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okay so Id like to present some notes or an overview on model reduction in particular were thinking about this whole concept of reduce sort of modeling and what the theme of these sets of lectures will be on is on nonlinear model reduction and I want to give us sort of a high-level overview of what we want to accomplish in this so theres a lot of different aspects of model reduction and this is just one where were going to think about thinking about nonlinear dynamical systems and how to think about solving them in an efficient way using the fact that there is in fact usually some low dimensional embedding which you can do computations in a much faster more efficient way so let me give you an example of what it means to think about the idea of dimensionality reduction and Im going to motivate this by several examples that come from biological physical engineering Sciences just so you get a concept of what were trying to actually do with this model reduction framework the first e