Neuroscience with mathematical emphasis

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Discussion Overview

The discussion centers around resources for learning about the mathematics of neuroscience, particularly in the context of computational neuroscience, modeling neural networks, and stochastic models. Participants share recommendations for textbooks, free resources, and foundational materials relevant to the field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant inquires about resources for understanding the mathematics involved in neuroscience, specifically mentioning the Hodgkin-Huxley model and interest in modeling networks of neurons.
  • Another participant suggests that the field of interest is called "Computational Neuroscience" and mentions the availability of related texts and courses, including those from MIT OpenCourseWare.
  • A third participant lists several recommended books and resources, including "Biophysics," "Theoretical Neuroscience," and free versions of certain texts, highlighting the importance of statistical field theory in the context of neuroscience.
  • One participant expresses intent to start with Gerstner's textbook, noting its free availability, and questions whether prior reading of David Tong's statistical field theory notes is sufficient preparation.
  • Another participant affirms the quality of David Tong's notes and suggests they are adequate for further reading in the field, while also praising MacKay's book for its aesthetic value despite the author's Bayesian perspective.

Areas of Agreement / Disagreement

Participants generally agree on the value of the recommended resources, but there is no consensus on a singular best starting point or preparation level, as individual preferences and backgrounds vary.

Contextual Notes

Some limitations include the potential dependence on prior knowledge of statistical field theory and the varying levels of accessibility of the recommended texts, particularly regarding free resources.

Who May Find This Useful

This discussion may be useful for individuals interested in the mathematical foundations of neuroscience, particularly students or researchers looking for resources in computational neuroscience and related fields.

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!]
 
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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.
 
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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)
 
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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?
 

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