Plain-language explanation.
Computational neuroscience uses mathematical models and computer simulations to understand how the brain works. Just as physicists use equations to describe gravity, computational neuroscientists use equations to describe how neurons fire, how information is encoded in neural activity, and how learning changes brain circuits.
Core concepts and standard treatment.
Computational levels of analysis (Marr): computational (what the system does and why), algorithmic (how it does it), and implementational (physical instantiation in neurons and synapses). Single-neuron models range from the biophysical Hodgkin-Huxley model through integrate-and-fire models to abstract rate models. Network models (recurrent neural networks, attractor networks) capture population-level dynamics.
Deeper theory, debates and edge cases.
Neural coding: rate coding (information in mean firing rate), temporal coding (information in precise spike timing), and population coding (information in activity patterns across many neurons). Dimensionality reduction methods (PCA, UMAP, GPFA) reveal low-dimensional structure in high-dimensional neural population activity. Bayesian brain hypothesis frames neural computation as probabilistic inference, with sensory cortex representing posterior probability distributions over environmental causes.
How it is applied in practice.
The Human Connectome Project, Allen Brain Atlas, and MICrONS project are generating unprecedented datasets on neural connectivity and function. Deep learning and neuroscience are in productive dialogue: recurrent neural networks trained on cognitive tasks develop representations resembling those in prefrontal cortex; convolutional networks model ventral visual stream hierarchy. Conversely, neuroscience inspires AI architecture design (attention mechanisms, sparse coding, predictive coding). Neuromorphic computing (Intel Loihi, IBM TrueNorth) implements spiking neural network computations with radical energy efficiency.