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

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?!?