Making a good start with Mathematics and Statistics

Hello readers.LSE Study guides

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.

m1Math1 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 trueMaths test paper 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.

maths equation

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.Graph

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.

s2The 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.

10 thoughts on “Making a good start with Mathematics and Statistics

  1. Dear Oscar,
    I was reading your article and i enjoyed it all the way to the end. I was studying Business Administration last year with UoL but i changed my course to economics and finance this year because of my huge interest at economics and when i received the books , i was kind of surprised reading through the math 1&2 guides and i felt i need to brush up on my High-school math once again , i disagree with you when you say( brush up on your basic maths), i believe you need more than basic and kind of advanced math to complete your math 1 and specially math 2 . I am familiar with Statistics because of my previous studies and in economics and finance it elaborate a lot more . I feel UoL should provide
    Lindley, D.V. and W.F. Scott New Cambridge Statistical Tables. (Cambridge: Cambridge
    University Press, 1995) second edition [ISBN 9780521484855].
    this book to all students rather than telling them to buy it as an essential book . As Statistical Tables are extremely important to study Statistics 1&2. You could tell this message to UoL and students through your writing .

    I agree with you that we can understand math better by reading recommended books ,But as we live in a digital world , I can suggest to brush up on your basic and advance maths through http://www.khanacademy.org
    Sometimes you can learn better watching than reading , and i believe some of students is unable to buy so many essential books with a high cost. In khan academy, you can access from beginner to advanced level (algebra,linear-algebra,differential-equations,calculus,statistics-probability,trigonometry,geometry) and also they have advanced tutorial on Economics & finance, all those are for free.
    https://www.khanacademy.org/economics-finance-domain
    https://www.khanacademy.org/math/geometry-home
    https://www.khanacademy.org/math/trigonometry
    https://www.khanacademy.org/math/statistics-probability
    https://www.khanacademy.org/math/calculus-home
    https://www.khanacademy.org/math/differential-equations
    https://www.khanacademy.org/math/linear-algebra
    https://www.khanacademy.org/math/algebra-home

    With love and best wishes for exam ,Tanvir Hossain -EMFSS student .

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  2. Hi Tanvir.

    Many thanks for your comment. It’s always a pleasure to see people actually read what one writes and express their views. I appreciate that. Moreover, I’m happy to know there’s a new aspiring economist around!

    Now, let me comment further on some points you raise.

    I agree with you Math1 is not basic. In fact, when saying ‘brush up on your basic maths’, I had in mind potential situations where students struggle to understand the exposition of the subject guide, especially its earlier sections. Thanks for pointing that out.

    However, I can assure you it’s not advanced either. Even if one doesn’t know what derivatives and integrals are, the concepts are introduced in an accessible way and students need to remember how to apply a limited set of rules to standard problems. As I said, Math2 substantially expands on Math1. Nevertheless, I’m sure by the end of the course you’ll realise it’s not advanced.

    As for relatively more advanced modules, we have Calculus and Algebra. These are foundation units for those interested in rigorous mathematics and economics. The treatment is pretty formal and require students to start working with precise definitions and proofs. Conversely, Math1 and Math2 focus on the application of given rules to a narrow set of economic problems, which is considerably less burdensome for those of us not inclined to abstract mathematical reasoning.

    This is not to say that Math1 and Math2 are easy. Again, it depends on your background. If one hasn’t been doing maths for a while, they might even look seriously difficult, hence apparently advanced. On the other hand, some fellow students with solid high-school mathematical bases already know most of the material covered in these half-units and they complete them rather quickly. In this case, they find them rather basic. So, it’s indeed a subjective matter.

    What I can safely say is that, objectively, looking at maths from a broad perspective, these are elementary subjects – even for economists :-D

    The most demanding mathematical subject available to our degrees in economics – except for the BSc in Mathematics and Economics and the Graduate Diploma in Mathematics – is probably Further Mathematics for Economists. In that case, yes, the maths is substantially different from Math1 and Math2. There’s quite a big leap, in my opinion, as we need to work with definitions, theorems, and proofs.

    Now, Khan Academy is an excellent resource and Salman Khan is doing an extraordinary job in helping people world-wide, especially those who don’t have alternative ways to educate themselves. So, feel free to use its videos, particularly given you find it helpful to learn by watching. I encourage other students to integrate their preparation with any useful resource available on the web. There are plenty of nice videos on YouTube!

    As for the books I suggest, you don’t need to buy them. If you prefer digital copies, you can easily find them on the web in PDF form. So, zero costs – excluding, of course, the cost of electricity. Even if I prefer second-hand hard copies, you can find old digital copies of the suggested books. Perhaps, don’t do this for subjects where recent information is essential. In maths, however, not only this is possible but also advisable.

