Mathematical Tools for Neuroscience

NEU 314, Spring 2016
time: Tu/Th 10:00-11:00
location: NEU A02
instructor: Jonathan Pillow
AIs:Adam Charles, Alex Piet, & Alex Song.
Princeton University
prerequisites: Good working knowledge of calculus and high school math (e.g., a friendly relationship with log, exp, cos, sin). Some 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.
syllabus: pdf
piazza: course page
Lecture Schedule

DateTopic Reading / Handouts Slides (pdf) HW
T 2.02 Course introduction and announcements syllabus.pdf lec01.pdf
Th 2.04 Intro to linear algebra: vectors, norm, and inner product matlab primer: pdf (39-pages), online
matlab tutorial: pdf (17 pages).
T 2.09 linear projection & vector spaces lec03.pdf hw0.pdf
Th 2.11 trichromactic color vision lec04.pdf
T 2.16 trichromacy part 2 lec05.pdf hw1.pdf
(due 2/23)
Th 2.18 Orthogonal matrix, change of basis, row / column space lec06.pdf
T 2.23 Linear systems, SVD lec07-08.pdf hw2.pdf
(due 3/1)
Th 2.25 SVD and its applications
T 3.01 no class hw3.pdf
(due 3/11)
Th 3.03 PCA lec09.pdf
T 3.08 Least-squares Regression lec10-11.pdf hw4.pdf
(due 3/25)
Th 3.10 derivations: LS regression and PCA
T 3.15 spring break
Th 3.17 spring break
T 3.22 Intro to Probability lec12.pdf
Th 3.24 Bayes' Rule lec13.pdf hw5.pdf
(due 4/5)
T 3.29 Expectations, Independence, & Gaussians lec14.pdf
Th 3.31 Estimation: Bias & Variance lec15.pdf hw6.pdf
(due 4/12)
T 4.05 Maximum Likelihood lec16.pdf
Th 4.07 GLMs and logistic regression lec17.pdf hw7.pdf
(due 4/19)
T 4.12 Bayesian estimation lec18.pdf
Th 4.14 Information Theory & Efficient Coding lec19.pdf hw8.pdf
(due 4/26)
T 4.19 Cross-validation and Overfitting lec20.pdf
Th 4.21 Bootstrap and permutation lec21.pdf
T 4.26 Linear Shift-Invariant Systems and Fourier Analysis lec22.pdf
Th 4.28 Convolution Theorem, Linear Dynamics lec23.pdf hw9.pdf
(due 5/10)

page maintained by Jonathan Pillow