Mathematical Structures in Neuroscience

Course Notes, 2010-2011

Jonathan Victor

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

Introduction

• Notes download (5 pgs) first posted 1/30/11

Groups, Fields, and Vector Spaces

• Notes for 2/1/11 download (9 pgs) minor corrections 2/1/11, first posted 1/30/11
• Homework 1 questions answers minor corrections 2/6/11, first posted 2/1/11

• Notes for 2/8/11 (up to "Tensor products") and 2/15/11 ("Tensor products" to end) download (19 pgs) minor correction 2/16/11, additions and minor corrections 2/15/11, first posted 2/8/11
• Homework 2 questions (do only Q1 and Q2A, Q2B) answers first posted 2/8/11

Linear Transformations and Group Representations

• Notes for 2/15/11 (up to "Eigenvalues define subspaces"), 2/22/11 (up to "Spectral Theorem") and 3/1/11 ("Group Representations" to end) download (25 pgs) minor corrections 3/1/11, material added 2/21/11, first posted 2/15/11
• Homework 1 questions (for 2/15/11, do only Q1) answers minor correction 2/22/11, first posted 2/15/11
• Homework 2 questions (do also Q2 of 2/15/11) answers minor correction 3/1/11, first posted 2/21/11
• Homework 3 questions answers first posted 3/1/11

Linear Systems: Black Boxes and Beyond

• Notes for 3/8/11 (up to "Renewal processes"), 3/15/11 (up to "Estimation of the power spectrum is not trivial"), 3/22 ("Using the power spectrum" to end) download (29 pgs) material added 3/20/11 begining on page 21, material added 3/13/11 beginning on page 13, first posted 3/8/11
• Homework 1 questions answers first posted 3/8/11
• Homework 2 questions answers first posted 3/13/11

Information Theory and Data Analysis

• Notes for 4/5/11 download (16 pgs) first posted 4/3/11

Multivariate Methods

• Notes for 4/12/11 through 5/17/11 (up to "Multidimensional scaling"), 5/31/11 ("Procedures that seem like simple extensions" to end) download (22 pgs) first posted 5/29/11

Exam

• Questions download (5 pgs) first posted 5/29/11
• Answers download (14 pgs) first posted 6/22/11

Participant presentations

Additional course notes, exercises, and exams

Home pages (with complete notes, homework exercises, exams) for prior years are here: 2003-2004, 2008-2009. Selected links follow:

Groups, Fields, and Vector Spaces

• 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
• 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

Exam 2004

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

Exam 2009

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

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