The only required textbook for the course is Numerical Recipes: The Art of Scientific Computing, Third Edition, ISBN 0521880688. Students in the course can access the electronic version for free here. You can optionally buy the hardcopy book at Amazon.com or elsewhere.
Although this don't cover exactly the same material as the course, it has a lot of overlap with our topics and is a good book to own. Although the applications are from bioinformatics, the coverage is generally relevant to other fields.
Ewens and Grant, Statistical Methods in Bioinformatics, Second Edition (Springer 2005). Amazon.com link
Givens and Hoeting, Computational Statistics (Wiley, 2005). A somewhat different set of topics from this course, and thus a useful adjunct.
Marin and Robert, Bayesian Core: A Practical Approach to Computational Bayesian Statistics (Springer, 2007). Yet another selection of topics. Somewhat more of a statistics text.
Wasserman, All of Statistics: A Concise Course in Statistical Inference (Springer, 2004). Nice reference, especially for non-statisticians, on a wide variety of standard results in statistics. Theorems are precisely stated even when the proofs are (generally) omitted.
Durbin, Eddy, Krogh, and Mitchison, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids (Cambridge U.P., 1999). The classic book on hidden Markov models as applied to sequence analysis.
Gusfield, Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology (Cambridge U.P., 1997). Classic book on fast string search algorithms in biology. Recommended for computer scientists.
Several students who haven't had a previous probability and statistics course have asked for references to fairly elementary texts that define basic concepts (that is, for consumers of statistics, not for mathematicians). Two such are:
Devore, Probability and Statistics for Engineering and the Sciences (Duxbury, various editions)
Montgomery and Runger, Applied Statistics and Probability for Engineers (Wiley, various editions)