Guy's Statistics and Mathematics for Economics blog

Equations in Google

2011-12-14T09:09:00.002Z

You can now stick equations into Google.Try this one: sqrt(cos(x))*cos(400*x)+sqrt(abs(x))-0.4)*(4-x*x)^0.1 (Thanks to Alex Bellos for this tip)

There is no maths gender gap

2011-12-13T10:26:00.000Z

A soon to be published paper by Jane Mertz of the University of Wisconsin-Madison and Jonathan Kane of the University of Wisconsin-Whitewater has debunked the idea that there are genetic differences between males and females in their mathematical ability.Mertz J and Kane J (2012) Debunking Myths about Gender and Mathematics Performance, Notices of the AMS, Volume 59 Number 1 pp 10-21

RPI versus CPI

2011-08-24T08:20:00.003+01:00

Jill Leyland has written an excellent summary of the issues on the Significance website of the Royal Statistical Society.

Gender and confidence in mathematical ability

2011-06-15T08:54:00.003+01:00

A new study of 14 year old Swedish high school students has found that whereas boys are overconfident, girls are actually underconfident regarding their mathematics performance. The students were asked what grade they thought they would get in a mathematics test a week later. The results were then compared with their actual grade.

I might try this out with my second year economics undergraduates next semester.

Dahlbom, L et al (2011) Gender and overconfidence: are girls really overconfident?
Applied Economics Letters Volume 18, Issue 4, Pages 325 - 327.
http://www.informaworld.com/10.1080/13504851003670668

TED talks on maths and stats

2010-12-09T10:02:00.007Z

You probably know about the wonderful TEDtalks online videos that are available on a whole range of subjects, but in case you don't they are well worth checking out.

I have recently been contacted by someone at bachelorsdegree.org where they have helpfully highlighted the 20 best maths TEDtalks on a page called 20 Incredible TED Talks for Math Geeks. I found the talk by Peter Donnelly (number 17 on their list) particularly interesting (and enjoyable).

If you want to keep up to date on maths and stats TEDtalks you can of course just put "TED talks on maths and stats" into Google and it will give you the currently available talks. You can also create an e-mail alert to be told about new talks as they are added.

The Joy of Stats

2010-11-29T08:52:00.002Z

Hans Rosling is Professor of Global Health at the Karolinska Institute in Stockholm. For a BBC TV programme "The Joy of Stats" he has created a wonderful dynamic graphic analysis showing the evolution of health and wealth in diiferent parts of the world over the last 200 years. A YouTube video clip is available here.

Comic books to help you learn mathematics

2010-11-11T14:08:00.007Z

"Effective teaching of math has two parts. One is imparting the particulars of symbol twiddling. The other is explaining how to use the symbol twiddling to solve a problem" writes Kenneth Chang in his recent review in the New York Times of three comic books that aim to make maths understandable to those who fear it.

The one he likes best is HOT X: ALGEBRA EXPOSED! by Danica McKellar, who is also an actress appearing in the TV show "The Wonder Years". She has two other maths comic books out, “Math Doesn’t Suck” and “Kiss My Math,” and, according to Chang, strikes the right note in being entertaining but also accurate in terms of the maths content.

"Management information" versus statistics

2010-08-12T08:17:00.003+01:00

There is a very interesting story on the Straight Statistics web page about the difference between "management information" and official statistics. It follows a spat between Francis Maude, Minister for the Cabinet Office, and Sir Michael Scholar, chair of the UK Statistics Authority, over measures of the number of people on the public sector payroll. Both men agree that there is a difference between "management information" and official statistics, but have different views on what practical implications this has.

The Straight Statistics blogger thinks that this issue might come up again in relation to the kind of information that we usually rely on the Census for.

Straight Statistics

2010-06-23T08:53:00.001+01:00

"Straight Statistics is a pressure group whose aim is to detect and expose the distortion and misuse of statistical information, and identify those responsible. It has been formed by a group of legislators, statisticians and journalists, chaired by the Labour peer Lord Lipsey."

The Steven Strogatz column in the New York Times

2010-06-16T07:54:00.002+01:00

I have mentioned this wonderful mathematics column before. Now there is a single web page where you can see all the topics he has covered.

Go to http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/

Another Maths cartoon

2010-05-29T09:29:00.001+01:00

Randy Glasbergen has produced another cartoon about mathematics.

Statistical literacy guide

2010-05-19T15:28:00.003+01:00

Statistical literacy guide
How to spot spin and inappropriate use of statistics by Paul Bolton, House of Commons Library, Soical & General Statics section, April 2010.

Algebra cartoon from Randy Glasbergen

2010-05-12T15:09:00.003+01:00

"Algebra will be useful to you later in life because it teaches you to shut up and accept things that seem pointless and stupid."
http://www.glasbergen.com/wp-content/gallery/cartoons/toon_81.gif

"..the derivative tells you how fast something is changing; the integral tells you how much it’s accumulating"

2010-04-13T07:49:00.002+01:00

There is a nice piece on calculus from STEVEN STROGATZ writing in the New York Times.

Maths cartoons

2009-08-24T14:32:00.002+01:00

I love maths cartoons. Check this one out from xkcd

Gauss, Lagrange and the others: who were they?

