
"Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate. This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory."--BOOK JACKET.
Purves's Neuroscience
Kandel's Principles of Neural Science (grad level, but really the bible for neuro)
Dayan and Abbot's Theoretical Neuroscience (good for compneuro)
The Art of Electronics, 2nd edition (cheating here, but it's good to go back through the fundamentals before going into the edge cases that is neuro)
In general, AI is so new that there really isn't a good classical text between AI thingys and neuro. It will take time to suss one out and write one.
Some books I enjoyed (but which don't necessary achieve that status) are:
- Theoretical Neuroscience by Dayan & Abbott (this has math - but it's quite polite about it, and remains readable if you skip the equations)
- Handbook of Brain Theory and Neural Networks:http://mitpress.mit.edu/0262011972
But those are more theory than biology - would be really interested in a "nuts & bolts" presentation of the brain that is readable and engaging (i.e. nice exercises spread throughout the text, if such a thing is possible)
Kandel is the gold standard, but it is quite hefty and technical -- a great slimmer one is "From Neuron to Brain" (advanced undergrad/early grad): http://www.amazon.com/Neuron-Brain-Cellular-Molecular-Approa...
If you're more interested in the computational end, try "Theoretical Neuroscience": http://www.amazon.com/Theoretical-Neuroscience-Computational...
And I'll also add in a great computational textbook on spike recording: http://www.amazon.com/Spikes-Exploring-Neural-Computational-...
I'll also note that if you apply to a "Neuroscience" grad program, you're probably going to be doing biology experiments all day, or psychology experiments if you pursue cognitive neuroscience.
If you want to use CS and Math, the best you can do in a neuroscience program is data analysis. Hence, I would recommend AI or Mathematical Psychology (though the latter is about modeling high-level events).
- Theoretical Neuroscience Computational and Mathematical Modeling of Neural Systems - Peter Dayan, L. F. Abbott (2001) is quite good, more mathematical than computational.
- Neuronal dynamics, available here: https://neuronaldynamics.epfl.ch/ is also quite good, and free to read. Has python exercises as well. If I recall correctly, it mostly goes into simulations of singular neurons, and not so much entire networks and what we can do with them, but it does a good job at bridging the chemistry / biology / math to computation.
If we're talking about papers, one I mentioned in my other comment:
- Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations, https://doi.org/10.1162/089976602760407955
- Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons, by Nicolas Brunel (Don't have a DOI on hand for this one)
- Spiking Neural Networks and Their Applications: A Review, https://doi.org/10.3390/brainsci12070863 , is a very nice review of methods and does some nice explaining on concepts.
If you're looking for keywords on the topic:
- Leaky Integrate and Fire (LIF) neurons
- Spiking neural networks
- Liquid State Machines (LSM)
- Synaptic plasticity (Models of synaptic plasticity)
- Spike-based synaptic plasticity
Then there is "Spikes: Exploring the neural code" https://mitpress.mit.edu/books/spikes This one is focusing a lot on information theory.
