Neuroscience with mathematical emphasis

[etotheipi]

What is a nice resource to learn about the mathematics of neuroscience? I read a little bit about the Hodgkin-Huxley model for propagation of action potentials and also stuff like synaptic junctions, but I like to learn some more about modelling networks of more than one neuron, stochastic models, and other interesting sub-topics that I haven't come across yet.

What are, the classic texts in this field? Thank you

[Edit: Also, if there's any decent free stuff available, that'd be even better!]

 

[marcusl]

It’s not my field so I cannot give you recommendations, but I can steer you in the right direction The field you are interested in is called “Computational Neuroscience.” You’ll find many texts with that in the title as well as at least one course offering from MIT OCW.

 

[atyy]

Biophysics
https://www.amazon.com/dp/0262100533/?tag=pfamazon01-20
https://www.amazon.com/dp/0195181999/?tag=pfamazon01-20

Theoretical Neuroscience
https://www.amazon.com/dp/0262541858/?tag=pfamazon01-20
https://www.amazon.com/dp/0521890799/?tag=pfamazon01-20
https://www.amazon.com/dp/B00KL8CI7E/?tag=pfamazon01-20
https://neuronaldynamics.epfl.ch/ (free version of Gerstner's textbook)

It's also useful to know some statistical field theory
https://www.amazon.com/dp/052187341X/?tag=pfamazon01-20
https://ocw.mit.edu/courses/physics...ii-statistical-physics-of-fields-spring-2014/ (free notes on which the book is based)

Because a lot of pioneering work was done by Daniel Amit, who worked in statistical physics before neuroscience. Other key pioneers are Hanoch Gutfreund and Haim Sompolinsky.
https://www.amazon.com/dp/9812561196/?tag=pfamazon01-20

And you can see some of the methods used in a paper like
https://www.researchgate.net/publication/41173809_The_Asynchronous_State_in_Cortical_Circuits

A weird but wonderful book
https://www.amazon.com/dp/B01FKS1J2Y/?tag=pfamazon01-20

Old classic, still useful to know
https://www.amazon.com/dp/B07B9XW1QP/?tag=pfamazon01-20

This is also useful and has some chapters on Neural Networks
https://www.amazon.com/dp/0521642981/?tag=pfamazon01-20
http://www.inference.org.uk/mackay/itprnn/book.html (free version of MacKay's book)

Reinforcement learning, mostly machine learning, but there psychology and neuroscience chapters (14 & 15)
https://www.amazon.com/dp/0262193981/?tag=pfamazon01-20
http://incompleteideas.net/book/the-book.html (free version of Sutton and Barto's book)

 

[etotheipi]

Oh wow, thanks! In that case, I'll probably start with Gerstner's considering that it's free, and I might also take a look at MacKay's one. I did read quite recently the first two parts of David Tong's statistical field theory notes [see here], I wonder if that's good enough preparation on that front?

 

[atyy]

Sounds like a good plan.

David Tong's notes are good. They should be good enough if you want to read eg. https://pubmed.ncbi.nlm.nih.gov/8939866/ or https://pubmed.ncbi.nlm.nih.gov/20110507/.

MacKay's book is beautiful, even though he was a card-carrying Bayesian.