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This free, self-paced data science course will introduce you to some key ideas in data science.

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This free, self-paced data science course will introduce you to some key ideas in data science.

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The course provides you with some valuable insights into the career opportunities in this exciting field. You will be introduced to what data science is, how it works and how it can be applied.

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Data Science

Learn about data science and how it's applied to the world of work, suitable for both Core Maths and A level Mathematics students

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COURSE OVERVIEW

This free, self-paced data science course will introduce you to some key ideas in data science.

The course provides you with some valuable insights into the career opportunities in this exciting field. You will be introduced to what data science is, how it works and how it can be applied.

Each lesson will have video tutorials, activities, and further reading to supplement your learning.

The lessons involve coding activities that can be accessed in Python notebooks, a web-based programming environment. No previous coding experience is needed to access the course as all the commands used are given. You will interact with activities by copying, pasting and editing existing code.
6 online study sessions
The course is offered via the MEI website , but an alternative version is available on , and all the resources will be accessed via this page . The coding tasks can be accessed via Kaggle Google Colab.

Summary

FORMAT

On Demand

AUDIENCE

Teachers, Students

DURATION

12.5 Hours

SESSIONS

6

TIME

Online

COST

Free

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Introduction to Data Science

The Lessons

The lessons involve coding activities that can be accessed in Kaggle, a web-based programming environment.

Frequently asked questions

Your common Data Science questions and concerns answered

How much does it cost?

All of our Data science courses and resources are free to all students and teachers.

Who can I contact for more information on how MEI can support Data Science?

If you would like to discuss how MEI can support you in your teaching journey, then please contact us:

Email: datascience@mei.org.uk

Phone Number: +44 (0)1225 776776

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Introduction to Data Science - An MEI Course

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A free self-study course in data science will introduce you to key concepts and offer valuable insights into career opportunities.

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Buy Humble Pi: A Comedy of Maths Errors 1 by Parker, Matt (ISBN: 9780141989143) from Amazon’s Book Store. Everyday low prices and free delivery on eligible orders.

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Helen Ball (Author), Peter Ransom (Author)

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AQA Level 3 Mathematical Studies Student Book (Collins AQA Core Maths)

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Buy AQA Level 3 Mathematical Studies Student Book (Collins AQA Core Maths) Student diction by Ball, Helen, Ransom, Peter (ISBN: 9780008116200) from Amazon’s Book Store. Everyday low prices and free delivery on eligible orders.

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How to use statistics to face up to life's major risks.

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How to use statistics to face up to life's major risks.

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Cambridge Ideas - Professor Risk - YouTube

David Spiegelhalter's proper title is Professor of the Public Understanding of Risk. He is in two minds (literally) about playing it safe or chucking caution to the wind. Decisions, decisions!? Are bacon sandwiches really that dangerous and is it wise to drive when you love cycling? David shows us how to use statistics to face up to life's major risks.

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People have used money – and made counterfeits - for thousands of years. Archimedes came up with a clever way of finding out if you’ve been cheated by a goldsmith. Making coins with the right proportions of the right metals presented a huge mathematical challenge for Fibonacci and other mathematicians in the middle ages.

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Professor Sarah Hart 11th October 2022
How can you detect a counterfeit coin? Why aren't coins square? Why is the wizarding money used in the Harry Potter universe so implausible? In this lecture we discuss the mathematics of coins. I'll focus on three main areas: creating, and testing for, the correct mix of metals, choosing the best coin shapes, and deciding on the ideal range of denominations.
Creating and detecting the real thing
Money has been used for thousands of years, and in that time there has been a huge range of materials in use, everything from gold and other precious metals to shells, leather, and of course paper. Many of these materials are "token" currency, in that they are not in themselves inherently of value. A five-pound note does not consist of five pounds worth of material. This is all very well if everyone agrees on the system. The advantage of gold and silver coins was that their value is intrinsic. If you have a gold coin then it is, literally, worth its weight in gold. Or at least, it is unless it is a counterfeit.

