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Teaching computer programming Using mathematics: Examples from Middle-School and Graduate School

SN computer Science 2024年第8期5卷 1-12页

作者： Pattichis, Marios S. Lee, Hakeoung Hannah Celedón-Pattichis, Sylvia LópezLeiva, Carlos Department of Electrical and Computer Engineering University of New Mexico 211 Terrace Street NE ECE Building Albuquerque 87131-0001 NM United States Department of Curriculum and Instruction The University of Texas at Austin 1912 Speedway Stop D5700 Austin 78712 TX United States Department of Language Literacy and Sociocultural Studies (LLSS) University of New Mexico MSC05 3040 1 Albuquerque 87131-0001 NM United States

Our goal is to provide integrated lessons where computer programming concepts are introduced based on mathematics. We consider the development of lessons that would be interesting to our students. At the middle school level, digital video generation is used to introduce coding. At the graduate level, we look at the convergence of machine learning models during training. We introduce middle-school students to computer programming through the use of variables, linear equations, and basic algebraic expressions. We motivate students to create digital images using NumPy arrays by experimenting with number representations and coordinate systems. The students create digital videos by building their video characters and moving them around from frame to frame. At the graduate level, we describe how Real Analysis can be applied in Optimization Theory. The students saw and appreciated the connections between mathematics and computer programming. In the graduate course, the students appreciated the rigorous results on the convergence of neural network models. The approach also produced conditions for guaranteeing that the neural network models are uniformly continuous. We have found that the students strongly appreciated the integration of mathematical concepts into basic and advanced coding courses. © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2024.

关键词： Machine learning algorithms mathematics and computer programming Teaching computer science Uniformly continuous neural network models

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