Mathematical Tools for Neuroscience

NEU 314, Fall 2021
time: Tu/Th 1:30-3:00p
location: PNI A02
instructor: Jonathan Pillow
AIs: Rober Boshra, Edan Daniel, Aditi Jha, Alex Nguyen
Princeton University
prerequisites: Good working knowledge of calculus and high school math (e.g., a friendly relationship with log, exp, trig functions). Programming experience is helpful but not required.
brief description: This course aims to provide a comprehensive introduction to the mathematical and computational tools used for analyzing neural systems and neural data. The course will introduce students to topics in linear algebra, differential equations, and probability & statistics, with a heavy emphasis on applications to neurobiology. The course will seek to give students both a good intuitive understanding and a practical mastery of various mathematical and computational methods, and equip them with programming and data visualization skills that are increasingly important to scientific inquiry in general, and neuroscience in particular. Students will learn to program in Python, and homework problem sets will focus heavily on programming.
syllabus: pdf
ed: course page
Lecture Schedule

Date Topic Reading / Handouts Slides (pdf) HW
Th 9.02 Course introduction and announcements syllabus.pdf slides01.pdf
Tu 9.07 Intro to linear algebra: vectors, norm, and inner product slides02.pdf hw0_neu314_Q.ipynb
(due date: none)
Th 9.09 Linear combination, vector spaces, & matrices slides03.pdf linear algebra basics
(due 9/21, 1:30pm)
Tu 9.14 Application: trichromactic color vision slides04.pdf
Th 9.16 Matrix multiplication, outer product, transpose, inverse slides05.pdf color vision & linear systems
(due 10/05, 1:30pm)
Tu 9.21 Row / column / null spaces; Linear Systems slides06.pdf
Th 9.23 no in-person class
Tu 9.28 Application: null spaces in the brain Kaufman et al 2014 slides07.pdf row & null spaces
(due 10/12, 1:30pm)
Th 9.30 Singular Value Decomposition (SVD) notes_SVD.pdf slides08.pdf
Tu 10.05 SVD applications slides09.pdf
Th 10.07 Low-rank matrix approximation ( recorded; no in-person class ) slides10.pdf SVD
(due 11/02, 1:30pm)
Tu 10.12 Principal Components Analysis (PCA) notes_PCA.pdf slides11.pdf
Th 10.14 Least Squares Regression notes_LSregression.pdf slides12.pdf
Tu 10.19 fall break
Th 10.21 fall break
Tu 10.26 Intro to Probability slides13.pdf PCA & regression
(due 11/16, 1:30pm)
Th 10.28 Bayes' rule slides14.pdf
Tu 11.02 Independence slides15.pdf
Th 11.04 Correlations and Gaussian distributions slides16.pdf
Tu 11.09 Information theory I: entropy slides17.pdf Probability
(due 11/23, 1:30pm)
Th 11.11 Information theory II: mutual information, KL, and efficient coding slides18.pdf
Tu 11.16 Estimation slides19.pdf
Th 11.18 Maximum Likelihood for spike count models slides20.pdf
Tu 11.23 GLMs & Logistic regression slides21.pdf
Th 11.25 Thanksgiving
Tu 11.30 Intro to Dynamics slides22.pdf Info Theory & GLMs
(due: 12/14)
Th 12.02 Multi-dimensional dynamics notes_Dynamics.pdf slides23.pdf

page maintained by Jonathan Pillow