Counterfeiting is as old as trade, and one of the first stories about detecting it involves Archimedes. The story goes that the king (Hiero II of Syracuse, where Archimedes was from) had commissioned a golden crown and had given his goldsmith a certain amount of gold with which to make it. But Hiero suspected that the goldsmith may have in fact kept some of the gold for himself, making up the weight with silver. So, he asked Archimedes to find out the truth, without, of course, damaging the beautifully-wrought crown. An object made of a mixture of gold and silver, which is less dense than gold, would have a larger volume than one made of the same weight of gold. But it's surely impossible to measure the exact volume of so intricate an object as a crown. So how did Archimedes do it? Vitruvius, the Roman architect, wrote an account in his De Architectura (around 30 BCE) - it's a story we all remember: Archimedes sitting in his bath pondering the problem, suddenly realising that when he got into the bath he displaced exactly the same volume of water as the volume of his body, and then jumping out of the bath and running naked through the streets shouting "Eureka". The crucial realisation was that this is a way to measure volume without damaging an object (at least, not a metal one). Archimedes, goes the story, proceeded to take a block of pure gold the same weight as the crown, a block of pure silver the same weight as the crown, determine how much water they displace, and then compare how much water the crown displaced. With this information he could calculate exactly how much silver had been substituted. Legend has it that the goldsmith had indeed cheated the king.

The tale of Hiero's crown is an early instance of using the mathematics of density and volume to detect a forgery. The issue is somewhat simpler if you are comparing objects that are supposed to be the same size and composition, like coins. A suspect "gold" or "silver" coin can be weighed against one known to be genuine. It's also possible to determine the composition of a particular class of coin (say ones minted by a different country's mint) to determine exchange rates, by assaying. If you have a mixture of silver and gold plus other impurities you can determine the precise amounts by melting a sample, oxidising away the impurities, weighing what's left, which will be a mix of silver and gold, then dissolving the silver with nitric acid, to leave only the gold. You can then work out how much silver there had been, and what proportion of both of these were in the original alloy.

The other side of the coin, so to speak, is the challenge of the official mint: creating coins that have the precise legally required proportions of given metals. There's a nice paper by former Gresham geometry professor Norman Biggs on it if you are interested - the details are at the end of the transcript. An Italian mathematician and merchant called Leonardo of Pisa described techniques for producing alloys of a desired purity, or "fineness", in his extraordinary 13th century book Liber Abaci. You may not have heard of anyone called Leonardo of Pisa, but you probably have heard of him by his nickname Fibonacci. The so-called Fibonacci sequence was not invented by him, it had been known in India and elsewhere for a long time, but Liber Abaci was probably the first Western book to include it.
The shape of money
Now we know how to make a coin of the desired composition. But what does it look like? Most coins through history have been circular, though not all. There are examples of triangular and square coins, and other polygons with up to sixteen sides, as well as coins with round, square, and hexagonal holes. There are also rectangular and oval coins. Holes are useful for storing coins on strings or necklaces. Originally, coins would have been basically rounded lumps of metal. Then, when they began to be stamped with for example the Emperor's profile, they became flat. The round shape naturally forms a roughly circular shape when impressed with a stamp like this. A circular shape is more robust than one with lots of sharp corners, as these would wear down more quickly or possibly break off. A final reason is a more modern one. Vending machines find it easier to differentiate between different coins if each coin has a fixed diameter that's different from all the other coins. Circles, of course, almost by definition, are shapes with a constant width - their diameter at any point is exactly twice the radius. (This is useful for coins because of vending machines, but it also explains why most manhole covers are round. You don't want the cover to accidentally fall down the hole. With a circular cross-section, there is no way it can be aligned to be any narrower, so you are safe from that calamity.) But the circle is not the only shape with this property.

The same reasoning works for any higher odd number of sides. We can have a "pentagon of constant width", and also (pertinently for money) a "heptagon of constant width". This is exactly the shape of British 20p and 50p coins. (I have a soft spot for the 20p coin, which was introduced in 1982, because when I was a child it was the coin the tooth fairy brought me. My own children got one-pound coins: there's inflation for you.)

