Whoever tells you that teaching and research don

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Whoever tells you that teaching and research
dont go together is talking rubbish
Chris Budd
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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 its great fun
trying
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Why not some myths

• Researchers are bad teachers and ..
• Good teachers are bad researchers
• Faraday, Feynmann, Zeeman, Stewart, ..
• You dont have time to do both
• Research is too complicated for students to
  understand
• The RAE doesnt like it
• Nor does the EPSRC (this is true by the way!!)

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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
• Thats research!!

Also
Lots of undergraduate maths is very close to
leading end research P-NP, Number theory,
Most of Applied Maths
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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
  dont 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

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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
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Case Study One A research based investigation
which can be used for all ages
Maths in Celtic and African Art
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(5,6)
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(4,8)
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How many pieces of string are needed?
(2,2) 2
(3,2) 1
(5,3) 1
(4,4) 4
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Chased Chicken Sona
What patterns do we find here?
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Case study two Research illuminating
undergraduate teaching (literally)
An example from nonlinear dynamics Fluorescent
light
Temperature at each AC cycle
V Applied voltage
Q. Why do fluorescent tubes need a starter?
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T
V
Tilted Cusp bifurcation
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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
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Example Stiff solvers for ODEs
Want to solve
Teaching without research

• Use a standard method eg. 4th order Runge-Kutta,
  ode45
• Which doesnt work for real problems
• But the students go on and use it in industry
• And tell others to use it too!

Disaster
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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

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Conclusion

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

All go together