# Teachand Res

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```					Whoever tells you that teaching and
research don’t go together is talking
rubbish

Chris Budd
It is natural in maths to link teaching and
research

That is real gut wrenchingly hard, theorem
proving, model developing mathematical
research!!!

Each can learn from the other

And it’s great fun trying
Why not … some myths …

• Researchers are bad teachers … and ..
• Good teachers are bad researchers

• You don’t have time to do both
• Research is too complicated for students to
understand
• The RAE doesn’t like it
• Nor does the EPSRC (this is true by the way!!)
Why the myths are rubbish .. Especially for maths!

• Maths is a subject best learnt by DOIN G
• Doing maths means solving problems
• The best problems are open ended and require
creative thinking and investigation
• That’s research!!

Also …

research
P-NP, Number theory, Most of Applied Maths
Even better
• We live in a Golden Age of maths with new discoveries
all the time .. Students enjoy seeing what is out there

• Research develops a sense of awe, wonder, play and
excitement in students of all ages
Maths is the only experimental subject that you don’t
need a laboratory for

• Research (especially in applied maths) leads to
Fantastic examples in lectures
Plagiarism free project subjects
Great for public understanding of science
Even, even better

• Good teaching is also good for research

•Exposure to different subjects and ideas can
often lead to new research insights

•As does thinking hard about how to explain a
problem
CJB: Global bifurcation and 1.61803, Monge-Ampere
Case Study One: A research based investigation
which can be used for all ages

Maths in Celtic and African Art
(5,6)
(4,8)
How many pieces of string are needed?

(2,2)          2

(3,2)          1

(5,3)          1

(4,4)          4
Chased Chicken Sona

What patterns do we find here?
Case study two: Research illuminating

An example from nonlinear dynamics: Fluorescent light

Tn      Temperature at each AC cycle

V        Applied voltage

3
Tn
Tn 1  V Tn  Tn 
2

2

Q. Why do fluorescent tubes need a starter?
T

V

‘Tilted Cusp’ bifurcation
Case Study Three: How research illuminates
service teaching

Common accusation: Maths service teaching is not
relevant to the needs of non-maths students SEMTA!

Research based teaching addresses this by:

Giving really relevant examples

Making sure that all students learn the latest, up to
date, mathematical methods
Example: Stiff solvers for ODEs

du
Want to solve            f (u, t )
dt

Teaching without research

• Use a standard method eg. 4th order Runge-Kutta, ode45
• Which doesn’t work for real problems
• But the students go on and use it in industry
• And tell others to use it too!

Disaster
Research: Be aware and develop the latest methods
and be prepared to use them

• Teach students to use variable order BDF methods or
geometric integration methods, collocation
• And modern software eg. DDASSL, ode15s, snsqe
• Students end up using much better methods
• Which work!

Teaching and research: Best of all!

• Get the students to compare and analyse different methods
and find which is best for their own problems
Conclusion

• Maths teaching
• Maths research
• Good practice
• Interesting and relevant lectures

All go together

```
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