how maths can change your life exciting careers in mathematics chris budd
TRANSCRIPT
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
• Pursued by police
Nasa
GOOD NEWS
Police take a photo
BAD NEWS
Photo is blurred
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
ydygyxfxh 2)()()(
An example of Image Processing
2// 222 dxgdexhdeef xixiyi
Inversion formula
h(x) f(x)
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 PROCESSTHE PICTURES BY USING MATHEMATICS
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
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
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
Mathematics finds the land mines!
Who says that maths isn’t relevant to real life?!?