HOW MATHS CAN CHANGE YOUR LIFE

HOW MATHS CAN CHANGE
YOUR LIFE
EXCITING CAREERS IN MATHEMATICS

Chris Budd


SOME COMMON VIEWS OF MATHEMATICS

• MATHS IS HARD
• MATHS IS BORING
• MATHS HAS NOTHING TO DO WITH REAL LIFE
• ALL MATHEMATICIANS ARE MAD!

BUT I CAN SHOW YOU THAT MATHS IS IMPORTANT IN
CRIME DETECTION

MEDICINE

FINDING LANDMINES

AND MANY OTHER CAREERS!!!!!!!!!


Maths and crime: Deblurring a number plate

A short crime story
• Burglar robs a bank
• Escapes in a getaway car
Nasa

• Pursued by police


GOOD NEWS
Police take a photo

BAD NEWS
Photo is blurred


SOLUTION
Find a model of the blurring process
Blurring function g

Blurred image

Original image

h
f

• Blurring formula

h( x ) = ∫ f ( x − y ) g ( y ) d 2 y

• Inverting the formula we can get rid the blur
• BUT need to know the blurring function g


f = ∫ e iϖy (

− iϖ x
2
− iϖ x
2
2
)
e
hd
x
/
e
gd
x
d
ϖ / 2π
∫
∫

Inversion formula

h(x)

f(x)

An example of Image Processing
Maths is widely used in the forensic service!!


HOW MATHS WILL GET YOU ON TV

PICTURES AND IMAGES ARE ALL AROUND US
• TV
• DVD
• COMPUTER GRAPHICS
• SPECIAL EFFECTS
IMAGES ARE STORED AS NUMBERS

USING THESE NUMBERS WE CAN PROCESS
THE PICTURES BY USING MATHEMATICS


SOME APPLICATIONS
PRODUCING THE PICTURES IN THE FIRST PLACE

Lots of mathematicians
work in computer
graphics, computer
games and Hollywood
TRANSMITTING THE PICTURES WITHOUT MISTAKES

Lots of mathematicians work in IT and mobile phone
companies

Galois


MATHS AND MEDICINE
Modern medicine has been transformed by methods of seeing
Inside you without cutting you open!
• Ultra sound: sound waves

• MRI:

magnetism

• CAT scans:

X rays

ALL USE MATHS TO WORK!!


Modern CAT scanner

CAT scanners work by casting many shadows with X-rays and
using maths to assemble these into a picture

Lots of mathematicians work in medicine


Some interesting mathematical facts
• Over 70% of all jobs require maths

• On average maths graduates earn more than any other
profession
• Many degrees require maths including statistics, physics,
engineering, economics, chemistry, medicine, IT, computer
games, computer science, social-science, psychology, fashion
design, business studies, accountancy, actuarial studies,
electronics, aeronautics, cryptography, ..
• Without maths we would have no TV, mobile phones, Internet,

credit cards, computer games, CDs, Radar, aeroplanes, DNA
profiling, …
• Maths is vital working out your mortgage payments, APR
calculations, family budget
• Florence Nightingale was a mathematician



FINALE: USING MATHS TO FIND
ANTI-PERSONEL LAND MINES

Land mines are hidden in foliage and triggered by trip wires

Land mines are well hidden .. we can use maths to find them


Find the trip wires in this picture


Digital picture of foliage is taken by camera on a long pole
Image intensity f(x,y)
Trip wires are like X-Rays
R(ρ,θ)

f(x,y)
Radon
transform

y

•
•

•
•

x
Points of high intensity in R correspond to trip wires
Isolate points and transform back to find the wires

θ

ρ


Mathematics finds the land mines!
Who says that maths isn’t relevant to real life?!?