Mathematical Structures in Neuroscience

Course Notes, 2003-2004

Jonathan Victor

These are scanned notes used in class, along with homework questions and solutions. 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 8 questions answers first posted 1/6/04
• Homework 2, for pages 9 to 10 questions answers first posted 1/6/04
• Homework 3, for pages 11 to 21 questions answers download (21 pgs) first posted 1/6/04
• Supplement: 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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