    I have to disagree with you when you say Khan Academy offers advanced tutorials in economics. It doesn’t at all. Again, you can watch whatever economics-related videos you find useful but don’t expect to get an advanced preparation in economics on Khan Academy, at least at the moment.

    As regards the New Cambridge Statistical Tables, I cannot tell students and UoL what you suggest to do because that would mean encouraging copyright infringement. Therefore, it’s not advisable for me to suggest this practice publicly simply because it’s illegal.

    Despite this, you can find the essential tables at the end of several past examination papers – see, for instance, 2016 ST104a or 2014 ST104b exam papers. I suggest you print them to practise over the year as they’re exactly the same we’re given on the examination day. So, you don’t need to buy the entire set of tables. It’s an essential reading, not an essential purchase! Just make sure you become fast at retrieving the relevant information to solve specific questions.

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  3. Dear Oscar,
    Thank you for writing back on the points that i have mentioned . Your this article was very helpful to many of the students including me who is on first year of economics at UoL, i recommended and shared your article to many of my friends on the same course and they appropriate your article as very helpful .
    Now let me express some my disagreement and agreement from your comment

    I would like to point out ,when you say ”its not basic and/ its not advanced either ”, if you look in to my previous comment you will find where i say ” i believe you need more than basic and kind of advanced math to complete your math 1 and specially math 2”, i did not mentioned you need advanced math but said kind of advanced.
    University of London has students all around the world ,and when UoL register a student they look into their exam marks of secondary study. Theoretically you can assume that study quality will be same according to their marks around the world but in reality there is a huge differences on the study quality around the world not to mention language barriers and those students who start study just one month before of the exam and collect some suggestion and get a good mark on the exam not even knowing the main theory of the study subject. Now if you look into those students you will find kind of advanced situation for them on the math. Now in math 2 i believe there is some use of Differential equations and Linear algebra, which i can ensure you i didn’t got on high-school or if they taught i didn’t follow it but still got good grades .
    Now i can agree with you when you say ”This is not to say that Math1 and Math2 are easy. Again, it depends on your background” yes its depends on your background ,now if we assume 10% of the UoL student are like Sal Khan(khan academy founder) ,whom we can call the newton brain . But what about the rest of the 90% who is not a newton brain but still a UoL student and got good grades.you can count me one of them :D. so on my argument i can say its a kind of advanced math situation for 90% of them.
    I agree with you when you say khan academy doesn’t offer advanced tutorial on economics for the moment but i believe they have enough resources for the 1st year students and they are expending their resources a lot faster than they ever did before.
    About the New Cambridge Statistical Tables i thank you for your suggestion and will do as you recommended.
    On the last i would like to Quote few words from Sal Khan(khan academy founder) and recommend a video
    Sal Khan”Let’s teach for mastery — not test scores” those words does show the foundation of future study ,why not start now !

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  4. I’ve just read through my comment again and I need to explain a sentence more appropriately as it sounds contradicting. Namely, ‘these are elementary subjects’ sounds contradicting because a few paragraphs above I agreed with you Math1 is not basic.

    What I meant was that Math1 and Math2 keep the algebra and calculus at an elementary level. So, obviously, they’re not basic like addition and multiplication we study in primary school but they’re elementary in the sense that their content is neither at intermediate nor advanced level.

    This is fair in my opinion as we’re not studying for a BSc in Mathematics or other STEM disciplines. If you look at maths courses studied via STEM degrees, you’ll get an idea of what advanced maths means.

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  5. Dear Oscar,
    Thank you for clearing-out the fact more widely . I do have a knowledge on advanced Mathematics , as some of my cousin did it on the BSc level and they are doing it on MA level. A statement can be described in many ways/views .I do understand your point of view ,since your looking it from a senior position , but if your read my comment deeply ,i believe you can understand my point of view too.

    Hope and wish to read your wonderful article on new subjects more :)

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  6. Sorry Tanvir. I didn’t see your message when commenting on my contradicting sentence :-D

    I agree with you on what you say in your second comment. I had not solid math bases myself when starting with UoLIP so I understand the situation of many students around the world and appreciate the challenges. My knowledge of maths was indeed quite rough!

    I always try and look at things from a broader perspective. That’s the reason of my statements above. The fact is that, having friends studying for STEM degrees, associating the words ‘advanced maths’ to Math1 or Math2 sounds almost disrespectful :-D

    I didn’t want to convey wrong messages and I hope my successive explanation made it clearer.

    Sure, I hope too Khan Academy will expand its (already huge amount of) resources! I totally support his approach to education and I watched several videos where he explains his views on learning. Amazing. Plus, doing private tutoring for free makes me feel very close to inspiring people like Sal.
    My comment on economics material on Khan Academy derives from objectiveness (i.e. no advanced-level economics there). I wasn’t trying to denigrate the organisation and I do agree with you there are valid resources.

