1. What is the future of
applied mathematics?
Chris Budd

2. 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

3. 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

4. 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)?

5. 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

6. 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