What is the future of applied mathematics? Chris Budd
We live in interesting times with applied mathematics in a process of great transition! 20th century .. Great drivers of applied maths are physics, engineering and more recently biology Expertise in …. Fluids Solids Reaction-diffusion problems Dynamical systems
Deterministic Continuum problems, modelled by Differential Equations Solutions methods Simple analytical methods eg. Separation of variables Approximate/asymptotic approaches Phase plane analysis Numerical methods eg. finite element methods PDE techniques eg. Calculus of variations
What are the drivers of 21st century applied mathematics? Information/Bio-informatics/Genetics? Commerce/retail sector? Complexity? What new techniques do we need to consider? Discrete maths? Stochastic methods? Very large scale computations? Complex systems? Optimisation (discrete and continuous)?
Example: 2005 Study Group with Industry 10 industrial problems One on fluids/PDE One on dynamical systems All others discrete/optimisation 1995 Study Group with Industry 8 industrial problems .. All on continuum maths
Q. Do you agree with this assessment? Q. What is the best way to train the next generation of applied mathematicians? Q. What do YOU think is the future of applied mathematics