Mathematical Structures in Neuroscience

Course Notes, 2008-2009

Jonathan Victor

These are scanned notes used in class, along with homework questions and solutions from this year and previous years. Apologies for inaccuracies and penmanship. All rights reserved.

Groups, Fields, and Vector Spaces

• Notes download (21 pgs) minor corrections 1/16/04, first posted 1/6/04
• Homework 1, for pages 1 to 4 questions answers first posted 10/6/08
• Homework 2, for pages 4 to 9 questions answers first posted 10/6/08
• Homework 3, for pages 9 to 16 questions answers first posted 10/6/08

Algebraic Overview

• Notes download (10 pgs) minor corrections 2/20/11, first posted 10/6/08
• Homework 1, for pages 1-10 questions answers minor corrections 2/10/11, first posted 10/6/08

Linear Systems Theory

• Notes download (10 pgs) first posted 10/22/08
• Homework 1, for pages 1-10 questions answers first posted 10/22/08

Noise and Variability

• Notes download (15 pgs) first posted 11/06/08
• Notes download (10 pgs) first posted 11/06/08
• Demo: Slepian functions (a.k.a. discrete prolate spheriodal sequences): the "windows" for the multitaper method) matlab code and its output first posted 11/06/08
• Matlab implementation at MathWorks
• Chronux toolbox home page
• Homework 1, for pages 1-25 questions answers first posted 11/06/08
• Notes (channel noise, 3 ways) download (8 pgs) minor correction 3/20/11, first posted 11/12/08
• Demo: Channel noise (the "windows" for the multitaper method) matlab code and its output first posted 11/12/08
• Notes (non-stationary time series: multitaper, wavelets, autoregressive methods) download (13 pgs) first posted 12/1/08

Nonlinear Systems Theory

• Notes download (13 pgs) first posted 12/9/08
• Notes download (15 pgs) first posted 12/22/08
• Homework 1, for pages 14 to 22 questions answers first posted 01/09/09
• Notes download (15 pgs) minor correction 2/21/09, first posted 12/22/08 download (10 pgs) first posted 1/05/09
• Notes download (11 pgs) first posted 1/22/09
• Homework 2, for pages 39 to 49 questions answers first posted 2/11/09

Multivariate Methods

• Notes download (18 pgs) minor corrections 2/15/09, first posted 2/11/09
• Homework 1, for pages 1 to 12 questions answers first posted 2/15/09
• Notes download (8 pgs) first posted 2/17/09
• Homework 2, for pages 13 to 26 questions answers first posted 2/15/09

Exam

• Questions (not handwritten) download (3 pgs) first posted 2/25/09
• Answers download (10 pgs) first posted 3/28/09

Additional course notes, exercises, and exam from 2003-2004

Groups, Fields, and Vector Spaces

• Supplemental homework 1, for pages 1 to 8 questions answers first posted 1/6/04
• Supplemental homework 2, for pages 9 to 10 questions answers first posted 1/6/04
• Supplemental homework 3, for pages 11 to 21 questions answers download (21 pgs) first posted 1/6/04
• Supplemental notes: 3x3 determinant; tensor-products and SO(3) download (5 pgs) first posted 1/16/04

Eigenvectors, Eigenvalues, Inner Products

• Notes download (7 pgs) minor corrections 1/16/04, first posted 1/6/04
• Homework 1, for pages 1 to 7 questions answers first posted 1/6/04

Group Representations

• Notes download (14 pgs) first posted 1/16/04
• Homework 1, for pages 1 to 6 questions answers first posted 1/16/04
• Homework 2, for pages 7 to 13 questions answers first posted 1/16/04

Fourier Analysis: Application to Linear Systems Theory

• Notes download (12 pgs) first posted 1/22/04
• Notes download (15 pgs) first posted 2/5/04
• Homework 1, for pages 1 to 7 questions answers first posted 1/22/04
• Homework 2, for pages 8 to 12 questions answers first posted 1/22/04
• Homework 3, for pages 13 to 27 questions answers first posted 2/5/04
• Supplement: The Fast Fourier Algorithm download (6 pgs) first posted 1/22/04

Point Processes

• Notes download (8 pgs) minor corrections 2/18/04, first posted 2/10/04
• Homework 1, for pages 1 to 8 questions answers first posted 2/10/04

Ensembles, Estimators, and Gaussians

• Notes download (18 pgs) minor corrections 2/29/04, first posted 2/21/04
• Homework 1, for pages 1 to 10 questions answers first posted 2/21/04
• Homework 2, for pages 11 to 18 questions answers first posted 2/21/04

Power Spectra

• Notes download (14 pgs) first posted 3/3/04
• Notes download (13 pgs) first posted 3/15/04
• Notes download (14 pgs, including 2 figures) minor corrections 3/30/04, first posted 3/22/04
• Notes download (6 pgs) first posted 3/30/04
• Homework 1, for pages 1 to 14 questions answers minor corrections 3/10/04, first posted 3/3/04
• Homework 2, for pages 15 to 27 questions answers first posted 3/15/04
• Supplement: asymptotic behavior of Slepian functions (ms. by Victor and Knight; see sections 2.1 to 2.7) download
• Demo: matlab scripts illustrating various windows ("tapers") and their Fourier transforms download

Entropy and Information (Selected Topics)

• Notes download (14 pgs) minor corrections 4/7/04, first posted 3/30/04
• Homework 1, for pages 1 to 14 questions answers first posted 3/30/04

Exam

• Questions (not handwritten) download (2 pgs) first posted 3/30/04
• Answers download (11 pgs) first posted 5/11/04

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