These curved shapes I've just described are called Reuleaux polygons (after the German engineer Franz Reuleaux who investigated their possible mechanical applications). The technique only works for odd numbers, because regular polygons with an even number of sides have the problem that every vertex is opposite another vertex, and the distance between two opposite vertices is always going to be greater than any other cross-sectional slice, however much you bulge out the sides. Reuleaux polygons do have some applications outside of coinage, too. For example, one property they have is that they can make a complete rotation inside a square such that at all times every edge of the square is in contact with the shape. A Reuleaux triangle drill bit will produce a very nearly square hole. This isn't just theoretical. One such drill bit was patented by Harry Watts in 1916 - it needs a special chuck to allow the centre of rotation of the bit to move, but with that in place, it covers over 98% of the square.

As well as the heptagonal coins in UK currency, there's also the Canadian one-dollar coin (nicknamed the "loonie" because it has a picture of a loon on one side): this is an eleven-sided Reuleaux polygon. Some Bermudian coins are Reuleaux Triangles. There's the 1997 one dollar coin, as well as several "Bermuda Triangle" commemorative coins.

This is cute, but why do it? Why not just make circular coins - it's easier after all? Of course, it's just fun to have a bit of variety. It's also harder to counterfeit a Reuleaux polygon than a simple circle, but there's one possible other reason, and it's to do with areas.

Firstly, there's a theorem called Barbier's Theorem that says all shapes of constant width s have the same perimeter, namely πs . This is fairly easy to see for circles (diameter s means circumference πs ) and Reuleaux polygons, whose perimeters are arcs making up half the circumference of a circle of radius s , but far from clear that it holds in general. However, it does. On the other hand, the areas of these shapes can vary. A Reuleaux triangle with constant width s can be thought of as the superimposition of three 1/6th slices of a circle of radius s . So you can find the area by adding three of these together, but then remembering that this counts the equilateral triangle inside three times. So the formula for the area is

This is less than any other Reuleaux polygon and also less than a circle of diameter s , which would have area 1 4 π s 2≈0.79 s 2 . In fact it can be shown that the Reuleaux triangle has the smallest area of any shape of constant width s . So, in terms of material used, for a given width you save money with the Reuleaux triangle. You might like to work out the area of a Reuleaux pentagon with constant width s . Is it better or worse than a circle?

Of course, anyone familiar with British coins will have spotted that not all coins can possibly have constant width, because we have a twelve-sided coin: the £1 coin. This has an even number of sides, so it can't (and indeed doesn't) have constant width. So, what's going on? It's not the first twelve-sided coin in British currency. Many years ago the threepenny bit had twelve sides. However, you'll notice that the modern £1 coin does have slightly curved sides. This makes the discrepancy between its smallest (23.03mm) and largest (23.43mm) widths small enough for vending machines to cope. The old threepenny coin would have caused more issues (if you wish, you can calculate the difference between smallest and largest width to confirm this), and that is why the curved sides were adopted.

So, the coin is a "near enough" design that satisfies vending machines. That doesn't mean I have to like it.
Coin values and denominations
Now we have coins made of the right alloys and the right shape. Our final currency decision is what denominations they should have.

Essentially everyone has decimal currency nowadays - in other words, a currency where units are subdivided into powers of ten sub-units. For example, Euros, and US dollars, are divided into 100 cents; pounds sterling are divided into 100 pence. The Nigerian Naira is 100 Kobo, one Russian rouble is 100 kopeks (and has been for over 300 years). And so on.

There are only a handful of exceptions, mostly where the subdivisions are now too small to be used, or where the currency is not in use for other reasons. For example the scudo is still the official currency of the Sovereign Military Order of Malta, though everyone uses Euros and has done for many years. The scudo is divided into 12 tari, with 1 tari equivalent to 20 grani.

