Whoever tells you that teaching and research dont 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 its great fun trying

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!!)

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

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

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 , 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)

(2,2) 2 (3,2) 1 (5,3) 1 (4,4) 4 How many pieces of string are needed?

Chased Chicken Sona What patterns do we find here?

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?

Tilted Cusp bifurcation T V

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 Want to solve Teaching without research Use a standard method eg. 4 th 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

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