2020

Dynamical Systems is basically taking functions and analysing their orbits on points in order to solve problems. This is a relatively nice module for a 4th year one, and has some interesting examples, such as sequence maps which depend on matrices, and maps on the unit circle. Very straightforward module, would definitely suggest it for anyone who doesn’t know what 4th year modules to fill up their CATS with. Also very accessible for 3rd years.

MA4K8 Maths-in-Action

2019/2020

Judging by my housemates’ long struggles with their research projects, the Maths in Action project seems like the easier option, but is still a lot of work. Like with the 2nd year essay, make sure you decide what you want to do early and that will encourage you to work on it, in which the Christmas holidays is the perfect time to do so! You also get free pizza at the presentation sessions!

MA4H4 Geometric Group Theory

2019/2020

Honestly, I didn’t pay much attention to this module because the safety net had me covered. The lectures were rather dull and the content was a tad dry, but it incorporated graph theory into the geometry, which was a bonus. Would definitely recommend Intro to Topology to get an understanding of fundamental groups beforehand though.

MA475 Riemann Surfaces

2019/2020

A Riemann Surface is a one dimensional complex manifold. The module is about exploring the properties of these surfaces. This often involves generalising what you have learned in complex analysis to manifold theory and mixing in some topology.

It might not be surprising then that the results of this module are as ‘nice’ as complex analysis and the content of the module is of interest to many types of mathematicians. Riemann surface theory is important to Algebraic Geometers, Differential Geometers, Dynamical Systems people and even Algebraic Number theorists.

The module is taught very well, with a good lecturer and insightful example sheets. The content of the module is taken form Beardon’s Primer on Riemann Surfaces.

Overall, a good module which should be interesting to many people!

MA4L7 Algebraic Curves

2019/2020

Algebraic Curves is the study of one dimensional Algebraic Varieties. Despite what is written on the module webpage, Algebraic Geometry is a NECESSARY prerequisite for the course. It is impossible to take this module without taking Algebraic Geometry.

In my opinion, the course was lectured very badly but the lecture notes were ok. The example sheets were tersely written, which made doing assignments a painful experience.

I would say the module is only useful for future Algebraic Geometers or Algebraic Number Theorists.

If you do intend to take this module, I recommend that you take a few books out of the library. This is because the content of this module is not contained in any one book. Miles Reid’s UAG and UCA are helpful.

In addition, Chapter 4 of Hartshorne’s Algebraic Geometry may help you understand the course better, even though you may not understand his proofs (which use schemes and sheaf cohomology).

Fulton’s Algebraic Curves is also useful.

2020/2021

In this year, algebraic curves was lectured by Diane Maclagan, so the course was very different to how Miles lectured it. A curve is a 1 dimensional algebraic variety, you’ll study field extensions, local rings of regular functions, function fields and so on. These things lend themselves to concrete examples which were taught well in general with plenty of approachable (non-assessed) exercises. All the of this year’s lectures are good to revise from if you have access to them

MA4C0 Differential Geometry

2019/2020

I will go as far as to say that Differential Geometry is BY FAR the hardest to understand mathematics module offered at Warwick. To put that into perspective, I also took Algebraic Geometry, Cohomology and Algebraic Curves in my final year.

The course is about Riemannian Geometry. There is a lot to say about Riemannian Geometry! Therefore, there is a lot to learn if you take this module.

I recommend Lee’s “Introduction to Riemannian Manifolds” and Jurgen Jost’s “Riemannian Geometry and Geometric Analysis” as textbooks for the module. You may also want to have a look at Lee’s “Intro to Smooth Manifolds” to remind yourself off the necessary manifold theory needed to understand this module.

This module is important to any future geometer and/or theoretical physicist (General relativity uses “pseudo-Riemannian geometry”). Obviously, only take the course if you are interested in differential geometry. It will be a lot of hard work!

MA4A2 Advanced PDEs

2019/2020

The Advanced PDEs module is about the theory of existence and regularity of solutions to 2nd order linear elliptic PDEs.

It turns out that, in general, “solutions” to such problems are best formulated in spaces called Sobolev spaces. About 7 weeks of the module is devoted to developing the theory of these spaces and their associated embedding theorems. The rest of the course is about applications of this theory to some PDEs.

In my opinion, the module contains some very interesting analysis (you will need measure theory and functional analysis 1). You will also see applications of many results in functional analysis that you learned in the previous year, which might have otherwise appeared to have been unmotivated at the time.

The lecturer for my year was good, but I still think the module is quite hard, with many difficult example sheet questions (get support class notes!) and many hard to remember proofs. The bible for PDEs is given by Evans (the module is equivalent to chapters 5 and 6 of his book), and it is a very good book. His book should make things easier to learn.

Partial differential equations are important to wide range of disciplines: from fluid mechanics to stochastic analysis to differential geometry. Therefore, the content of this module will be important to most people reading this.

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