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 CR
Trang 1HOW MATHS CAN CHANGE
YOUR LIFE
EXCITING CAREERS IN MATHEMATICS
Chris Budd
Trang 2SOME 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!!!!!!!!!
Trang 3Maths and crime: Deblurring a number plate
A short crime story
• Burglar robs a bank
• Escapes in a getaway car
• Pursued by police
Nasa
Trang 4GOOD NEWS
Police take a photo
BAD NEWS
Photo is blurred
Trang 5Find 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
Trang 6An example of Image Processing
ϖ e hd 2x / e gd 2x d 2 / 2
e
f = ∫ i y ∫ −i x ∫ −i x
Inversion formula
Maths is widely used in the forensic service!!
Trang 7HOW 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
Trang 8SOME APPLICATIONS
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
Trang 9MATHS 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!!
Trang 10Modern 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
Trang 11Some 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
Trang 13FINALE: 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
Trang 14Find the trip wires in this picture
Trang 15Digital 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
Points of high intensity in R correspond to trip wires
θ
ρ
Isolate points and transform back to find the wires
Trang 16Mathematics finds the land mines!
Who says that maths isn’t relevant to real life?!?