Contours 2016-17

Contours 

Stories from the School of Mathematics

The team 

IMAGE CREDITS 

P7: ©ISTOCK.COM/DANIL MELEKHIN 

P8: ©ISTOCK.COM/ALEKSANDARVELASEVIC 

P13: ©ISTOCK.COM/EDWARDSAMUELCORNWALL 

P14: ©ISTOCK.COM/IGOR ZHURAVLOV 

2 Contours

Contents 

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16 

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Contours 3

Projects: Knot as hard as they seem 

Fourth Year Project 

■ 


Summer Vacation Project 

■ 

◄ The output from Imogen's Matlab 

program, showing a 12x24 Celtic 

plait, with each link component 

of the plait coloured differently. 

Find out more about options for the 

summer vacation scholarships online: 

www.wiki.ed.ac.uk/display/SciEngSc 

hol/Scholarships+Overview 


MathPALs 

All first‐year students can take part in a weekly MathPALs session 

led by two higher‐year students who have been trained in Peer 

Assisted Learning. 

The sessions are informal, giving students a chance to ask 

questions and meet other students on the course – as well as 

benefiting from the experience of the higher‐year students. 

“the best way to 

learn and improve is 

to ask questions, 

and to learn from 

other peoples’ 

experiences” 

■ 


The Alan Turing Institute 

■ 

Why Alan Turing? 

There is no doubt that Alan Turing is 

a giant in the world of computer and 

data science. During the Second 

World War, Turing played a pivotal 

role in decoding intercepted German 

messages – work which is thought to 

have shortened the length of the war 

by two to four years. But Turing was 

also a pioneer in computer science, 

taking steps towards artificial intelligence 

many years before it became a 

mainstream idea. It was partly thanks 

to his ability to combine techniques 

from mathematics, computing and 

statistics that Turing was so successful, 

and so he truly represents the 

spirit of modern data science research. 

Naming the institute after 

Alan Turing seeks to to give people a 

visionary understanding of its aims. 


From molecules to Big Data 


■ 

Thermostat methods 

Say we want to find out the distribution 

of certain particles in a system. 

The movement of these particles can 

be simply modelled using Newton’s 

equations. In reality, this model is 

fairly poor, because it doesn’t take 

into account friction, and other 

forces, amongst the particles. Taking 

these forces into account, we obtain 

a modelling equation with two extra 

terms. 

But when we simulate the system using 

the equations, we find that the 

temperature of the simulated system 

changes over time, when this 

doesn’t actually happen in real life. 

To solve the problem, mathematicians 

like Ben and his PhD student 

Xiaocheng Shang introduce what’s 

called a ‘thermostat’ into the system. 

Like a thermostat that keeps a 

house a constant temperature, a 

thermostat in this context is an extra 

term in the modelling equation that 

regulates the temperature of the 

model. Similarly, when studying 

large sets of data, introducing a 

thermostat is essential to remove 

the ‘noise’ that appears when 

sampling. 

Various thermostat methods exist, 

but the traditional ones are not appropriate 

when looking at such large 

sets as those studied in Big Data research, 

being either too slow or too 

inaccurate. The method produced by 

Ben and Xiaocheng has performed 

very well in tests, converging much 

faster than former methods, and 

having a high accuracy. Similar 

methods are also used by Google, in 

machine learning – the study of pattern 

recognition. It’s this that allows 

Google to optimize its search results 

so that you can find what you’re 

looking for faster. 

► 

Contours 

9

Hunting for Data 

“You get to derive 

cool results and then 

on top of that you 

can play with 

numbers” 


XKCD.COM/1132 

▲ This is one of Ruth's favourite XKCD comics. Next year, Ruth will be teaching 

a postgraduate course called Bayesian Theory, as part of the newly 

established MSc in Statistics with Data Science. 

■ 

Statistics is very important in Big 

Data research because statistical 

modelling allows you to deal with 

missing data in formal ways. The 

techniques Ruth has worked on can 

be really useful when your data set 

is imperfect, for example, if you 

don’t have full access to people’s 

salaries because of privacy. 

Ruth is on the programme committee 

for the Alan Turing Institute (see 

p.7), providing advice regarding the 

scientific and innovation programmes 

for the institute, and is 

also a part of the recruitment committee 

for the institute. 


The Stochastic Nature of Life 

“Research is not 

always easy. It can be 

a lengthy procedure, 

and sometimes 

frustrating as things 

often don’t work out 

the way you intend 

them to. As such, it’s 

imperative to really 

enjoy the process, not 

just the end result.” 


■ 

José is one of the founding members 

of the Edinburgh Mathematical 

Physics Group. Founded in 1999, it 

is a joint research institute made up 

of the Mathematics departments of 

the University of Edinbugh and Heriot‐Watt 

University. The group covers 

many areas of research, including 

Gravitational physics, noncommutative 

geometry and field theory 

amongst many others. 

To find out more on the group visit 

https://empg.maths.ed.ac.uk/ 


Great Waves 

“...you have to go 

further than anyone 

else to make 

progress. You’re way 

more likely to do 

that if you’re 

passionate about 

what you’re doing.” 


■ 

Maths in Action 

This year, Lyuba has been teaching a 

brand new course which is closely 

related to her research interests. 

Mathematics in Action is aimed at 

students in years 4 and 5, and focuses 

on using mathematical techniques to 

analyse real‐world data – usually 

building on mathematics that appears 

in earlier courses. The course is very 

hands‐on, giving practical experience 

of analysing data in Matlab – ranging 

from comparisons of different imageprocessing 

methods, to analysing Met 

Office data on the mean temperature 

in Scotland. 


Analysing a Hiro 

“His office is full of 

academic books, and 

when asked if he has 

any hobbies, Hiro 

gestures towards the 

books and says: ‘I 

think of mathematics 

as a hobby’” 


■ 

Contours 17

Travels in mathematics 

“This could have 

been a safe position 

for a settled life… 

I decided to try 

something new” 


▲ Vanya's Brompton bike has been with him around the world. These are just a few of the images he has posted on his 

website – you can see the full collection at www.maths.ed.ac.uk/cheltsov/brompton 

■ 


Spreading Inspiration 


■ 

▼ As an undergraduate, David made a series of stained glass windows to illuminate mathematical concepts he found 

inspiring. The common tile motif at top and bottom is a ‘proof by pictures’ of the Pythagorean theorem. 

Perhaps you can try and figure out why! 

1 The Klein bottle, and its ‘fundamental 

group’. 

2 A proof that the same number, pi, is the ratio 

of a circle's circumference to its diameter, 

and of its area to the square of its 

radius. 

3 Designed by David's brother, Alex Jordan, 

this depicts Tartaglia's solution of the cubic 

equation. 

4 The golden spiral, and its relationship to the 

Fibonacci numbers and the golden ratio. 


Why Mathematicians Should Knit 

■ 


Puzzles 

Stuck? Solutions are on the website: 

www.maths.ed.ac.uk/contours 

Sangaku problems were hung on tablets in shrines and temples during 

the sakoku period (1639‐1853) in Japan. Since the country was secluded 

in those years, Japanese mathematicians used a distinct kind of mathematics 

known as wasan to solve the problems. 

In the School, Professor José Figueroa‐O'Farrill (p. 12) offers a 4th year 

project which involves studying some sangaku, and their connections 

with Western approaches to similar problems. 

ρ 

ρ 

The radius of each 

circle is written at 

its centre. 

Show that R=5r. 

1 2 

3 

4 

Maths 

Cryptic 

No 2 

r . 

R

Contours 2016-17

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