Equations Stripped: Normal Distribution

Stripping back the most important equations in maths so that everyone can understand…

The Normal Distribution is one of the most important in the world of probability, modelling everything from height and weight to salaries and number of offspring. It is used by advertisers to better target their products and by pharmaceutical companies to test the success of new drugs. It seems to fit almost any set of data, which is what makes it SO incredibly important…

You can watch all of the Equations Stripped series here.

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What is the graph of x to the power x?

The answer to the latest question sent in and voted for by YOU.

A tricky question, but one that we can answer by breaking the problem down into simpler cases, solving them, and then putting it all back together. This question is also a favourite with university admissions tutors…

 

To vote for the next question that you want answered next remember to ‘like’ my Facebook page here.

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BBC News – Maryam Mirzakhani’s Legacy

Live interview on BBC News about the legacy of Iranian Mathematician Maryam Mirzakhani who tragically passed away today (July 15th 2017). She was the first female winner of the Fields Medal – the mathematical equivalent of the Nobel Prize.

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Oxford Alumni Voices

Interview with the University of Oxford alumni team about my mission to popularise maths. You can listen to the full interview here.

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Naked Maths Trailer

Naked Maths is finally here!

Here’s the trailer for the new video series I’m making with the Naked Scientists taking a look at the maths that’s all around us.

 

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Anglerfish

In the final Critter of the Week for Marine Month, I introduce the villainous Anglerfish with the help of SeaLife Europe’s Joe Lavery…

  • There are more than 200 species of anglerfish identified and they can range in size from a tiny thumbnail to a small dog.
  • The name Anglerfish comes from the ‘fishing rod’ on their head which is in fact a modified dorsal spine called an illicium that’s used for hunting.
  • They can go for days on end without eating but when the time does come they’re able to eat a fish which is twice their own size.
  • The deep-sea Anglerfish lives more than a mile underwater on the desolate ocean floor, meaning that when a male and female cross paths they don’t hang around.
  • The male angler bites into the female and fuses its mouth to her body, eventually becoming a part of her used only to fertilise her eggs.

You can listen to the full interview for the Naked Scientists here.

Funbers 8

The number of legs on a spider, tentacles on an octopus and planets in our solar system… Eight is also a big deal in Asia – listen below to find out why!

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire here.

Funbers 7

From the number of seas sailed by pirates, to the number of days in the week named after ancient Gods, seven is a popular number. It also happens to be the maximum number of circular items that can be bundled together securely. Now there’s something you don’t hear every day…

You can listen to all of the Funbers episodes from the series with BBC Radio Cambridgeshire here.

Funbers 2 Pi

Two times pi is such an important number in maths that it deserves its very own edition of Funbers… featuring angles, trigonometry and pie jokes.

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire here.

Tom Rocks Maths Episode 04

The fourth and final episode of Tom Rocks Maths this term on Oxide – Oxford University’s student radio station. Featuring my favourite shapes, cannibals with a hat fetish, the golden ratio and the weekly maths puzzle for you to solve. Plus, music from Foo Fighters, Green Day and Sum 41…

Turning useless Methane into useful Methanol

Methane is 20 times worse than C02 as a greenhouse gas, so when it’s created as a by-product at oil rigs it’s burned. This is better than releasing the methane into the atmosphere, but it’s not an ideal solution as it creates more C02. Jeroen Van Bokhoven and his team at ETH Zurich have found a new way to convert the methane into something cleaner, and a bit more useful…

Jeroen – We form it into methanol. Methanol itself is a resource for many chemicals, we can even convert this to fuels in the end. Methanol is a base chemical which has many different applications.

Tom – Is methane generally quite a reactive substance?

Jeroen – Methane is a rather unreactive substance. One of the difficulties to activate methane is the product that you make, the methanol, is more reactive than the methane itself. That’s why this reaction is so difficult to perform selectively, because the methanol will react further and then you will not end up with the useful product. That’s why this reaction is called the ‘dream reaction’ because it’s so difficult to perform and to achieve a high yield.

Tom – How do you do this? How do you convert methane into methanol?

Jeroen – Well we defined a stepwise process where we have a material which we activate and this activated material is then reacting with methane. Then we switch the conditions and then we have the activated methane reacting with water and this generates the methanol and at the same time it reactivates the material so it can react with another molecule of methane. The novelty is that we use the water and oxygen from the water molecule ends up in the methanol. The previous methods that have been used will always use an oxidant. The novelty here is that we use water, it simplifies the process very much.

Tom – Before your discovery, how do we currently convert methane into methanol?

Jeroen – Currently that is a very involved process. There are two largescale processes involved. One is the steam reforming of methane making ‘sin gas’ that is carbon monoxide and hydrogen. This is high temperature, high pressure process and then in the second step this mixture is reacted over a novel catalyst to methanol. This is only commercially viable if it’s done at largescale. And that’s why at smaller scales the methane is not viable to convert into methanol, so that’s why its burnt. Our process, we envision you can do it at much smaller scales and that it would be profitable to do it that way.

