All classes are in Seminar (except July 22 is in Auditorium)
- lecture on Mondays 12-2pm
- lecture/problem set session on Thursdays 3:30-5:30pm
- programming session on Fridays 3:30-5:30pm (only weeks 3,4,6) in python
We will also have office hours each Wednesday 1-3pm (in 2W.124 POD). You can also post questions to the Janelia slack #mathclub thread.
1: Calculus basics (Marcella)
derivatives, chain rule, gradients, Lagrange multipliers
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June 17: NOTES
- limits (watch before class)
- derivatives (watch before class)
- differentiability
- chain rule
- minima, maxima, and critical pts; and testing critical pts
- fundamental theorem of calculus and integration: part1, part2
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June 20: NOTES
- vector fields and visualizations (up to time 2:14) (watch before class)
- partial derivatives (watch before class)
- gradients; gradient graphs; and contour maps
- intro to lagrange multipliers; constrained optimization with lagrange multipliers; and an example
Other resources
2: Linear algebra basics (Susu)
vector/matrix multiplication, basis vectors, span, subspaces, eigenvalues/vectors
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June 24: lecture NOTES
- vector intro (watch before class)
- real coordinate spaces (watch before class)
- linear combinations, span, and basis vectors
- linear transformations and matrices
- matrix multiplication as composition
- determinant
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June 27: lecture NOTES
Other resources
- MIT online course taught by Prof. Gilbert Strang
- BOOK: LINEAR ALGEBRA AND ITS APPLICATIONS by Prof. Gilbert Strang
- Khan Academy linear algebra online course
3: Eigenvalues and Principal Components Analysis (Carsen)
Eigenvalues/vectors, linear differential equations, PCA and SVD derivations
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July 8: pre-class problems, notes
- Euler's method (watch before class if needed)
- complex numbers, complex roots (watch before class if needed/want to)
- eigenvalues and eigenvectors
- diff-eq resources: linear systems of differential equations, phase diagrams
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July 11: pre-class problems, notes
- matrix diagonalization (watch before class)
- similar matrices (watch first 5 min before class)
- two-neuron example
- matrix properties: symmetric matrices, positive semi-definite matrices
- PCA derivation (15:00 - 37:00)
- SVD derivation
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July 12: programming
Resources
- Euler's method
- MIT diffeq notes (page 61 has linear ODEs)
- first order ODEs
- nice PCA blog post
- thorough PCA video
- PCA chapter from PRML by Bishop
- Another PCA tutorial - with a nice explanation of how PCA and the SVD related
4: Linear regression (John)
linear regression - derivation, application and non-linear approaches
- July 15: lecture notes
- July 18: problem set
- July 19: programming exercise
Resources
- one variable linear regression
- multiple linear regression
- visualizing overdetermined systems of equations
- least squares + ridge regression
- linear regression with basis functions (video)
- linear regression with basis function (notes)
- Abstract vector spaces (video)
- Difference between linear regression and PCA
5: Probability and random variables
random variables, gaussian/poisson distributions, moments, central limit theorem
- July 22: lecture notes
- July 25: lecture and problem set
Resources
- khan academy stats
- nice interactive stats resources
- Intro and Prob chapter from PRML by Bishop (includes ML)
6: Maximum likelihood estimation
log likelihood, analytical derivation of spike rate for a poisson model
- July 29: lecture notes
- Aug 1: problem set
Resources