But historically, the situation was reversed - almost every currency was non-decimal. Why? And why did it change? Just as an example, if we look at historical British money, we had shillings divided into twelve old pennies, and twenty shillings in the pound, or sovereign. (And 21 shillings in a guinea.) Pennies in turn were divided into four farthings (from the word "fourthling"). They were legal tender until 1960. So, you can divide up a shilling into two, three, four, six whole numbers of pennies, and into greater subdivisions with halfpennies and farthings. A few hundred years ago there were coins worth ¼ penny (the farthing), ½ penny, 1 penny, 2 pence (the half groat), threepence, fourpence (groat), sixpence, a shilling, half a crown (2 shillings and sixpence), a crown (five shillings), and gold sovereigns (1 pound). This is simplifying matters slightly because the values of the silver and gold coins fluctuated with the prices of these metals - that's why guineas ended up being worth slightly more than a pound - and the purity of the coins; silver coins had ever-increasing amounts of copper, with the currency being repeatedly debased because of it. The values weren't formally fixed until later.

You could divide a pound equally, using whole numbers of pennies, into 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240. There's not as much flexibility in the decimal pound, which can be divided equally into 1, 2, 4, 5, 10, 20, 25, 50, and 100. That's the big advantage of pre-decimal shillings and pounds. The big disadvantage is the arithmetic. Once you start writing down calculations, it is very cumbersome to use our decimal number system for calculations in a system that has twelve pence to the shilling and twenty shillings to the pound. (Consider also our baffling imperial units of sixteen ounces to a pound and fourteen pounds to a stone, but obviously (!) twenty fluid ounces to a pint in the UK, and sixteen in the US. Our American friends have a rhyme for converting water volume to weights: "a pint's a pound the world around". Only it isn't because in England "a pint of water weighs a pound and a quarter".)

If you think pre-decimal currency is bad, spare a thought for Harry Potter and his Hogwarts friends. In J.K. Rowling's books, wizard money consists of golden galleons, silver sickles and bronze knuts. There are 17 sickles in a galleon, and 29 knuts in a sickle. This is an insane system that wouldn't even allow amounts like half a galleon, never mind the formidable arithmetic that would be required to make transactions.

Back in the real world, people have been making the case for decimalisation for hundreds of years. In 1696, Christopher Wren, former Gresham Professor of Astronomy, proposed the introduction of a silver "noble", divided into 10 "primes" and 100 "seconds", "which Centessimal Division will be very proper for Accounts". The objections to this idea and others were mostly that, desirable though it would be, people would never be able to learn a new system. Of course, if a country is brand new that's less of a problem. The United States dollar, introduced in 1792, was divided not into "pieces of eight" like the Spanish silver dollar from which it took its name and initial value, but from the start into tenths (dimes) and hundredths (cents). The debate in Britain rumbled on, and in the 19th century several commissions and a lot of parliamentary time was taken up with it. The florin (two shillings) was introduced in 1849 as a possible precursor to decimalisation, because it's a tenth of a pound (and some of them - the so-called Gothic Florins - even had "one tenth of a pound" written on them). There was even a double florin, briefly, which is equivalent to our modern 20 pence piece, because it is a fifth of a pound. The double florin, though, worth four shillings, was very close in size to, and easily confused with, the five-shilling crown, so it was withdrawn. It was only minted for four years, from 1887-1890 [15]. After yet more Royal Commissions, including in 1918 and 1961, decimalisation was finally agreed, and the big switchover happened on 15th February 1971.

So, what coins should we have? It makes sense for whole numbers of smaller coins to go into the pound. This means the possibilities for coins are 1, 2, 4, 5, 10, 20, 25, 50. In the UK we have six of these eight: 1p, 2p, 5p, 10p, 20p, 50p (as well as £1 and £2 coins). A 4p coin would not be very useful - it can already be made with two 2p coins, and is too close in value to the 5p. In the US, they have fewer coins: 1 cent, 5 cents (nickel, though at 75% copper and 25% nickel, perhaps it should be called a copper), 10 cents (dime), and 25 cents (quarter). There is a dollar coin but, due to the enduring popularity of the dollar bill, it hasn't caught on.

