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
  • PYTHON TUTORIAL

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

• 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
• 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

• basic calculus videos

2: Linear algebra basics (Susu)

vector/matrix multiplication, basis vectors, span, subspaces, eigenvalues/vectors

• 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

• June 27: lecture NOTES

  • inverse matrices, column space and null space
  • big picture of linear algebra
  • change of basis

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

(typed notes)

• 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
• 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
• July 12: programming
  • first 30 min - python notebook
  • PCA notebook

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
  • PopIn questions
• July 18: problem set
  • PopIn questions 2
• 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
  • PopIn questions
  • Combinatorics notes
  • Reference sheets for set theory
  • Problem set
• 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