Date  Topic 
Reading/Supp Material 
Homework 
Thur 8.28 
Preliminaries: Introduction to course aims. Linear algebra, vectors: Cricket cercal system. 
Textbook Secs 1.3, 1.4, slides (pptx). Supplemental reading (optional): Review article on the cercal system (pdf) 

Fri 8.29, 1112pm and 45pm @SEA 2.122 
MATLAB tutorial part I 
Tutorial I slides, test.m file with examples 

Tues 9.02 
Linear algebra: Vector spaces. 


Tues 9.02, 67pm and 78pm @SEA 2.122 
MATLAB tutorial part II 
Tutorial II slides 
Homework 1 assigned 
Thur 9.04 
Linear algebra: matrices, matrix products, intro to trichromacy. 
Linear algebra primer and slides.
(Optional: more detailed Linear algebra primer II, pp. 115.)


Fri 9.5, 45pm and 78pm @SEA 2.122 
MATLAB tutorial part III 
Tutorial III slides 

Tues 9.09 
Decoding the Cercal system response (population vector). Systems of linear equations, exact solution. 
Supplemental reading (optional): Article on decoding the cercal system (pdf) 
Homework 2 assigned
Datafiles
Sample matlab file for decoding

Thur 9.11 
Under and overdetermined systems: Pseudoinverse solution. 


Tues 9.16 
Coding session, interim review. 

Homework 3 assigned
Datafile

Thur 9.18 
Pseudoinverse as linear leastsquares regression (overdetermined) or picking smallest L2norm solution (underdetermined). Intro to nonlinear leastsquares regression. 


Tues 9.23 
Overfitting and crossvalidation in nonlinear regression. Back to linear systems: correlation and covariance. 
Slides similar to material we covered in class 
Homework 4 assigned
Datafiles and matlab code 
Thurs 9.25 
Linear dependence: Variance, covariance, and the Pearson correlation coefficient. Linear regression on a single pair of variables in terms of covariance. 


Tues 9.30 
Covariance matrices. Crosscorrelation and autocorrelation functions. Analyzing temporal structure in spike trains. 
Notes on crosscorrelation and covariance (from Seung) 
Homework 5 assigned
Datafile 
Thurs 10.02 
Convolution and applications: smoothing, generating rates from spike trains. 
Notes on crosscorrelation and covariance (from Seung) 

Tues 10.07 
Convolution and applications: Mach bands, edgedetection in the retina. 
Supplemental readings (optional): Hartline
Nobel address on Limulus retina, Mach bands;
Marr
article on edge detection.

Homework 6 assigned
Matlab code to generate data 
Thur 10.09 
Convolution review, more examples. Q&A for midterm. 


Tues 10.14 
Inclass midterm 

No new homework 
Thur 10.16 
WienerHopf equations (reverse correlation) and the spiketriggered average. 


Tues 10.21 
Eigenvalues, eigenvectors and the spectral theorem. 

Homework 7 assigned
Matlab code to generate data 
Thur 10.23 
Change of basis. PCA and applications. 
Supplemental reading on PCA (optional): Shlens Tutorial. Sound separation demo (ICA): Readme file, Demo files. 

Tues 10.28 
Dimensionality reduction, denoising with PCA. Intro to probability. 

Homework 8 assigned
Datafiles and matlab code 
Thur 10.30 
Discrete probability distributions. Bayes Rule. 


Tues 11.04 
Common probability distrubtions and densities in Neuroscience. 


Thur 11.06 
Maximum likelihood estimation. 

Homework 9 assigned
Datafiles and matlab code 
Tues 11.11 
Nernst potential and subthreshold neural dynamics. 
Textbook chapter 2 (excluding 2.5), Section 3.4 

Thur 11.13 
Analytical and numerical integration of the membrane voltage equation. 
Textbook Sections 2.5, 3.1, 3.43.5 
Homework 10 assigned
Matlab code 
Tues 11.18 
The leaky integrateandfire model; spikefrequency adaptation. 
Textbook Section 10.1 

Thur 11.20 
Similarities between dynamical and statistical modeling and how they differ. Simple networks: 1neuron circuit (autapse). 


Tues 11.25 



Thur 11.27 



Tues 12.02 



Thur 12.04 



Fri 12.xx 



Fri 12.xx 