Is one system better than the other? The best systems combine simplicity (a small number of different denominations) while allowing change to be given using a small number of coins. The simplest system - just have 1p coins - would require us all to lug great big bags of coins around all the time. At the other extreme, if there were a coin of every value we would need gigantic cash registers for all the different coins and would no doubt never have a 47p coin when we needed one. As a measure of how efficient different systems are, Dr Adam Townsend at the University of Durham suggested using the average number of coins required to make up each amount of change up to the point where the currency switches to notes. For the US, that's one dollar. For the UK, it's five pounds. We can think about whether this is the right measure or not. Some currencies have notes starting at much lower values than others, and this may skew the results. I modified the Python script he recommended to calculate not just the mean but the median number of coins, and I also felt that a US - UK comparison would be more informative if we calculated the change up to the same amount in both currencies: 99p/99¢. My code, and links to his articles, are at the end of this transcript.

For values of change from 1p up to and including 99p, the current UK system needs a (mean) average of 3.43 coins, and a median of 3 coins. For up to 99¢ the US system needs a mean of 4.75 coins and a median of 5. So it's much worse, with some amounts needing eight or even (for 94¢ and 99¢) nine coins (the UK system never needs more than 6 coins). Adam Townsend calculates average change up to and including the smallest bill so it calculates 4.75 for the US system but 4.61 for the UK.

By the way, if we had eight fingers like most cartoon characters, rather than ten, we'd probably use a base 8 system with 8×8 pennies in the pound. Then we could have 1, 2, 4, 8, 16 and 32p coins, and with a £1 =64p and £2 = 128p coin, we'd need only a mean (and median) of 4 coins to make change up to the smallest note being a £4 = 256p note, and you'd need at most one of each coin for any given amount of change. But I digress!

Should the US switch to 20 cents rather than quarters? Then the coins are 1, 5, 10, 20. The mean average change is 5.05 coins, so the US should stick with quarters, unless it wants to add other coins, like a 2 cent or 50 cent coin. Does this mean the should UK switch to "quarters" rather than 20p? Curiously, this would make absolutely no difference to the amount of change received. The outcome is identical, given the other coins we have.

All this assumes we are getting change in the most efficient way. Anyone who has used an automated checkout at a supermarket knows that's not always the case. Because self-checkout machines are often based on global designs, and most countries have fewer different coins than us, these machines can take any of our eight coins but can usually only give six different kinds of coins in change. Most often, this is 1p, 2p, 5p, 20p, £1, £2. If we just look at amounts of change up to 99p, we now find we get 4.75 coins on average (or a median of 5), which is much more than we would get from a human. If we test amounts up to £4.99, we get a mean of 5.91 and a median of 6. Interestingly, as Adam Townsend points out, things would be much better if the coins instead were 1p, 2p, 5p, 20p, 50p, £2. For amounts up to 99p you would get a mean of 3.84 coins and a median of 4.

There are some issues with coins. The 5p is irritatingly small. The 1p and 2p are irritatingly heavy. (If you are outside the UK, you probably have similar gripes with your own currency.) Is it time to ditch some of them? We used to have halfpenny coins, even post-decimalisation, and we even had farthings within living memory. The farthing was discontinued in 1960 and the halfpenny in 1984. Now, I've done some calculations, with the aid of the Bank of England's inflation calculator (at time of writing, as it only covers complete years, the calculator only compares a given year to 2021 prices.) It turns out that £1 in 1960 would be worth £16.18 today (or actually at the end of 2021). One farthing is a quarter of an old penny, and so 1/960th of a pound. So that farthing would be worth 1.7 new pence as at 2021, and with inflation at over 10% in 2022, that's only going up. By that token we should get rid of the 1p coin and we are close to the point where we might consider getting rid of coppers completely.

How about halfpenny coins? They were discontinued in 1984, and £100 in 1984 is worth £263.02 today. So a 1984 halfpenny would be worth 1.3p today. Again, a strong case for getting rid of the 1p coin. (In fact, halfpennies would have been phased out sooner, except that the Bank of England were worried that it might worsen inflation, as all the prices might be rounded up to the nearest penny.) The halfpenny coin was not missed as a coin in itself, but some had other uses for it. A letter to the Times begged "let not its existence be imperilled. It is indispensable for levelling off pendulum clocks". We would manage perfectly well without the penny. The Canadian mint ceased production of the Canadian cent (fondly known as the penny) in 2013. They didn't have a two cent coin so their smallest coin is now 5 cents. Items can still be priced in pennies, and electronic transactions can still be done to the nearest penny, but change is given to the nearest five cents.

