EXCITING CAREERS IN MATHEMATICS

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 y • Inverting the formula we can get rid the blur • BUT need to know the blurring function g f = ∫ e iϖy ( − i ϖx − i ϖx 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?!? [...]... 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. .. 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?!? ...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,