Industrial Maths: Connecting Real Life with Mathematics

1. Animated by The demon Animator Confessions of an industrial mathematician Chris Budd

2. Traditional ‘school view’ of maths? • Maths is useless • The only jobs for mathematicians are in accountancy and teaching • Industry is full of people with oily rags • All mathematicians are mad

3. My own view: • Almost all maths can be applied to almost all problems • … And this simple fact is truly amazing!!!! • We can learn lots of new maths from almost • all applications: Calculus • My whole career has been involved in applying really nice maths to messy problems! • And then using this experience to enliven my teaching

5. We can see maths all around us in the physical world! Packing and folding rocks Swallow tail catastrophe: Find the curves:

6. .. And in engineering Didcot Power Station: mathsmathsmathsmathsmathsmathsmaths mathsmathsmathsmathsmathsmathsmaths mathsmathsmathsmathsmathsmathsmaths mathsmathsmathsmathsmathsmathsmaths Hyperboloid of revolution

7. A history lesson: Good applications of maths changes the world Vectors, Maxwell, Radio, FFT, digital revolution, computers Google Matrices, SVD, page-rank The computer

8. Mathematicians even save lives! Florence Nightingale

9. But … maths is also of great use in industry • And this can help our teaching by … • Motivating students with real life examples • Providing challenging problems for them to work on • Giving examples of future careers which use maths

10. In fact ….. Much of industry has problems which can potentially be formulated, and solved using mathematics Maths connects with all areas and knows no bounds or constraints! Too few people recognize that the high technology so celebrated today is essentially a mathematical technology Edward David, ex-president of Exxon R&D

11. Q. Which industries use maths? Traditional industrial users of maths are Telecommunications, aerospace, power generation, iron and steel, mining, oil, weather forecasting, security, defence, finance But they could equally well be … Retail, food, zoos, sport, entertainment, media, forensic service, hospitals, air-sea-rescue, education, transport, risk, health, biomedical, environmental agencies, art, …

12. What sort of maths does traditional industry need? • Expertise (big time!!!) and teaching in …. • Calculus • Differential equations • Mechanics • Matrices • Complex numbers • Number theory

13. Example 1: Forensic mechanics ..Catching a speeding motorist .. Was the car speeding? Forensic evidence: collision damage, witness statements, skid marks

14. Evidence: sdistance of skid Cause: uspeed Other data: F brake force Mechanics links speed to distance Given the distancemathsgives the speed

15. Example 2:Mechanics inAircraft undercarriage: AirbusCJB 2006

16. Example 3: Microwave cookingWhat gets hotter, the outside of the food or the inside?

17. Thermal image of surface of food after 5 minutes heating

18. L Starchy food L: Domain length: 2-14cm d: Penetration depth: 8mm Solving Maxwell’s equations for electric field predicts that the power absorbed decays exponentially. Temperature T satisfies a differential equation Challenge .. Solve this .. (a) in general (b) steady state.

19. But .. 21st century applications of maths will be driven by even more exotic industrial applications • Information/Bio-informatics/Genetics • Commerce/retail sector • Complexity • People based activity

20. What sort of maths do we now also need to learn and to teach for modern industry? • Decision maths!!!!!! • Data and data assimilation • Probability and uncertainty • Computational maths • Networks • Game theory

21. Crowd Dynamics and traffic flow Example 4:

22. Scramble crossing

23. Escape from a lecture theatre!

24. Can also model car traffic … cellular automaton models Challenge: Easy to make simulations and compare with real life

25. Example 5: FACEBOOK and global advertising!: Unilever/CJB

27. So the advantages of working with industry are … The challenges of industry make us think ‘out of the box’ and address new challenges Leading to new maths in the process Which leads to great teaching examples and lots of student motivation! But .. How can we achieve this in practice???

28. Study groups: a way of fostering interaction • Study Group Model (in use all over the world) • Bring academics, students and industrialists together • Pose industrial problems on the first day • Work on the problems for a week in teams • Great training experience! Case studies at http://www.maths-in-industry.org/miis/

29. Example 6: A team project from industry illuminating an equation (literally) Fluorescent light tubes Temperature at each AC cycle V Applied voltage Q. Why do fluorescent tubes need a starter?

30. Challenge: Find the steady states HINT: Solve a quadratic equation. T V ‘Tilted Cusp’ bifurcation

31. In Conclusion Industry will need all the mathematicians it can get if it is to survive and grow … And that means all of our students!!!!! Who can learn a lot of exciting maths from industrial problems Go for it!