Pedagogy

Notes

Long-form notes from courses in physics, mathematics, statistics, and machine learning.

Physics

01PDF · Yale PHYS 410Classical mechanicsSelected derivations from Yale’s classical mechanics course.

PDFContents

1. Poisson brackets 2. Conservation of angular momentum 3. Parallel-axis theorem 4. Lorentz transformations 5. Length contraction 6. Relativistic momentum and energy

02PDF · Yale PHYS 430ElectrodynamicsHandwritten course notes following Griffiths’ treatment of electrodynamics.

PDFContents

1. Mathematical review 2. Electrostatics 3. Potentials 4. Magnetostatics 5. Magnetic fields in matter 6. Electrodynamics 7. Conservation laws 8. Electromagnetic waves 9. Potentials and fields 10. Dipole radiation 11. Electrodynamics and relativity

03PDF · Yale PHYS 440 & 441Quantum mechanicsHandwritten notes from Yale’s two-course quantum mechanics sequence.

Quantum I Quantum IIContents

Quantum I — Vector spaces and operators Quantum I — Coupled systems Quantum I — Infinite and finite wells Quantum I — States and Schrödinger evolution Quantum I — Tunneling Quantum I — Product spaces and rotations Quantum II — Rotations and angular momentum Quantum II — Hydrogen atom Quantum II — Spin Quantum II — Addition of angular momentum Quantum II — Variational and WKB methods Quantum II — Time-independent perturbation theory Quantum II — Time-dependent perturbation theory Quantum II — Scattering theory

04PDF · Yale PHYS 420Statistical mechanics and thermodynamicsA typed reference and separate handwritten notes from Yale’s statistical mechanics course.

Typed reference Class notesContents

1. Introduction to statistical methods 2. Statistical descriptions of particle systems 3. Statistical thermodynamics 4. Macroscopic parameters 5. Macroscopic thermodynamics 6. Methods of statistical mechanics 7. Applications of statistical mechanics 8. Equilibrium between phases 9. Quantum statistics of ideal gases

05PDF · Yale PHYS 428Complex systemsCourse notes on bifurcations, stability, nonlinear dynamics, and deterministic chaos.PDF

06PDF · MIT Physics 8.334Statistical Physics of FieldsHandwritten course notes from Mehran Kardar’s Statistical Physics of Fields.

PDFContents

1. Collective behavior 2. Statistical fields 3. Fluctuations 4. Scaling hypothesis 5. Perturbative renormalization group 6. Lattice systems 7. Series expansions 8. Beyond spin waves

Mathematics, statistics & learning

01PDF · Yale MATH 310Complex analysisA review guide for Yale’s complex analysis course, organized around Gamelin.PDF

02PDF · Yale S&DS 242Theory of statisticsA course review of probability, estimation, hypothesis testing, and asymptotic ideas.

PDFContents

1. Review of probability theory 2. Hypothesis testing 3. Estimation and mean-squared error 4. Fisher information and asymptotics 5. Likelihood-ratio methods 6. Generalized linear models 7. Reference distributions

03PDF · Yale S&DS 551Stochastic processesCourse notes on Markov chains, martingales, Brownian motion, diffusions, and stochastic differential equations.

PDFContents

1. Markov chains 2. Markov-chain applications 3. Martingales 4. Gaussian random variables 5. Brownian motion 6. Diffusions 7. Stochastic differential equations

04PDF · Yale S&DS 664Information theoryCourse notes on entropy, coding, typicality, and channels, following Cover and Thomas.

PDFContents

1. Introduction and preview 2. Entropy and mutual information 3. Asymptotic equipartition 4. Entropy rates 5. Data compression 6. Gambling and data compression 7. Information and portfolio theory 8. Channel capacity 9. Differential entropy

05PDF · Yale S&DS 631Convex optimizationCourse notes on convex sets, duality, and optimality, following Boyd and Vandenberghe.

PDFContents

1. Introduction 2. Convex sets 3. Convex functions 4. Convex optimization problems

06PDF · Yale CPSC 365AlgorithmsHandwritten course notes on algorithms, data structures, and complexity analysis.PDF

07PDF · Yale S&DS 665Machine learningCourse notes on statistical learning, neural networks, reinforcement learning, and representation methods.PDF