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This lecture covers the fundamentals of scientific computing in neuroscience, focusing on the simulation of neurons and networks using tools like NEURON, NEST, and BRIAN. It discusses the history of computational science, the scaling of computing systems, and the challenges of computing at the forefront of technology. The lecture also delves into the modeling of neurons at different scales, the understanding of neural circuits, and the importance of biophysical and biochemical computational modeling in studying brain phenomena.