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54th Annual ACM SIGCSE Technical Symposium on Computer Science Education (SIGCSE TS)

作者： Castle, Sarah D. Michigan State Univ E Lansing MI 48824 USA

ISBN: (纸本)9781450394314

The nebulous relationship between mathematics and computation in education has led to questions surrounding computational science students' experiences in mathematics courses. However, many of these conversations are framed in terms of students' misconceptions or their 'poor mathematical skills'. In contrast, I propose leveraging student's computational strengths as a pedagogical approach for creating relevant and engaging mathematics experiences. In order to build an understanding of the ways in which computation affects student's experience and understanding of mathematics, a framework designed to link student's computational experiences and attitudes by adding explicit linkage to these mathematical experiences was implemented. A series of Jupyter notebooks were developed which focused on introducing linear algebra through computing. This study followed computational science students as they worked through the modules in small groups across six weeks. They completed weekly reflections, and pre/post-study interviews. The theoretical framework was operationalized as an analytical framework to link student experience and attitudes. Results highlighted the shift in students' views of the nature of mathematics, their abilities, and the interplay between disciplines. The computational environment enabled students to naturally consider multiple solution paths, develop resilience, and enhanced their ability to explore mathematical concepts in a novel way. This was in contrast with students' initial views that framed mathematics as a set series of steps and formulas to follow. This study both provides a novel perspective in the discourse surrounding research on computational students' experiences in mathematics and highlights the pedagogical power of computing as a novel environment for learning mathematics.

关键词： computational mathematics Jupyter Notebooks Resilience Coding Linear Algebra

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computational methods for rough classification and discovery

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JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 1998年第5期49卷 403-414页

作者： Bell, DA Guan, JW Univ Ulster Sch Informat & Software Engn Jordanstown BT37 0QB North Ireland

Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. To apply the theory, it is important to associate it with efficient and effective computational methods. With a little adjustment, a relation can be used to represent a decision fable for use in decision making. By using this kind of table, rough set theory can be applied successfully to rough classification and knowledge discovery. We present computational methods for using rough sets to identify classes in datasets, finding dependencies in relations, and discovering rules which are hidden in databases. The methods are illustrated with a running example from a database of car test results.

关键词： Classification Computation Data Analysis Databases Evaluation Methods Numbers Set Theorycomputational Models computational mathematics

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computational science and HPC education for graduate students: Paving the way to exascale

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2018年第Part1期118卷 157-165页

作者： Antonov, A. Popova, N. Voevodin, V. I. Lomonosov Moscow State Univ Moscow Russia

The article discusses the experience of teaching supercomputer disciplines to students specializing in computational mathematics. Graduates specializing in this field become future developers and users of complex supercomputing applications and systems. The article presents the structure of a training program that has been implemented at the Faculty of computational mathematics and Cybernetics of Lomonosov Moscow State University. It focuses on the content of disciplines related to parallel computing with a detailed description of the structure and content of the course "Supercomputing Simulation and Technologies", which is offered as part of the Master's degree training program at the Faculty. The content of practical assignments supporting this discipline is discussed in detail, along with the results produced by the students who performed these practical assignments on Lomonosov and IBM Blue Gene/P supercomputers. The main contribution of the paper is twofold: we draw attention to the importance of study of a wide set of parallel algorithms properties and provide a practical methodology to reach this goal. (C) 2018 Elsevier Inc. All rights reserved.

