# Theoretical Neuroscience: what tools are in your mathematical toolkit?

I believe that the following courses are a minimum math/engineering/(+cs) requirement for theoretical neuroscience research, specifically, Eliasmith's NEF/SPA approach. I wonder what other tools might be useful. Concretely, I am trying to workout the marginal utility of "learning more math just in case you'll need to apply it in some new context + improved mathematical maturity" versus "learning more neuroscience". Can you please list some math/engineering/(+cs) courses you found integral to your research and provide context?

Math: Precalculus, Calculus 1, Calculus 2, Multivariable Calculus, Ordinary Differential Equations, Linear Algebra (to Eigenvalues), Discrete Mathematics and Logic, Optimization and Numerical Methods

Engineering: Systems and Signals, Control Systems, Pattern Recognition, Information Theory and Applications, Machine Learning (Neural Networks in particular)

CS: Data Structures and Algorithms, Object-Oriented Software Development, Neuromorphic Computing

Your primary toolkit is going to be:

• Linear Algebra
• Probability and statistics
• python

If you want, you can add:

• Signal processing (filtering)
• Machine Learning (mostly just applications of linear algebra)

I am currently TAing at an online summer school called Neuromatch Academy. Check out their syllabus (3 week course) for an overview of tools useful in theoretical neuroscience. homepage: https://neuromatch.io/academy/ syllabus, tutorials: https://github.com/NeuromatchAcademy/course-content

Out of interest, why NEF? There are a wealth of frameworks out there, and NEF is relatively limited in its application.

• Thanks for getting back to me and sharing the course. Can you please elaborate on NEF being limited in its application. I am primarily interested in cognition as an emergent neurobiological phenomenon. I believe NEF is at the right level of description to offer significant cognitive results while complying with computing power constraints of simulating millions of neurons in realtime. Jul 28, 2020 at 17:10
• why do you need to simulate millions of neurons in realtime? NEF isn't simulating neurons that accurately represent brain neurons, so what's the benefit?
– honi
Jul 29, 2020 at 18:06
• Millions of neurons have to interact to yield cognitive phenomena, and hence models that process and influence their surroundings. Its is preferable to do both in realtime. NEF is an approximation of neurons which has temporal and population coding and therefore more accurate than deep learning neurons, but less accurate than say Blue Brain neurons. NEF’s cognitive ability stems from the abstraction balance it strikes. Jul 29, 2020 at 18:18