Today’s conversation marks roughly one year since I started collaborating with the Official Student Blog. To celebrate the event, I titled this post after my very first one, the subjects involved being obviously different.
I’m sure many newly-enrolled students in Economics, Management, Finance and the Social Sciences (EMFSS) programmes will have to take a combination of Mathematics 1, Mathematics 2, Statistics 1, and/or Statistics 2. With this in mind, why not share with you some general information about those units? Even prospective students might find it useful.
For convenience, I’ll use the abbreviations Math1, Math2, Stat1, and Stat2. Also, I’ll try and be more concise with respect to my first post since mathematics and statistics are supposedly familiar to most students, unlike economics. On top of that, I now have to condense my impressions on four subjects in one post only. Therefore, I must ignore some aspects and limit my contribution to a series of thoughts. Nevertheless, you’re free to comment below in case you have something to add or ask.
Let’s start with mathematics.
Math1 is popular with lots of students taking it every year. Its main goal is to bring students with sometimes significantly different backgrounds up to a common level, which is required to follow various intermediate courses.
It’s not particularly difficult but, if you struggle with it, you need to brush up on your basic maths. For this purpose, a good book to consider is Foundation Mathematics by Booth – I used it and definitely recommend it to fill potential gaps between high-school and university-level maths. Often, what seems like a tricky exercise actually involves simple rules: understanding mathematics’ building blocks is fundamental to not get stuck on more complicated topics.
Math1 essential reading is Mathematics for Economics and Finance by Anthony and Biggs. Prof. Martin Anthony authored Math1 and Math2 subject guides – among others – and I found his approach to teaching extremely valuable. Not surprisingly, he is head of the LSE Department of Mathematics.
As always, the single most important thing in maths is to practice it. It’s definitely true for most subjects but it’s even ‘more true’ for mathematics. If you do not have enough past examination questions, take a look at Introduction to Mathematical Economics by Dowling. It contains many exercises to practice with and – should you be interested in intermediate courses building on mathematical economics – you’re likely to use it again.
Another valuable resource is Calculus by Binmore and Davies. It’s slightly more formal than other recommended texts, but a good choice if you’re passionate about maths. As the subject guide says though, it is, at times, more advanced than we need.
As regards Math2, my suggestions are basically the same as above. Of course, it substantially expands on Math1. However, once you master the latter, you’ll have no problem with Math2. You’ll rather love it as it offers further insights into the application of mathematics to economic problems.
For those of you interested in more advanced modules like Further Mathematics for Economists and/or Mathematical Economics, there’s a book presenting all of the indispensable tools aspiring economists need. It also features among Math2 recommended texts. I’m talking about the widely-adopted Mathematics for Economists by Simon and Blume. If you intend to pursue graduate studies in economics, I warmly suggest you get a copy of it.
Irrespective of what I said within the preceding paragraphs, in order to do well in both Math1 and Math2 exams, make sure you fully cover the essential material: subject guides, video recordings, Anthony’s book, and past examination papers.
Finally, always keep a pen and a piece of paper when reading maths. Complete mathematical derivations on your own while reading and check your result against those in the book.
By the way, this applies to stats too. While reading books or subject guides, try to anticipate what follows in a particular sentence or paragraph. When you feel an important passage is going to be outlined, stop reading. Reflect on what you’ve read then try to predict where the author is going to go. This is an alternative way to ensure we understand what’s being described.
If we can ‘decipher’ a text and ‘predict’ it, we can have a conversation with it. We certainly want to listen to it but we also want to ask it questions, stop it, and finish what it has to say. It sounds weird but works pretty well!
Let’s move to statistics.
This is another subject I fell in love with since the beginning. I never took a stats course in high school but Dr. James Abdey made it possible for students to learn stats in such an accessible way that I overcame initial troubles rather smoothly.
For those who don’t know James Abdey yet, he wrote Stat1 and Stat2 subject guides. Plus, he provided us with excellent video-recorded lectures covering all of the topics presented in those two units. He’s been doing an incredible job to help us fully understand elementary statistics.
