Mathematical Structures in Neuroscience

Course Notes, 2024-2025

Jonathan Victor

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

Course Notes

Introduction

• Notes for 1/9/25 download (11 pgs) first posted 1/7/25

Groups, Fields, and Vector Spaces

• Notes for 1/9/25 - 1/23/25 download (37 pgs) first posted 1/7/25, last revised 1/17/25
• Homework for 1/9/25 (pages 1-5 of notes) questions first posted 1/7/25 answers first posted 1/15/25, revised 1/16/25
• Homework for 1/16/25 (pages 6-25 of notes) questions first posted 1/16/25 answers first posted 1/23/25
• Homework for 1/23/25 (pages 26-37 of notes) questions first posted 1/23/25 answers first posted 1/28/25

Linear Transformations and Group Representations

• Notes for 1/23/25 - 2/13/25 download (43 pgs) first posted 1/16/25, last revised 2/20/25
• Homework for 1/30/25 (pages 1-19 of notes) questions first posted 1/30/25 answers first posted 1/30/25, last revised 2/13/25
• Homework for 2/13/25 (pages 20-43 of notes) questions first posted 2/13/25 answers first posted 2/18/25

Linear Systems, Black Boxes, and Beyond

• Notes for 2/20/25 - 2/27/25 download (39 pgs) first posted 2/13/25, last revised 2/28/25
• Homework for 2/20/25 (pages 1-15 of notes) questions first posted 2/20/25 answers first posted 2/28/25
• Homework for 2/27/25 (pages 16-39 of notes) questions first posted 2/28/25 answers first posted 2/28/25

Multivariate Methods, PCA, ICA

• Notes for 3/13/25 - 4/3/25 download (27 pgs) first posted 3/12/25, last revised 3/20/25
• Homework for 3/13/25 (pages 1-8 of notes) questions first posted 3/14/25, revised 3/19/25 answers first posted 3/19/25, revised 3/20/25
• Homework for 3/20/25 [none]
• Homework for 3/27/25 [none]
• Homework for 4/03/25 (pages 9-27 of notes) questions first posted 4/03/25

Information Theory and Data Analysis

• Notes for 4/10/25 - 4/17/25 download (16 pgs) first posted 4/03/25

Class Presentations

• Yuxi (Jaden) Long, 3/13/25: Manifolds and Curvature (static copy)
• Aksharkumar Dobariya, 3/20/25: Brain Electrical Activity (link)
• William Khayyo, 3/27/25: Mechanism of selectivity in the major facilitator superfamily transporter MFSD2A: Use of computational chemistry techniques to identify critical residues in selectivity mechanism for LPC and the antibiotic Tunicamycin (static copy)
• Neil Ruthen, 3/27/25: Multivariate regression methods reveal correlational structures in institutional clinical datasets (static copy)
• Zhaokun Wang, 4/03/25: Tracing endoplasmic reticulum–plasma membrane contact sites by single particle tracking method (link)

Selected non-overlapping problems from earlier years

Additional course notes, exercises, and exams

Home pages (with complete notes, homework exercises, exams) for prior years are here: 2003-2004, 2008-2009, 2010-2011, 2012-2013, 2014-2015, 2016-2017, 2018-2019. 2020-2021. 2022-2023.

Exam 2004

• Questions download (2 pgs)
• Answers download (11 pgs)

Exam 2009

• Questions download (3 pgs)
• Answers download (10 pgs)

Exam 2011

• Questions download (5 pgs)
• Answers download (14 pgs)

Exam 2013

• Questions download (6 pgs)
• Answers download (16 pgs)

Exam 2015

• Questions download (4 pgs)
• Answers download (7 pgs)

Exam 2017

• Questions download (4 pgs)
• Answers download (12 pgs)

Exam 2019

• Questions download (7 pgs)
• Answers download (17 pgs)

Exam 2021

• Questions download (6 pgs)
• Answers download (14 pgs)

Exam 2023

• Questions download (1 pg)
• Answers download (5 pgs)

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