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

1. Whoever tells you that teaching and research don’t go together is talking rubbish Chris Budd

2. 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

3. Why not … some myths … • Researchers are bad teachers … and .. • Good teachers are bad researchers • Faraday, Feynmann, Zeeman, Stewart, .. • 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!!)

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

5. 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

7. 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

8. Case Study One: A research based investigation which can be used for all ages Maths in Celtic and African Art

9. (5,6)

10. (4,8)

11. How many pieces of string are needed?

12. Chased Chicken Sona What patterns do we find here?

13. 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?

14. T V ‘Tilted Cusp’ bifurcation

15. 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

16. Example: Stiff solvers for ODEs Want to solve 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

17. 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

18. Conclusion • Maths teaching • Maths research • Good practice • Interesting and relevant lectures All go together