Tom – So is that the end goal here? To use your process at oil well sites where currently methane is just being burnt as flares and you’re saying no what we can do is, ideally, at these sits convert this to methanol and then do something useful with it?

Jeroen – Yes, that is correct. It’s to do something useful with what us now considered a waste product.

Tom – How far away are you from that? What would a setup to do your process look like at, for example, a well site?

Jeroen – At the moment, we are far from a commercial and an actual application. We have shown that the concept works on the very small scale and the next steps in the lab are to scale-up this process as well as to make sure that the rates of reactions – the speed that the reactions run – are sufficient for a largescale operation.

Tom – When you say, you’ve done this in the lab, how much of this methanol are you making? Is it really quite small amounts currently then?

Jeroen – At the moment it is really small amounts yes, but we also have not optimised this at all, so there are huge opportunities for optimisation. We have shown the proof of concept – that’s what the paper is about – and of course the next steps are to understand what the chemical mechanism is better than we do now, and as well as directly trying to scale this up. There are huge opportunities to do the scale up, but the research is not in the stage that we have looked at it. That is really the next thing to do.

Funbers 6

The number of strings on a classical guitar, the number of points on a Star of David and the number of legs on an insect – which make up 80% of the world’s species! Six is also a perfect number: have a listen and see if you can work out the next three…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Volcanoes may have ended the Roman Empire

Volcanic eruptions can be both beautiful and destructive at the same time, but researchers have found evidence they may have also been linked to plagues, and even the fall of the Roman Empire. When a volcano erupts, chemicals are released into the atmosphere in huge quantities, which reflect light away from the earth and therefore cause climate change, in the form of summer cooling. These chemicals are also locked away in the ice, providing a snapshot of the time of an eruption. Now scientists have dated the ice cores, and the records of summer cooling, from tree rings and have found they match perfectly. Gill Plunkett from Queen’s University Belfast was one member of that team…

Gill – Now that we have much better dating for these events in the ice cores we can correlate them with other sets of evidence for past climate change and look at the historical records as well. And we can see that there’s a very strong correlation between summer cooling and volcanic eruptions. So, for example, of the sixteen largest events that are recorded in the ice cores fifteen of them are associated with summer cooling.

Tom – Did you look at a specific period over the last 2500 years?

Gill – One of the periods we were interested in was a very large acid spike. Well a species of large acid spikes in and around the middle of the 6th century. So we could see a very large acid spike at 536 AD, the acid tells us that volcanic eruptions occurred but it doesn’t tell us what volcanoes were erupting. To do that we have to look at volcanic particles. So when we looked at the particles associated with 536 acid layer we found that there was evidence not of just one eruption, but at least 3 eruptions.

Tom – And where were these eruptions from?

Gill – In this case it looks as if we have potentially unnoticed, unrecorded eruptions happening. The sources seem to be California, British Columbia and Alaska. The chemistry most closely matches volcanic systems in these areas. The idea is perhaps that these were relatively small eruptions that haven’t been noticed on the ground, but yet their combined effects were enough to cause a large acid spike and potentially climatic change.

Tom – How did you know then that these eruptions occurred at this time?

Gill – We can date the ice very accurately because snow is accumulating all the time in the polar areas. So within the ice there are seasonal changes in the chemistry, and by analysing these changes you can actually pick out changes from year to year.

Tom – I’ve also heard of things such as tree rings being used as a record for climate?

Gill – Yes, tree rings are an extremely good way of looking at past climate change. First of all, the trees grow on an annual basis so most trees would put on one growth ring per year. So, we can date the tree rings precisely to the year and also the trees respond to the climate conditions that they’re growing under. If the climate is favourable for the trees, the trees are going to grow well and if the climate is not favourable for the trees you’ll get less growth.

Tom – And so you were using a combination of the tree rings and the ice cores and this is what allowed you to get such precise dating?

Gill – Before it was recognised that the trees had these periods of unusual growth downturns suggesting that there was a severe climate deterioration. But they couldn’t link them up to the ice core records, because the dating didn’t seem to be the same. Now with the improved methods of dating we were able to show that the extreme events in the trees corresponded with the volcanic events in the ice cores.

Tom – So going back to the eruption in 536 with these three different eruptions happening, what were the actual effects that this caused?

Gill – We can surmise that the summer cooling could have been detrimental for crops growing and certainly in the historic records we start to see that there are issues happening. We start to see food shortages, famines, and from the 540’s we get the outbreak and spread of the Justinian plague. We have a series of volcanic events happening in close succession and this is likely to have put strain on crops, harvests and crop failure would have weakened populations potentially. That could have made a population more vulnerable to the spread of disease.

You can listen to the full interview with the Naked Scientists here.

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