2008-10-14T09:25:00.001+01:00

As economists we need to make use of mathematics in our work. We use equations to represent relationships between economic variables. We draw graphs to illustrate the nature of these relationships. We use algebraic methods to solve systems of demand and equations to find the equilibrium price of a good. We differentiate a total cost function to obtain an expression for marginal cost. We check necessary and sufficient conditions to ensure that we have located the optimal combination of consumption of various goods for a consumer aiming to maximize her utility subject to a budget constraint. We use matrix algebra to represent and manipulate equations linking final demand and intermediate demand for goods and services between different industries.

Sometimes the mathematical (and statistical) tools and methods that we use have the names of famous mathematicians of the past associated with them. Here are just a few of the names that students taking the course in Statistics and Mathematics for Economics at Portsmouth will come across - in no particular order: Cramer, Gauss, Lagrange, Fisher, Kuhn and Tucker. Perhaps you may wonder who these people were and what is was that prompted them to develop the mathematical tools and methods linked to their names.

Today, by making use of the Internet and a search tool like Google, it is easy to find out. For example a seach for "Lagrange" can lead you to the website at St Andrews Univesrity in Scotland at MacTutor History of Maths where you can read that Lagrange is alleged to have said "If I had been rich, I probably would not have devoted myself to mathematics." which refelects the fact that economics is often the impetus for the development of new mathematics.

Of course there are many excellent books available that give some historical background on the development of mathematics and statistics. One of my favourite books on the history of statistical methods is David Salsburg's The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century

If you would prefer to watch a video or a TV programme rather than reading a book or a text based web site I have good news for you. You can find a lot of useful maths and stats video clips on YouTube (although a search for Lagrange will lead you mostly to clips of ZZ Top!). But right now there is an excellent programme on TV called The Story of Maths: The Language of the Universe. It's a four part series presented by Oxford professor Marcus de Sautoy and covers important developments in mathematics from ancient Egypt, Mesoptamia and Greece up to more recent times. A joint production with the Open University, you can find more about the series on the open2.net website. Mind you, I am extremely envious of Professor du Sautoy. In making the programme he got to travel to Greece, Egypt, Syria, Italy, India, Morocco and several other places where important developments occurred in the history of mathematics; including Göttingen in Germany to find out about Gauss and his contribution.

A singular matrix

2007-07-16T15:07:00.001+01:00

They call me A and I am square
Of order 3 by 3
But I have a little secret
That it won't take long to see

I cannot be inverted
Whatever method you try
I have no power to the minus one
And here is the reason why

For I am not of full rank
Correlation between my columns is one
Some call me singular
And my determinant is none

I've got linear dependence across and down
That's all there is to be said
I just cannot be reciprocated
Or stood upon my head

Transpose me if you will
The result will be just the same
It won't make any difference
If my rows and columns are exchanged

I am a singular matrix and that is that
You can add to me or subtract
I can be multiplied too when I am conformable
But not inverted, and that's a fact.

Economics and the Matrix

2006-10-12T09:18:00.000+01:00

My title sounds like a new addition to the successful Matrix film series. Actually it is a cheap trick just to catch your attention!

Matrix algebra is widely used in economics to write compactly and to manipulate simultaneous equation linear economic models. Although ordinary algebra works OK when there are only two or three equations to worry about, it becomes increasingly cumbersome and unwieldy as the number of equations in the system increases. This is where the methods of matrix algebra come into their own. You will find economists use matrices (the plural of matrix) not just to solve systems of linear equations, but also to obtain the "reduced form" of a model expressing the equilibrium values of the endogenous variables in terms of the exogenous ones, to manipulate input-output models that show the inter-relations between different sectors of the economy and to work with different estimators and test procedures in econometrics. It is therefore essential that all students of economics have a good grasp of at least the basics of matrix algebra and an understanding of how it is used in economics.

The recommended textbook for my course on further mathematics for economists at Portsmouth is Fundamental Methods of Mathematical Economics by Alpha C Chiang and Kevin Wainwright. However this book is rather expensive and you might try to look for a second-hand copy of an earlier edition of this book, when it was just authored by Chiang.

Alternatively you might look for some free notes and material online. I have tracked down a few helpful sites for you - see below. But however much reading material you have the only way to learn maths is to do it. So if you are taking my course please make sure that you work on the problem sheets I have prepared (if you have mislaid them you can get hold of them from the unit website) and come to all my classes. If you are not on my course and have just stumbled on this blog because of an interest in mathematics, I hope that you find something interesting here!

Some useful links on matrix algebra

Matrix algebra notes from Aidan Kane at the National University of Galway, Ireland
Matrix Algebra: An introduction to the theory and application of matrices from Morello Publishing Ltd
notes from D S G Pollock
Matrix Algebra Review from Eric Zivot at the University of Washington
SOS MATHematics website
Matrix algebra notes from Phillip Wood in Missouri
Matrix algebra notes from xycoon.com
Matrix algebra material from Stefan_Waner including
a matrix algebra interactive tool and a True/False quiz

Welcome

2006-09-07T14:34:00.000+01:00

Hello everyone

I have created this blog to support a course that I teach to economics undergraduates at the University of Portsmouth called Statistics and Mathematics for Economics.

Students can get all the handouts for this course from the course web site which, of course, is to be updated as the course develops. However I shall also make use of this blog to provide a weekly update guiding you to other online material that you might find helpful and allowing interactive comments from you.

For a start if you feel that you need to revise basic maths you might go to the Resources in Maths for Economists section of the Higher Education Academy Economics Network website where you can find tutorial material and quizzes to help you fill in any gaps in your knowledge. You can set yourself an instant Remedial Maths test if you want first to see how you measure up.