Confessions of an industrial mathematician Chris Budd.

Confessions of an industrial

mathematician

Chris Budd

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

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

We can see maths all around us in the physical world!

Swallow tail catastrophe:

Find the curves:

2

2

2 12,

1),(

s

ts

s

stsyx

Packing and folding rocks

Didcot Power Station:

x 2 y 2 1 z2

.. And in engineering

Hyperboloid of revolution

mathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmathsmaths

A history lesson: Good applications of maths changes the world

Vectors, Maxwell, Radio, FFT, digital revolution, computers

Google Matrices, SVD, page-rank

The computer

Mathematicians even save lives!

Florence Nightingale

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

In fact …..

Much of industry has problems which can potentially be formulated, and solved using mathematicsMaths 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

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, …

Q. Which industries use maths?

What sort of maths does traditional industry need?

Expertise (big time!!!) and teaching in ….

• Calculus

• Differential equations

• Mechanics

• Matrices

• Complex numbers

• Number theory

Example 1: Forensic mechanics .. Catching a speeding motorist

..

Was the car speeding?

Forensic evidence: collision damage,

witness statements,

skid marks

Fsu 2

F

us2

2

Evidence: s distance of skid

Cause: u speed

Other data: F brake force

Mechanics links speed to distance

Given the distance maths gives the speed

Example 2: Mechanics in Aircraft undercarriage:

Airbus CJB 2006

QuickTime™ and a decompressor

are needed to see this picture.

Example 3: Microwave cooking

What gets hotter, the outside of the food or the inside?

Thermal image of surface of food after 5 minutes heating

L: Domain length: 2-14cm d: Penetration depth: 8mm

L

Solving Maxwell’s equations for electric field predicts that the power absorbed decays exponentially. Temperature T satisfies a differential equation

Starchy food

x

Tt

kTxx P e x / d , T(0,x)T0, kTx h(T T0)0 at x 0

Challenge .. Solve this .. (a) in general (b) steady state.

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

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

Example 4: Crowd Dynamics and traffic flow

QuickTime™ and a decompressor

are needed to see this picture.

Scramble crossing

Escape from a lecture theatre!

Can also model car traffic … cellular automaton models

Challenge: Easy to make simulations and compare with real life

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

y 0.0001 x 2 0.0015 x0.63, R2 0.912

QuickTime™ and a decompressor

are needed to see this picture.

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???

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!

http://www.maths-in-industry.org/miis/

Case studies at

Example 6: A team project from industry illuminating an equation (literally)

Fluorescent light tubes

2

32

1n

nnn

TTTVT

nT Temperature at each AC cycle

V Applied voltage

Q. Why do fluorescent tubes need a starter?

‘Tilted Cusp’ bifurcation

T

V

Challenge: Find the steady states

HINT: Solve a quadratic equation.

In Conclusion

Go for it!

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