Welcome to 7870

These are our lecture notes for 7870

Part 1. Linear Algebra

• A Deeper look at Vectors
• Linear Algebra in Python with Numpy
• Eigenvectors, Unitary Matrices, and Matrix Decompositions
• Linear Regression and Least Squares

Part 2. Probability

• Intro to Probability
• Using Random Numbers in Numpy
• Conditional Probability and Bayes Rule
• Bayesian Inference
• Monte Carlo
• Markov Chain Monte Carlo
• Detailed Balance and the Metropolis-Hastings Algorithm

Part 3. Numerical Differential Equations

• Intro to Numerical Integration
• More on Numerical ODEs
• From ODE to PDE
• Optimization
• Nonlinear Regression
• Automatic Differentiation and JaX