This document discusses how mathematics is important in many exciting careers and aspects of everyday life. It provides examples of how math is used in crime detection by deblurring images to read license plates, in medicine for ultrasound, MRI, and CAT scans, in television and computer graphics by processing digital images, and in detecting land mines by using transforms to find trip wires in photos of foliage. The document aims to show that math is not just hard or boring, but rather has many real-world applications and is crucial in fields like forensics, healthcare, technology, and humanitarian efforts.

1. HOW MATHS CAN CHANGE
YOUR LIFE
EXCITING CAREERS IN MATHEMATICS
Chris Budd

2. 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!!!!!!!!!

3. Maths and crime: Deblurring a number plate
A short crime story
• Burglar robs a bank
• Escapes in a getaway car
• Pursued by police
Nasa

4. GOOD NEWS
Police take a photo
BAD NEWS
Photo is blurred

5. SOLUTION
Find a model of the blurring process
Original image
f
Blurred image
h
• Blurring formula
• Inverting the formula we can get rid the blur
• BUT need to know the blurring function g
Blurring function g
y
d
y
g
y
x
f
x
h  
 2
)
(
)
(
)
(

6. An example of Image Processing
  




2
/
/ 2
2
2
d
x
gd
e
x
hd
e
e
f x
i
x
i
y
i






Inversion formula
h(x) f(x)
Maths is widely used in the forensic service!!

7. 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

8. SOME APPLICATIONS
PRODUCING THE PICTURES IN THE FIRST PLACE
TRANSMITTING THE PICTURES WITHOUT MISTAKES
Lots of mathematicians work in IT and mobile phone
companies
Galois
Lots of mathematicians
work in computer
graphics, computer
games and Hollywood

9. 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!!

10. 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

11. 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

13. 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

14. Find the trip wires in this picture

15. Digital picture of foliage is taken by camera on a long pole
Image intensity f(x,y)
•
•
•
•
Trip wires are like X-Rays
Radon
transform
x
y
f(x,y) R(ρ,θ)
Points of high intensity in R correspond to trip wires
θ
ρ
Isolate points and transform back to find the wires

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