## Year 2 Module Reviews

##### 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.

##### 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.

##### 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.

â€‹

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.

â€‹

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 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.

##### 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.

â€‹

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.

##### 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.

â€‹

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.

##### 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.

##### 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.

##### 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.

##### 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.

##### 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!