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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

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

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UCSB-129-comp-phys

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