Traditional engineering instruction is deductive, beginning with theories and progressing to the applications of those theories Alternative teaching approaches are more inductive Topics are introduced by presenting specific observations, case studies or problems, and theories are taught or the students are helped to discover them only after the need to know them has been established This study reviews several of the most commonly used inductive teaching methods, including inquiry learning, problem-based learning, project-based learning, case-based teaching, discovery learning, and just-in-time teaching The paper defines each method, highlights commonalities and specific differences, and reviews research on the effectiveness of the methods While the strength of the evidence varies from one method to another, inductive methods are consistently found to be at least equal to, and in general more effective than, traditional deductive methods for achieving a broad range of learning outcomes

Inductive Teaching and Learning Methods: Definitions, Comparisons, and Research Bases

by J. Biggs and C. Tang, Maidenhead, England,
Open University Press, 2007, 360 pp., £29.99, ISBN-13: 978-0-335-22126-4

Teaching for quality learning at university

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle extra irregularity from three aspects: (1) the number of the nonzero entries in the result sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the result sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input matrices. Recent work on GPU SpGEMM has demonstrated rather good both time and space complexity, but works best for fairly regular matrices. In this work we present a GPU SpGEMM algorithm that particularly focuses on the above three problems. Memory pre-allocation for the result matrix is organized by a hybrid method that saves a large amount of global memory space and efficiently utilizes the very limited on-chip scratchpad memory. Parallel insert operations of the nonzero entries are implemented through the GPU merge path algorithm that is experimentally found to be the fastest GPU merge approach. Load balancing builds on the number of the necessary arithmetic operations on the nonzero entries and is guaranteed in all stages. Compared with the state-of-the-art GPU SpGEMM methods in the CUSPARSE library and the CUSP library and the latest CPU SpGEMM method in the Intel Math Kernel Library, our approach delivers excellent absolute performance and relative speedups on a benchmark suite composed of 23 matrices with diverse sparsity structures.

/pdf/an-efficient-gpu-general-sparse-matrix-matrix-multiplication-58sndn0by0.pdf

An Efficient GPU General Sparse Matrix-Matrix Multiplication for Irregular Data

Python has become the de facto language for scientific computing. Programming in Python is highly productive, mainly due to its rich science-oriented software ecosystem built around the NumPy module. As a result, the demand for Python support in High Performance Computing (HPC) has skyrocketed. However, the Python language itself does not necessarily offer high performance. In this work, we present a workflow that retains Python's high productivity while achieving portable performance across different architectures. The workflow's key features are HPC-oriented language extensions and a set of automatic optimizations powered by a data-centric intermediate representation. We show performance results and scaling across CPU, GPU, FPGA, and the Piz Daint supercomputer (up to 23,328 cores), with 2.47x and 3.75x speedups over previous-best solutions, first-ever Xilinx and Intel FPGA results of annotated Python, and up to 93.16% scaling efficiency on 512 nodes.

Productivity, Portability, Performance: Data-Centric Python

A framework for general sparse matrix-matrix multiplication on GPUs and heterogeneous processors

Bohrium: Unmodified NumPy Code on CPU, GPU, and Cluster

In this paper we introduce, Bohrium, a runtime-system for mapping vector operations onto a number of different hardware platforms, from simple multi-core systems to clusters and GPU enabled systems. In order to make efficient choices Bohrium is implemented as a virtual machine that makes runtime decisions, rather than a statically compiled library, which is the more common approach. In principle, Bohrium can be used for any programming language but for now, the supported languages are limited to Python, C++ and the. Net framework, e.g. C# and F#. The primary success criteria are to maintain a complete abstraction from low-level details and to provide efficient code execution across different, current and future, processors. We evaluate the presented design through a setup that targets a multi-core CPU, an eight-node Cluster, and a GPU, all preliminary prototypes. The evaluation includes three well-known benchmark applications, Black Sholes, Shallow Water, and N-body, implemented in C++, Python, and C# respectively.

Bohrium: A Virtual Machine Approach to Portable Parallelism

This paper describes how a concept-based approach to teaching was used to update how concurrent and distributed systems were taught at the University of Copenhagen. This approach focuses on discussion to drive student engagement whilst fostering a deeper understanding of the presented topics compared to more traditional displays of crude facts. The course is split into three sections: local concurrency, networked concurrency, and concurrency in hardware. This allows for an easier student journey through the course, as they are introduced to all core concepts in the first section, then have them reinforced in greater detail in the subsequent sections. Finally, the experience gained in updating this course is presented so others attempting to do similar may learn from it.

Teaching Concurrent and Distributed Programming With Concepts Over Mathematical Proofs

As multicore processors are now the standard for high performance machines, scientists must develop complex programs to fully utilize the processing power. In this article we present NumCIL, a new framework for expressing scientific and financial algorithms. By using n-dimensional arrays, a scientist can write sequential code without knowledge of parallel constructs. The library is a CIL library and can thus be used from languages as diverse as IronPython, F# and C#. As the ndimensional arrays are compatible with numpy ndarrays, it is possible to run some existing numpy programs unmodified on NumCIL. The NumCIL library can run entirely in CIL or offload computation to an external library. We compare NumCIL to numpy and show that the implementation is able to perform on par with numpy for a variety of problems taken from imaging, physics and financial computing domains.

http://www.aicit.org/JNIT/ppl/JNIT113PPL.pdf

NumCIL: Numeric Operations in the Common Intermediate Language

The CELL-BE processor provides high performance and has been shown to reach a performance close to the theoretical peak, however, the high performance comes at the price of a quite complex programming model. Central to the complexity of the CELL-BE programming model is the need to move data in and out of non-coherent local storage blocks for each special processor element. In this paper we present a software library, namely the Distributed Shared Memory for the Cell Broadband Engine (DSMCBE). By using techniques known from distributed shared memory DSMCBE allows programmers to program the CELL-BE with relative ease and in addition scale their applications to use multiple CELL-BE processors in a network. Performance experiments show that a quite high performance can be obtained with DSMCBE even in a cluster environment.

Kenneth Skovhede

Papers

Bohrium: Unmodified NumPy Code on CPU, GPU, and Cluster

Bohrium: A Virtual Machine Approach to Portable Parallelism

Teaching Concurrent and Distributed Programming With Concepts Over Mathematical Proofs

NumCIL: Numeric Operations in the Common Intermediate Language

Distributed Shared Memory for the Cell Broadband Engine (DSMCBE)