关键词： HPC education Parallel computing Supercomputer computational mathematics Supercomputing simulation

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A computational framework to systematize uncertainty analysis in the sediment fingerprinting approach using least square methods

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computational & APPLIED mathematics 2024年第8期43卷 1-26页

作者： Buligon, Lidiane Buriol, Tiago Martinuzzi Minella, Jean Paolo Gomes Evrard, Olivier Univ Fed Santa Maria Dept Math Roraima Ave 1000 BR-97105900 Santa Maria RS Brazil Univ Fed Santa Maria Dept Soils Roraima Ave 1000 BR-97105900 Santa Maria RS Brazil Univ Paris Saclay CEA Saclay Lab Sci Climat & Environm LSCE F-91191 Gif Sur Yvette France

Simulating sediment transfer processes in catchments has contributed significantly to solving environmental problems due to its importance in the silting of rivers and reservoirs and for controlling the pollution of water bodies. Among the methods used to improve data collection and modelling, the "sediment fingerprinting approach" uses tracers reflecting the composition of eroded soils and sediments in multivariate statistical analyses and mathematical models for optimizing equation systems. Based on generalized least squares (GLS) method and Mahalanobis distance, this study sought to present a computational framework to solve over-determined systems applied to sediment tracing, systematize the uncertainty analysis and sample number optimization. Hence, this approach takes into account the influence of collinearity among the chemical variables that compose the tracer set to be evaluated by the presence of the variance-covariance matrix. A dataset from the Arvorezinha experimental catchment in southern Brazil was used to validate the modeling, and our findings confirmed the assumption of increased uncertainty as the number of target samples decreases in the sources or eroded sediment samples. Sharing the code files with the PySASF (Python package for Source Apportionment with Sediment Fingerprinting) contributes to improving the technique as it allows other researchers to systematically improve the definition of the number of samples required based on the uncertainty analysis.

关键词： computational mathematics Generalized least squares Sediment source identification Mahalanobis distance Confidence region PySASF Python package

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Semigroup congruences: computational techniques and theoretical applications

Semigroup congruences: computational techniques and theoreti...

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作者： Torpey, Michael University of St Andrews

学位级别：博士

computational semigroup theory is an area of research that is subject to growing interest. The development of semigroup algorithms allows for new theoretical results to be discovered, which in turn informs the creation of yet more algorithms. Groups have benefitted from this cycle since before the invention of electronic computers, and the popularity of computational group theory has resulted in a rich and detailed literature. computational semigroup theory is a less developed field, but recent work has resulted in a variety of algorithms, and some important pieces of software such as the Semigroups package for GAP. Congruences are an important part of semigroup theory. A semigroup’s congruences determine its homomorphic images in a manner analogous to a group’s normal subgroups. Prior to the work described here, there existed few practical algorithms for computing with semigroup congruences. However, a number of results about alternative representations for congruences, as well as existing algorithms that can be borrowed from group theory, make congruences a fertile area for improvement. In this thesis, we first consider computational techniques that can be applied to the study of congruences, and then present some results that have been produced or precipitated by applying these techniques to interesting examples. After some preliminary theory, we present a new parallel approach to computing with congruences specified by generating pairs. We then consider alternative ways of representing a congruence, using intermediate objects such as linked triples. We also present an algorithm for computing the entire congruence lattice of a finite semigroup. In the second part of the thesis, we classify the congruences of several monoids of bipartitions, as well as the principal factors of several monoids of partial transformations. Finally, we consider how many congruences a finite semigroup can have, and examine those on semigroups with up to seven elements.

关键词： Semigroups computational algebra computational mathematics Congruences Algorithms Diagram semigroups Bipartitions Bipartition semigroups Partition semigroups Motzkin monoid Finite semigroups Finitely presented semigroups Simple semigroups 0-simple semigroups Inverse semigroups

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computational (Numerical) Diameter in a Context of General Theory of a Recovery

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RUSSIAN mathematics 2019年第1期63卷 79-86页

作者： Temirgaliyev, N. Zhubanysheva, A. Zh. LN Gumilyov Eurasian Natl Univ Ul Satpaeva 2 Astana 010008 Kazakhstan

We discuss a C(N)D-statement, consisting of the known and elaborating in decades C(N)D-1 statement that can be and should be interpreted as quantitative statement of approximation theory and computational mathematics, which, in common with new prolongations of both C(N)D-2 and C(N)D-3, is suggested as a natural theoretical and computational scheme of further numerical analysis development.

