# 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.

MA112 Experimental Maths

2016/2017

I thoroughly recommend this module. Most people were put off by it being in term 3 but it was a nice module. Firstly, you work in groups of 3 on the assignments so they don’t take up too much revision time. Also, the lab teachers are very helpful when you’re stuck on a question. The labs don’t take the full 3 hours allocated. Personally, I liked having a coursework module and I found it gave some structure to the first few weeks of term 3.

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.

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.

MA125 Introduction to Geometry

2017/2018

Would 100% recommend for any maths student. It’s a short 6 CAT module, and although the lectures can be quite confusing (Mondino likes to go through really complex arguments) the exams are really nice – none of the confusing stuff from lectures comes up, and you can easily get a 2:1 just by learning definitions and standard proofs. No assignments either so less workload during term.

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.

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.

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!

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.

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.

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.

MA244 Analysis 3

Note: This module has had considerable changes to its syllabus as of 2018.

2017/2018

This module is all integration and then norms. The exam was partly assignment questions but don’t just learn the answers as other questions rely on understanding the content. Examples of functions and norms are really useful to have up your sleeve. The lecture notes for this module are good.

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.

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.

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.

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.

MA125 Introduction to Geometry

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.

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.

2017/2018

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.

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!

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.

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.

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!

MA256 Introduction to Mathematical 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.

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.

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.

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.

2018/2019

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.

MA3F1 Introduction to Topology

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.

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.

2018/2019

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.

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

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.

2019/2020

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.

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.)

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.

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

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!

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.

MA3H5 Manifolds

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.

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.

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).

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).

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.

MA427 Ergodic Theory

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.

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!

MA4A5 Algebraic Geometry

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.

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.

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.

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.

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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