One day we may not use coins at all. But I think that day is still (happily) quite far off. I hope you've enjoyed this mathematical guide to coins. In my next lecture on "maths and money" we look at how maths can help us to find the best strategies when we buy, sell, bargain, barter, and bid at auctions. I hope to see you then.

© Professor Sarah Hart 2022
Further Reading

Hiero's Crown: for a description of how the account of Vitruvius could have been correct, see The Vitruvius Tale of Archimedes and the Golden Crown, by Amelia Carolina Sparavigna, https://arxiv.org/ftp/arxiv/papers/1108/1108.2204.pdf. Professor Chris Rorres at Drexel University has posted the relevant passages of Vitruvius, the treatise of Galileo, and other sources, alongside English translations, at https://www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html

For a much more in-depth history than I can give on alligation and linear programming, read the excellent paper Linear programming from Fibonacci to Farkas, by Norman Biggs, which you can download at http://eprints.lse.ac.uk/106596/.

If you want to read Liber Abaci and your Latin is on the rusty side, there's an English translation (we only had to wait 800 years!) Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation, by Laurence Sigler (Springer New York; 2002, ISBN 978-0387407371).

Marianne Freiberger wrote a good article in 2017 about the introduction of the 12-sided £1 coin in Plus magazine: https://plus.maths.org/content/new-1-coin-gets-even

You can read a short summary of the history of decimalization at the Royal Mint website: https://www.royalmint.com/discover/decimalisation/decimal-debate/

Adam Townsend's entertaining blogs about coin denominations in different currencies and about vending machine change appeared in Chalkdust magazine.

https://chalkdustmagazine.com/blog/forget-a-new-1-pound-coin-we-need-a-1-pound-23-coin/

https://chalkdustmagazine.com/blog/self-service-machines-give-awful-change/
He also made a programme on change for Radio 4's "Boring talks" about it, which is well worth a listen: Boring Talks Episode 33: Change https://www.bbc.co.uk/programmes/p06xvmpz

The Python script I used is adapted from the one Adam Townsend used. My script is below, and you can play around with it at one of the many free online Python compilers, for example https://www.w3schools.com/python/trypython.asp?filename=demo_compiler

coins = [1,2,5,20, 100, 200]

rangecoin=99

min_coin = [100] * (rangecoin+1)

min_coin[0] = 0

for min_of_i in range(rangecoin+1):

for c in coins:

if c <= min_of_i and (min_coin[min_of_i - c] + 1 < min_coin[min_of_i]):

min_coin[min_of_i] = min_coin[min_of_i - c] + 1

print(min_coin)

print(sum(min_coin)/rangecoin)

import statistics

print(statistics.median(min_coin))

The Bank of England's inflation calculator https://www.bankofengland.co.uk/monetary-policy/inflation/inflation-calculator can show how prices compare to today, for any year since 1209!

Image Credits

Unless otherwise specified, the technical diagrams are drawn by me and are ©Sarah Hart; photos/images are either taken by me or are public domain images.

Hiero II coin, photo by Sailko, CC BY 3.0, via Wikimedia Commons. https://en.wikipedia.org/wiki/Hiero_II_of_Syracuse

Reuleaux triangle drill bit gif by LEMeZza, CC BY 3.0, via Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Rotation_of_Reuleaux_triangle.gif

Images of coins (20p, 50p, £1, Canadian "loonie" dollar, Bermuda currency), are copyright the various national mints, but their use falls under the fair use policy.

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People have used money - and made counterfeits - for thousands of years. Archimedes came up with a clever way of finding out if you've been cheated by a goldsmith. Making coins with the right proportions of the right metals presented a huge mathematical challenge for Fibonacci and other mathematicians in the middle ages.

