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On arrival at a crime scene or at an accident, the police may be faced with a set of evidence, but no clear indication of the precise cause of this evidence. For example, a speeding motorist may leave a set of tyre skid marks, but can we tell from these how fast they were going before an accident occurred? One way to obtain an answer to this question is to use the method of mathematical modelling. In this, an agreed model is determined for the event under investigation which allows a link to be made between a cause and its effects. From this a possible set of causes consistent with the evidence can be found, and from this we can learn more about what happened. In the case of the speeding motorist we can find an estimate for the speed, provided that we know the other factors involved, such as the frictional force between the tyres and the road. This process of finding a mathematical model for an event and then linking cause to effect is called solving an inverse problem and is an important modern application of mathematics. It is very like trying to work out the shape of an object knowing what shadows it casts. Very similar techniques are also used in medical imaging, oil prospecting and remote sensing by satellites. Mathematics gives a means for rapidly transferring ideas from one application to another!
In my presentation I will be looking at five different applications of this method to problems involving crime detection. In addition to the speeding motorist these will be: an investigation of finding where a contaminant was released into a water supply, deblurring a blurred photograph of a number plate, finding out what or who killed King Tutankhamen and (in helping to solve a crime against humanity) a method for detecting anti-personel land-mines. Remarkably the maths which is used to find the land-mines is closely related to a method for finding brain tumours in a CAT scan and has its origins in a formula discovered by the mathematician Radon at the beginning of the 20th Century!
Mathematics is also used in such diverse areas as fingerprint recognition, finding the trajectories of bullets and assessing the reliability of evidence such as marks left by tools. I should emphasise that the use of mathematics won't (nor should it) solve every problem, and it has its limitations like any other procedure, but it a useful tool in the set of techniques used in the forensic service.
My objective in this presentation is to show that mathematics is important and highly relevant to crime fighting in particular, and to many other real life problems in general. Hopefully this will give an answer to the often asked question what's the use of mathematics?
Most of the work I will present will be a summary of techniques used by others. However, the University of Bath is very active in applying mathematics to many problems arising in industry and medicine, ranging from micro-wave cooking to the design of aircraft structures and from studies of epidemics to complex systems. It is remarkable how often ideas which might be thought of as pure mathematics often find very real and important applications. The newly formed Bath Institute for Complex Systems exists to promote links between mathematics and many other disciplines and is always on the look out for new applications and challenges.
This lecture was broadcast live on Tuesday, 6th September 2005, as part of the BA Mathematics Section, Part 1.
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| Time | Title, Description, Teacher Notes |
| 0:00 | Introduction Common views of maths: It's dull and boring BUT this is not the case. This lecture will explain how maths can be used to fight crime better than any superhero in town. |
| 2:48 | Challenges A who dunnit investigation begins. What are the challenges facing police? |
| 4:12 | Inverse problems Using probability and statistics. How can maths be used to de-blur fingerprinting. Using this as a starter for a lesson on probability or statistics would get KS3 or KS4 students enthused about these subjects. |
| 7:36 | Examples of inverse problems This shows how the shadow of an aeroplane can be used to theorise the shape and size of the actual model. It highlights cause and effect of problems and uses formula for calculations. Remote sensing solutions for inverse problems such as the length of time a body has been dead. |
| 12:55 | Case study one Uses of mechanics to help solve crime. What happens if you find a bullet embedded and how can you determine where the bullet came from? How can you tell if a car has been speeding by the skid marks? Again this can be used in either KS3 or KS4 as a starter and to get the students interested in the topic. |
| 18:02 | Case study two What poisoned the water? Uses maths to calculate flow rates and catch the perpetrator. |
| 22:16 | Case study three De-blurring a number plate! Description; How maths can decipher a number plate even if it only partially seen. This is an excellent example to show students although the formula used is complicated. |
| 26:38 | Case study four Who killed tutankamon? Uses maths to solve a crime that happened over 3,300 years ago! I won't spoil this for you, watch for yourself. It is definitely worth watching. |
| 32:40 | Case study five How maths can be used to find anti-personnel mines. This is extremely interesting and will allow students to see many different applications of maths. This will encourage students to follow professions in maths in three minutes! |
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