Part I. Machines and Computation: 1. Introduction - the nature of high performance computation; 2. Theoretical considerations - complexity; 3. Machine implementations; Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra; 5. Direct methods for linear systems and LU decomposition; 6. Direct methods for systems with special structure; 7. Error analysis and QR decomposition; 8. Iterative methods for linear systems; 9. Finding eigenvalues and eigenvectors; Part III. Monte Carlo Methods: 10. Monte Carlo simulation; 11. Monte Carlo optimization; Appendix: programming examples.