I just finished a Statistics M.S. at Stanford. I’m actually surprised that I could have gone through high school and college without having taken statistics. I would place statistics far before calculus in terms of importance for daily life.
Some of the good books I’ve come across are:
- Mathematical Statistics and Data Analysis, by John Rice. This book is probably the best all purpose statistics reference, covering from basic probability theory to limit theorems, parameter estimation, tests and some Bayesian inference.
- The Elements of Statistical Learning, by Trevor Hastie, Robert Tibshirani, and Jerome Friedman. This is a good book for doing more advanced computational statistics. It is available as a pdf here: http://www-stat.stanford.edu/~tibs/ElemStatLearn/.
- Monte Carlo Strategies for Scientific Computing, by Jun Liu.
- Pattern Recognition and Machine Learning, by Christopher M. Bishop.
Classes with lecture notes or readings online:
- STAT 345, Computational Algorithms for Statistical Genetics, taught by Hua Tang and Nancy Zhang
- CS 229, Machine Learning, taught by Andrew Ng
- BMI 214, Representations and Algorithms for Computational Molecular Biology, taught by Russ Altman
- STAT 315c, Learning from Matrix Valued Data, taught by Art Owen