The importance of scientific computing in simulation and data driven science and engineering. The goal of scientific computing as an itinerary across models (mathematical, numerical, discrete, arithmetic, computational). Loss of information effects. Code profiling, performance evaluation criteria and good practices. Benchmarking and benchmarks. The central role of matrix computations in HPC. Computational models and the communication-computation tradeoffs in algorithm design for simple hierarchical memory systems. Computational kernels and the BLAS hierarchy. Basic principles of code design and compilation techniques for HPC. Matrix multiplication, from BLAS-1 to BLAS-3 and superfast methods. Arithmetic model: Review of floating-point arithmetic, backward error analysis, problem conditioning. Compensated summation methods. Block LU and BLAS-3 implementations of LU and QR. From LAPACK to MATLAB. Iterative refinement. Sparse and structured sparse matrix computations. Introduction to projection methods for numerical linear algebra and the Arnoldi algorithm. Discrete model: Simulations via the numerical solution of differential equations: The 2 point boundary value problem and initial value problems. Ranking in large networks and the example of PageRank