关键词： computational (numerical) diameter (C(N)D) approximation theory in quantitative statement computational mathematics recovery from exact and inexact information limiting error new scheme of numerical analysis

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Supporting Education in Advanced Mathematical Analysis Problems by Symbolic computational Techniques Using Computer Algebra System 22nd

Supporting Education in Advanced Mathematical Analysis Probl...

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22nd Annual International Conference on computational Science (ICCS)

作者： Wojas, Wlodzimierz Krupa, Jan Warsaw Univ Life Sci SGGW Dept Appl Math Ul Nowoursynowska 159 PL-02776 Warsaw Poland

ISBN: (纸本)9783031087608;9783031087592

In this paper we present two didactic examples of the use of Mathematica's symbolic calculations in problems of mathematical analysis which we prepared for students of Warsaw University of Life Sciences. In Example 1 we solve the problem of convex optimization and next in Example 2 we calculate the complex integrals. We also describe a didactic experiment for students of the Informatics and Econometric Faculty of Warsaw University of Life Sciences.

关键词： Symbolic calculations computational mathematics Mathematical didactics CAS Convex optimization Complex integrals

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Insight Through Computing. A MatLab Introduction to computational Science and Engineering

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丛书名： Other Titles in Applied mathematics

2010年

作者： Charles F. Van Loan K.-Y. Daisy Fan

ISBN: (数字)9780898717648

ISBN: (纸本)9780898716917

This introduction to computer-based problem solving using the MATLAB environment is highly recommended for students wishing to learn the concepts and develop the programming skills that are fundamental to computational science and engineering (CSE). Through a “teaching by examples” approach, the authors pose strategically chosen problems to help first-time programmers learn these necessary concepts and skills. Their approach puts problem solving and algorithmic thinking first and syntactical details second.

• Each section formulates a problem and then introduces those new MATLAB language features that are necessary to solve it. The solution is followed by a “talking point” that concerns some related, larger issue associated with CSE.

• Collectively, the worked examples, talking points, and 300+ homework problems build intuition for the process of discretization and an appreciation for dimension, inexactitude, visualization, randomness, and complexity. This sets the stage for further coursework in CSE areas.

• The interplay between programming and mathematics throughout the text reinforces the student's ability to reason numerically and geometrically.

关键词： Programming Matlab computational science computational engineering computational mathematics

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MODIFIED DISCREPANCY PRINCIPLES WITH PERTURBED OPERATORS AND NOISY DATA

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Journal of computational mathematics 1996年第2期14卷 108-119页

作者： Chen, H Hou, ZY WUHAN UNIV DEPT MATHWUHAN 430072PEOPLES R CHINA FUDAN UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

We investigate a class of a posterior parameter choice for iterated Tikhonov regularization with perturbed operators and noisy data by using modified Arcangeli's method. The rate of convergence of regularization a... 详细信息

关键词： Ill posed problems computational mathematics Approximation Linear transformations

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INCOMPLETELY PARABOLIC PROBLEMS IN FLUID-DYNAMICS: 收藏
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引用; SIAM JOURNAL ON APPLIED mathematics 1978年第2期35卷 343-357页; 作者： GUSTAFSSON, B SUNDSTROM, A NATL DEF RES INST STOCKHOLMSWEDEN; Some partial differential equations encountered in physical applications are of incompletely parabolic type; the Navier–Stokes equations in fluid dynamics are a typical example. In this paper we analyze such systems;... 详细信息; Some partial differential equations encountered in physical applications are of incompletely parabolic type; the Navier–Stokes equations in fluid dynamics are a typical example. In this paper we analyze such systems; in particular we treat the mixed initial-boundary value problem. In many applications there is a small parameter $\varepsilon$ multiplying the coefficient for the highest derivative. The energy method is used to derive well-posed boundary conditions such that, when $ε$; 关键词： Boundary conditions Eigenvalues Coefficients Energy methods Cauchy problem Navier Stokes equation Constant coefficients computational mathematics; 来源：评论; 学校读者我要写书评

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