UCSB-129-comp-phys
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Syllabus
Final
Practice Final and Solution
Course Overview, Vector Space, Duality, Tensors, Metric, Covariant Derivatives
Convex Hull, Mesh Generation, Parallel Transport, Geodesics, and Differential Forms
Turing Machine, Computational Complexity, and P,NP problems
Master Theorem, Divide-and-conquer, Dynamic programming,Data Structures, and Matrix Operation
Indistinguishable Particles, Fermi-Dirac, Bose-Einstein, Probability, Legendre Transforms, Partition Function, Phase Space, Liouville Equation
Central Limit Theorem, Statistical Processes, Stochastic process, Markov Chain, Classical/Quantum Master Equation
Markov Birth-Death Process, Stochastic Process, Wiener process, fluctuation-dissipation theorem, Langevin Equation
Lecture Notes: Chapman–Kolmogorov equation, Birth-Death Process, Kolmogorov forward(Fokker-Planck)/backward euqation, Poisson Process from pure birth process, Wiener process, Brownian motion, Ito’s lemma, Stratonovich form, Langevin Equation, fluctuation-dissipation theorem, autocorrelation
Bayesian Inference, Frequentist, Fisher Information
Monte Carlo integration, Random Number Generators, Box–Muller transform, inverse transform, Rejection Sampling, importance sampling
Markov Chain Monte Carlo
Quadrature methods, Gauss-Legendre Quadrature
Optimization and Numerical Solvers
Supervised deep learning, Multilayer Perceptron
Backpropagation, convolutional neural network, and Recurrent Neural Networks
Quantum Monte Carlos and Density Functional Theory
Section 1, Git and Github
Section 2, Convex Hull Algorithms and Delaunay Triangulation
Section 3, Turing Machine on Binary multiplication and Transition Optimization
Section 4, Master Theorem, Time Complexity, Strassen’s Algorithm,Heisenberg XXX Hamiltonian on a Ring
Section 5A, Density of States, Lagrangian, Hamiltonian, Classical Phase Space Trajectory
Section 5B, Fermi-Dirac and Bose-Einstein statistics, Bose-einstein Condensates
Section 6A, Poisson, Lorentzian, Revisit the Heisenberg XXX Hamiltonian on a Ring, Markov Chain
Section 6B, to lemma and Stratonovich formulation, Autocorrelation, Langevin equation
Section 7A, Frequentist, Bayesian Inference, Stirling’s approximation, Bootstrapping,
Section 7B, Sobol sequence, Monte Carlo Integration, Inverse transformation Sampling, Box–Muller Transform, Rejection Sampling
Section 8A, Classical 2D Ising Model, Gibbs Sampler, Order Parameter, Landau theory, Phase transition, Magnetic Susceptibility, Specific Heat
Section 8B, quadrature methods ,test function, Simpson's Rule ,Gauss-Legendre Quadrature,Legendre polynomials, Newton's Method,Harmonic Oscillator
Section 9A, Black Body Radiation, Orbits with symplectic methods,Gradient descent, Metropolis–Hastings algorithm, Simulated Annealing
Section 9B, Multilayer Perceptron, Convolutional neural network, and MNIST dataset, Traning and validation of MLP and CNN
Section 10, Quantum Espresso
Problem Set 1, Bash Commands and Shell Script
Problem Set 2, Parallel Transport on Sphere, Stereographic Projection, Lifting Maps
Problem Set 3, Correlation in multivariate normal distributions, Local Density of States on 2D Moire Lattice
Problem Set 4, Bifurcation and Chaos in the Logistic Map, Julia Set, Area, and Fractal dimension,Lorenz system
External Resource
UCSB-129-comp-phys
Markov Birth-Death Process, Stochastic Process, Wiener process, fluctuation-dissipation theorem, Langevin Equation
Readings and Lectures Notes
Lecture Notes: Chapman–Kolmogorov equation, Birth-Death Process, Kolmogorov forward(Fokker-Planck)/backward euqation, Poisson Process from pure birth process, Wiener process, Brownian motion, Ito’s lemma, Stratonovich form, Langevin Equation, fluctuation-dissipation theorem, autocorrelation
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