**Faculty: Larry Abbott, Stefano Fusi, Ashok Litwin Kumar, Ken Miller****TAs: Matteo Alleman, Dan Biderman, Salomon Muller, Amin Nejatbakhshesfahani, Marjorie Xie**

**Meetings: **Tuesdays & Thursdays, JLGSC L5-084, Lecture 2.00 - 3.30pm

**Text:** Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)**January **

21 (Larry) Introduction to the Course and to Theoretical Neuroscience

23 (Larry) Mathematics Review: Notes

28 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model (Assignment 1, neuron models)

30 (Larry) Adaptation, Synapses, Spiking Networks (Numerical methods)

**February **

4 (Larry) Numerical Methods, Filtering (Assignment 2)

5 Assignment 1 Due

6 (Larry) The Hodgkin-Huxley Model (I&F Model, White Noise, Synapses-Networks)

11 (Larry) Types of Neuron Models and Networks (Assignment 3, Poisson Spiking, Networks)

12 Assignment 2 Due

13 (Ashok) Linear Algebra I (Notes)

18 (Ashok) Linear Algebra II (Notes, Assignment 4)

19 Assignment 3 Due

20 (Ashok) Introduction to Probability, Encoding, Decoding (Notes)

25 (Ashok) GLMs (Notes, Assignment 5)

26 Assignment 4 Due

27 COSYNE

**March**

3 COSYNE

5 (Ashok) Decoding, Fisher Information I

10 (Ashok) Decoding, Fisher Information II (Assignment 6)

11 Assignment 5 Due

12 (Ashok) Information Theory

17 Spring Break

19 Spring Break

24 (Ken) – PCA and Dimensionality Reduction I

25 Assignment 6 Due

26 (Ken) – PCA and Dimensionality Reduction II

31 (Ken) – Rate Networks/E-I networks I (Assignment 7)

**April**

1 Assignment 6 Due

2 (Ken) – Rate Networks/E-I networks II

7 (Ken) – Unsupervised/Hebbian Learning, Developmental Models (Assignment 8)

8 Assignment 7 Due

9 (Ken) – Optimization

14 (Ken) – Optimization II (Assignment 9)

15 Assignment 8 Due

16 Research Topic

21 (Stefano) Perceptron (Assignment 10)

22 Assignment 9 Due

23 (Stefano) Multilayer Perceptrons and Mixed Selectivity

28 (Stefano) – Deep Learning I (backpropagation) (Assignment 11)

29 Assignment 10 Due

30 (Stefano) – Deep Learning II (convolutional networks)

**May**

5 (Stefano) Learning in Recurrent Networks (Assignment 12)

6 Assignment 11 Due

7 (Stefano) Continual Learning and Catastrophic Forgetting

12 (Stefano) Reinforcement Learning

13 Assignment 12 Due

14 Research Topic

**Meetings: **Wednesdays, 10.15 - 11.45am

**Location** – Jerome L Greene Science Center, L6-087

See course website for updated schedule

Control Theory and Reinforcement Learning

Jan 29 Examples of control theory in neuroscience (Bettina Hein, Laureline Logiaco)

Feb 5 Methods in control theory (Bettina Hein, Laureline Logiaco)

Feb 12 Reinforcement learning (James Murray)

Feb 19 From optimal control theory to reinforcement learning (Samuel Muscinelli)

Feb 26 Cosyne break

Mar 4 Cosyne break

Latent Variable Models

Mar 11 Hidden Markov Models (Matt Whiteway)

Mar 18 Latent Dynamical Systems (Josh Glaser)

Mar 25 Gaussian Processes (Rainer Engelken)

Apr 1 Modeling of Behavior (Juri Minxha)

Apr 8 Hackathon on Latent Variable Models

Miscellaneous

Apr 15 Phenomenological Renormalization Group (Serena Di Santo)

Apr 22 Additional and diverse perspectives in neuroscience (Laureline Logiaco, Matt Whiteway, Juri Minxha)

Apr 29 Introduction to replica theory (SueYeon Chung)

May 6 Classification and Geometry of General Perceptual Manifolds (SueYeon Chung)

**Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)**

**Faculty**: Ken Miller (kdm2103@columbia.edu)**Instructor**: Dan Tyulmankov (dt2586@columbia.edu)**Teaching Assistant**: Amin Nejatbakhsh (mn2822@columbia.edu)

**Time**: Tuesdays, Thursdays 8:40a-10:00a**Place**: JLGSC L5-084**Webpage**: https://ctn.zuckermaninstitute.columbia.edu/courses**Credits**: 3 credits, pass/fail only

**Description**: An introduction to mathematical concepts used in theoretical neuroscience aimed to give a minimal requisite background for NBHV G4360, Introduction to Theoretical Neuroscience. The target audience is students with limited mathematical background who are interested in rapidly acquiring the vocabulary and basic mathematical skills for studying theoretical neuroscience, or who wish to gain a deeper exposure to mathematical concepts than offered by NBHV G4360. Topics include single- and multivariable calculus, linear algebra, differential equations, dynamical systems, and probability. Examples and applications are drawn primarily from theoretical and computational neuroscience.

**Prerequisites**: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level

**Grading**: 100% attendance-based

**Readings** **and exercises**: Lecture notes and optional practice exercises will be provided for each lecture, and supplementary readings will be assigned from various textbooks.