Date  Topic 
Reading 
Homework 
Thur 8.29 
Preliminaries: Introduction to course aims, mathematical notation, review of basic math objects and operations.

Textbook Secs 1.3, 1.4 
Homework 1 assigned (pdf) 
Fri 8.30, 10:00am and 3:00pm SEA 2.122 
MATLAB tutorial 


Tues 9.03 
Subthreshold cellular properties: Nernst potential, cell membrane as an RC circuit. 
Textbook Ch 2 (excluding 2.5), Sec 3.4, slides (pdf) 

Thur 9.05 
Subthreshold cell voltage equation; numerical integration of functions; steady states. 
Textbook Section 3.1 
Homework 2 assigned (pdf) 
Tues 9.10 
Exact integration of subthreshold voltage equation, synaptic dynamics. 
Textbook Sections 2.5, 3.1 
Homework 1 solutions (pdf) 
Thur 9.12 
Synaptic dynamics, numerical integration of differential equations including voltage equation. 
Textbook Sections 3.5, 3.4 

Tues 9.17 
Simple spiking model (leaky integrateandfire neuron). 
Textbook Section 10.1 
Homework 3 assigned (pdf) 
Thur 9.19 
The Dirac Delta function; spikes in the synpatic activity equation. 
Wikipedia page on the Dirac Delta function. For more details on the Dirac Delta, see book: Mathematical Methods for Physicists, by Arfken (7th ed. Elsevier, 2013), Section 1.11, p. 75. 
Homework 2 solutions (pdf) 
Tues 9.24 
Synaptic activation with trains of spikes. Method of averaging I: numerical integration of differential equations that involve delta functions. 

Homework 4 assigned (pdf) 
Thurs 9.26 
Method of averaging II: deriving a ratebased equation for synaptic activation. 

Homework 3 solutions (pdf) 
Tues 10.1 
Stability of fixed points: Graphical stability analysis. Example: The autapse as a bistable switch. 

Homework 5 assigned (pdf) 
Thurs 10.3 
Graphical stability analysis continued. Linear stability analysis. The autapse as an integrator. 
Linear stability notes (pdf) 
Homework 4 solutions (pdf) 
Tues 10.8 
Review 

No new homework; Homework 5 solutions (pdf) 
Thur 10.10 
Midterm: inclass, closed book. 


Tues 10.15 
Positive feedback in a mutual inhibition circuit: switches, integrators, perceptual bistability. 
Slides (pdf), Matlab code mut_inhib_switch.m 
Homework 6 assigned (pdf) 
Thur 10.17 
Decoupling coupled linear (differential) equations: heuristic. 

Homework 6 solutions (pdf) 
Tues 10.22 
Linear algebra: basis sets, vector spaces. 
Linear algebra notes by E. Simoncelli (pdf) 
Homework 7 assigned (pdf) 
Thur 10.24 
Matrices, pseudo inverse for linear leastsquares regression (overconstrained problems). 

Homework 7 solutions (pdf) 
Tues 10.29 
Pseudo inverse for underconstrained systems of linear equations; eigenvectors and eigenvalues. 

Homework 8 assigned (pdf) Related data file (mat) 
Thur 10.31 
Eigenvector decomposition of systems of linear equations. 

Homework 8 solutions (pdf) 
Tues 11.05 
Covariance. PCA. 
Textbook section 14.2; A tutorial on Principal Components Analysis, by J. Shlens (2009) (pdf) 
Homework 9 assigned (pdf) Related data and code files (zip) 
Thur 11.07 
Convolution. 
Notes by S. Seung (pdf) 

Tues 11.12 
Convolution: interpretations, examples. Correlation. 

Homework 9 solutions (pdf) 
Thur 11.14 
Linear neural coding problem: WienerHopf equations. 
Notes by S. Seung (pdf) 

Tues 11.19 
Probability distributions, Maximum Likelihood, GLMs (Professor Pillow) 
Slides (pdf) 

Thur 11.21 
Fourier series: sines and cosines as a basis set for periodic functions. Filtering and denoising. PROJECTS. 

Homework 10 assigned (pdf) Related code to generate data (mfile) 
Tues 11.26 
How to write a research report: target audience, style, content. PROJECTS. 


Thur 11.28 
Thanksgiving 


Tues 12.03 
Fourier transforms. Identifying frequency content of a signal. Convolution as product. PROJECTS. 


Thur 12.05 
Course evaluations. PROJECTS. 


Fri 12.06, 6 pm 
Homework # 10 due: drop in office (Ila Fiete) or send by email. 


Fri 12.13, 2:305 pm 
Final exam: project presentations. 





