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We describe a learning process that uses one of the simplest examples, matrix-matrix multiplication, to illustrate issues that underlie parallel high-performance computing. It is accessible at multiple levels: simple enough to use early in a curriculum yet rich enough to benefit a more advanced software developer. A carefully designed and scaffolded set of exercises leads the learner from a naive implementation towards one that extracts parallelism at multiple levels, ranging from instruction level parallelism to multithreaded parallelism via OpenMP to distributed memory parallelism using MPI. The importance of effectively leveraging the memory hierarchy within and across nodes is exposed, as do the GotoBLAS and SUMMA algorithms. These materials will become part of a Massive Open Online Course (MOOC) to be offered in the future. 

In this paper, we describe a trilogy of Massive Open Online Courses (MOOCs) that together expose knowledge and skills of fundamental importance to HPC. Linear Algebra: Foundations to Frontiers (LAFF) covers topics found in an introductory undergraduate course on linear algebra. It links abstraction in mathematics to abstraction in programming, with many enrichments that connect to HPC. LAFF-On Programming for Correctness introduces how to systematically derive programs to be correct. Of importance to HPC is that this methodology yields families of algorithms so that the best one for a given situation can be chosen. Programming for HPC (working title) is in the design stage. We envision using a very simple example, matrix-matrix multiplication, to illustrate how to achieve performance on a single core, on multicore and many-core architectures, and on distributed memory computers. These materials lower barriers into HPC by presenting insights, supports, and challenges to novices and HPC experts while scaling access to the world.