    I sincerely hope to keep discussing with you in the future! You might even consider becoming a blogger yourself!

    ‘See’ you!

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  7. Hi Oscar
    Thanks for your informative blog post.
    I am writing to get some information on the economics related courses that would be hard to tease out of a prospectus and hope your first hand knowledge would help.
    I’m a health professional who completed the MSc in Epidemiology via London International (through LSHTM). I had previously done a different in-house course at LSHTM and can honestly say their distance learning materials were brilliant and suited someone like me who learns at their own pace. As long as the resources are good, I prefer to go over things several times until I understand them, rather than half pay attention through a lecture taking away only my poorly made notes! In that way, I do like the Khan Academy approach as you’ve discussed above and have used it myself.
    I’d like to begin an economics related course next year and probably will go for the BSc over the graduate diploma. I have an A-level in mathematics and the MSc in epidemiology had a lot of statistics that were beyond A-levels.
    The question I had was which would be the best option. There are a few “economics and/with…” combinations, but even looking at the descriptions can’t tell what the best would be for me. If looking at healthcare related economics, would just the straight economics be a good option?
    The only other query I had was with regard to the quality of the learning material. With LSHTM, their materials were brilliant. Essentially they were downloadable lectures to view via your browser with online support/forums and practicals. Would you rate the learning resources from LSE highly.
    Many thanks for your help.

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  8. Hi DT.

    Thanks for your comment. Here are my thoughts.

    The Graduate Diploma in Economics (which you’re not currently considering as main option) might be a good compromise, if you’re looking for an intermediate-level knowledge in core economics subjects like Micro, Macro, Econometrics. These are the same fundamental courses you’d study in all of the Economics-related degrees. They’re widely applicable so, independent of the specific area of economics you’re interested in, they’d definitely provide you with sound bases.
    You also have an elective as part of the Diploma. Although there are a few modules you could find interesting, given your background and objectives, I’d definitely suggest Public Economics.

    Now, if you’re not happy with four modules only, the alternative (as you say) is the BSc.
    As you say, there are a few options. Yet, given your profile, I’d exclude with a fair degree of certitude the BSc Mathematics and Economics, BSc Economics and Finance, and BSc Economics and Management.

    Depending on your specific interests within the realm of healthcare as well as the geographic region you’ll mostly work in, the other remaining programmes offer a diverse array of options. These are (roughly in order of pertinence) the BSc Economics, BSc Development and Economics, and the BSc Economics and Politics.

    If development and/or politics are not areas where you intend to work most of your time, then I’d play it safe and go for the BSc Economics. In this case – assuming you’ll study via Graduate Entry Route – you’ll only have three electives among the following list of courses:

    http://www.londoninternational.ac.uk/courses/lse/one-300-course-prefix%1F-ec-chosen-selection-group-e

    The one you’d better take is Public Economics because, in my opinion, it’s highly relevant when it comes to healthcare. As for the other two, it’s up to you.

    I hope I’ve somehow restricted the pool of options you started with. Actually, as you can see, should you eventually decide to go for the BSc Economics, you won’t have many choices: only two electives (assuming, of course, you’ll follow my advice and take Public Economics!).

    Generally, as regards the material, I’m satisfied. All of the core courses have, at least, video-recorded lectures, subject guides, and discussion forum together with, at least, the past three annual examination papers.
    Most of the electives don’t have video-recorded lectures but you can safely rely on discussion forums, subject guides, and past examination papers.
    I’m one of those students who voraciously use discussion forums. That’s because they’re our main tool in terms of academic conversation. It’s a lot of self-studying but you’ll probably appreciate it as this aspect was part of your previous studies too.
    In particular, economic subjects primarily aim at developing our analytical skills. We mainly analyse problems via graphical, mathematical, and statistical tools. Logic is also part of the story as well as verbal explanations of the underlining economics principles.

    Do consider the Graduate Diploma though. I think it might be a good choice. Of course, if you plan to pursue graduate studies in economics where calculus and linear algebra are necessary requirements, in addition to elementary statistics and intermediate economics, then a BSc Economics is almost a must.

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  9. Just to clarify, when I say “…assuming you’ll study via Graduate Entry Route – you’ll only have three electives among the following list of courses…”, I meant in addition to the other six compulsory modules. That is, you won’t only have three modules (i.e. electives) as part of the BSc via Graduate Entry Route :-D

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  10. I am looking for a change in career, and have enrolled into Mathematics & Economics. I work full time, but also have rest days off as part of the shift pattern. Just wonder how many modules are advisable to take. My math is pretty good. I was thinking maybe three modules to start with.

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