Syllabus+(Spring),+Numerical+and+Statistical+Methods

 · // Mathematical Methods //  o Fourier transforms and convolution  o Filtering  o Power spectra, correlation, cross-correlation  o Nyquist sampling theorem  · // Numerical Methods //  o Basic numerical algorithms, such as root-finding (Newton-Raphson), interpolation (polynomial and spline), integration (Runge-Kutta), ordinary differential equations (adaptive stepping), linear systems and matrix inversion, boundary value problems  o Fast Fourier Transform  o Monte Carlo techniques  o Eigensystems and principal component analysis  o N-body codes; particle v. grid-based  · // Statistical Methods //  o Probability distributions and the central limit theorem  o Significance testing (chi-squared, f/t-tests, Kolmogorov-Smirnov)  o Maximum likelihood  o Bayesian inference and maximum entropy <span style="margin-left: 1.0in; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level2 lfo1; mso-pagination: none; text-autospace: none; text-indent: -.25in;"> o Least-squares fitting <span style="margin-left: 1.0in; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level2 lfo1; mso-pagination: none; text-autospace: none; text-indent: -.25in;"> o Bootstrap and jackknife error estimation
 * Numerical and Statistical Methods **<span style="font-size: 14.0pt; mso-bidi-font-family: Optima-Bold; mso-bidi-font-size: 12.0pt; mso-bidi-font-weight: bold;">