Stat1 and Stat2 are among the best EMFSS courses from an organisational perspective, if not The Best. The virtual environment is comprehensive in terms of both resources and guidance. Discussion among students is usually encouraged. Then, whenever we fail to find a proper solution to a given problem, James always gives us hints pointing to the correct answer.
Like maths, stats has wide applicability. The social sciences are no exception. Without even realising it, people do stats every day. The difference between them and stats students is that the latter learn how to channel through powerful models the huge amount of information generated by interactions at all levels. Thus, they can formally assess hypotheses and critically evaluate others’ statements, actions, and so on. I find it exceedingly stimulating.
Compared to Math1 and Math2, I didn’t read too much beyond the essential readings in Stat1 and Stat2. The reason is that UoLIP material is impressive as far as these two units are concerned.
The primary reading is common to both half-courses: Statistics for Business and Economics by Newbold, Carlson and Thorne. You may want to use it to check you thoroughly understand the subject guides as well as a source of additional exercises.
There’s another text I’d like to mention, which may be useful in Stat2: Introduction to Mathematical Statistics and its Applications by Larsen and Marx. Since I didn’t use this book, I cannot comment on it. Nonetheless, the subject guide classifies it as further reading so you can turn to it when dealing with tricky concepts. Different perspectives on a specific matter generally contribute to understanding it better.
In this respect, a few more words are necessary. We must be comfortable with mathematics if we are to appreciate Stat2, especially when it comes to probability and distribution theory – the core of the course. Hence, make sure you get a good grasp of your maths modules.
This leads us to a second point. Unlike Stat1, where routine calculations are frequent, Stat2 requires us not only to understand how things work the way they do but also why do they work that way. That means we need to make an extra effort. Probability scares you? It scared and fooled me too, more than once! So, besides the usual tip (i.e. practise as much as you can!), I suggest you spend a wealth of time reasoning on the why.
In other words, doing things mechanically – although intuitively easy – is surely part of the deal. However, in Stat2, the most important ingredient is deep understanding rather than proficiency in computation.
As above, it’s vital to go through the essential material meticulously: subject guides, online quizzes and practice questions, video recordings, the academic-moderated discussion forum, and past examination papers.
The most important lesson I learnt from stats? Awareness. Awareness of the power and limits of the instruments we adopt to make sense of the world in the social
sciences. Blind application of mathematics and statistics doesn’t get us very far. We make a great deal of assumptions in economics so we always need to evaluate their feasibility! Elements of Econometrics is the perfect place to put into practice what we learn in Stat1 and – to an even greater extent – Stat2.
Now, some comments on the difficulty of the modules.
When I was in my first year, someone told me Math2 and Stat2 were considerably tougher than Math1 and Stat1. In fact, it ended up being the other way around for me.
I wasn’t particularly talented in maths and stats. For this reason, I spent more time on Math1 and Stat1. Once I completed those, Math2 and Stat2 seemed easier. I soon realised Stat2 would have been my favourite subject. Incidentally (perhaps, not quite incidentally), I got my highest mark so far in that unit.
Moral of the story: don’t get agitated by those frightening statements you sometimes come across before studying a subject first hand. You may reach opposite conclusions about its difficulty. In spite of our similarity, we’re all different – and we should celebrate this fact!
Indeed, we all react differently to education and I think we also differ in the way we learn. Some of us find it easier to study for quantitative subjects while others prefer qualitative ones. Some even excel in both types of subjects. For instance, Dr. Abdey himself said the more mathematically-inclined students could actually find Stat2 easier than Stat1. It all boils down to our characteristics, in addition to our commitment and dedication.
Fine. That was my series of thoughts. As I said, given the nature of a post, it’s quite short and selective. I hope it has at least generated some interest.
Last but not least, some news for the aficionados.
Over the past year, I’ve been thinking about transferring from the BSc Economics and Finance to the BSc Economics due to my increasing interest in such a wonderful discipline and the fact that I plan to carry on with it at graduate level. The transfer has just been made official ;-)
Thus, whilst finance is naturally intertwined with economics, I’ll be chiefly exploring the latter realm in the near future.
Oscar is studying for the BSc Economics independently in Italy.