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In this TED Talk Hans Rosling presents the results of our public surveys that shows that people don't know key aspects of global development. And Ola Rosling shows that this has nothing to do with intelligence. It's a problem of factual knowledge. Facts don't come naturally. Drama and opinions do. Factual knowledge has to be learned. So Ola teachers 4 rules of thumb for not being ignorant about the world.

Date Posted: 2018-01-18

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In this TED Talk Hans Rosling presents the results of our public surveys that shows that people don't know key aspects of global development. And Ola Rosling shows that this has nothing to do with intelligence. It's a problem of factual knowledge. Facts don't come naturally. Drama and opinions do.

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Imagine all people in the World lived along one long street. And imagine all houses were sorted by income. The poorest to the left. The richest to the right. What would it look like, and where would you live?

Back in 2003 Anna got obsessed with the idea of making such systematic photo documentation of all common items from homes all over the world, to see what everyday life looks like, with different incomes. Her project launched in 2016 with more than 300 homes from 52 different countries documented. Anna was then invited to present it at TED in Vancouver in April 2017, and now you can watch her talk here. (Or scroll down to see how you can contribute to this unique free image bank, by adding more homes from more countries).

Even if we have 300+ families documented, we want more. Dollar Street is a one of a kind image bank of everyday life across the world. It uses photos as data to show what life looks like on all different income levels. If you like to contribute with more homes, please contact [email protected] (All images are free to use, under Creative Common License CC BY 4.0.).

Date Posted: 2018-01-18

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Imagine all people in the World lived along one long street. And imagine all houses were sorted by income. The poorest to the left. The richest to the right. What would it look like, and where would you live?

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Increasing participation in Core Maths, AS/A level Mathematics and Further Mathematics

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Why do Biology and Environmental Science students study Core Maths?

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Why do Biology and Environmental Science students study Core Maths?

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Why do geographers and Sociology students study Core Maths?

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Why do geographers and Sociology students study Core Maths?

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Tim Harford explains the numbers and statistics used in everyday life

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Graphs from the New York Times and student discussions about what they show

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Graphs from the New York Times and student discussions about what they show

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Graphs, maps and charts from The Times — and an invitation to students to discuss them live.

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If you’ve been trying to find resources for Core Maths revision, you’ll know it’s not easy.
It’s going to take me a while to build this resource up but here’s a starting point.

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How Not to Be Wrong: The Hidden Maths of Everyday Life

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Buy How Not to Be Wrong: The Hidden Maths of Everyday Life 1 by Ellenberg, Jordan (ISBN: 9780718196042) from Amazon’s Book Store. Everyday low prices and free delivery on eligible orders.

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The Art of Statistics: Learning from Data (Pelican Books)

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Buy The Art of Statistics: Learning from Data (Pelican Books) 1 by Spiegelhalter, David (ISBN: 9780241258767) from Amazon’s Book Store. Everyday low prices and free delivery on eligible orders.

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AQA Level 3 Mathematical Studies (Core Maths) Past Papers [PDFs & Mark Schemes]

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Increase your exam confidence with these AQA Level 3 Mathematical Studies (Core Maths) past papers. Includes exam papers and mark schemes organised by year.

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Why do Psychology students study Core Maths?

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Why do Psychology students study Core Maths?

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Stan Dolan (Author), June Haighton (Author)

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AQA Mathematical Studies Workbook: Level 3 Certificate (Core Maths)

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Buy AQA Mathematical Studies Workbook: Level 3 Certificate (Core Maths) by Dolan, Stan, Haighton, June (ISBN: 9780198417095) from Amazon’s Book Store. Everyday low prices and free delivery on eligible orders.

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This is Numberphile. We mainly post videos about mathematics and just numbers in general.

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Mathematics News - Math News, Mathematical Sciences

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Mathematics News - Math News, Mathematical Sciences

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Mathematics News - Math News, Mathematical Sciences

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Phys.org provides the latest news on mathematics, math, math science, mathematical science and math technology.