STATISTICS
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Probability: frequentist and Bayesian approaches
Classic frequentist tests
Bayesian slam-dunks (e.g. Occam's razor)
Binomial, Poisson, Gaussian distributions
Monte-Carlo basics
Least squares and fitting data
Entropy and information
COMPUTING
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How to write a C program
User interface:
information encapsulation and function arguments
GUIs
I/O:
boiler plate
FITS format
Displaying data
Fitting:
orthogonal functions
interpolation and extrapolation
splines
function minimization
Linear algebra:
matrix inversion
solving equations
Searching and sorting:
sort routines
medians
Differential equations:
ODE, PDE (Laplace)
Integration:
1-D, n-D
Fourier analysis:
Random numbers and Monte Carlo simulations:
POSSIBLE TEXTS
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Principles of Data Analysis cheap to free
by Prasenjit Saha
subtle but clear
Statistics: A Bayesian Perspective $98.95
by Donald A. Berry
elemenary, very clear
Bayesian Data Analysis $60.00
by Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin
amazon popular, good book
Bayesian Theory (Wiley Series in Probability and Statistics) $78.50
by Jose M. Bernardo, Adrian F. M. Smith
"new bible" to be followed by Bayesian Computation and Bayesian Methods
Numerical Recipes
by Press Flannery Teukolsky Vetterling
pretty good applied math