Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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A Study on Teaching of Convolution in Engineering Mathematics and Artificial Intelligence

인공지능에 활용되는 공학수학 합성곱(convolution) 교수·학습자료 연구

  • Lee, Sang-Gu (Department of Mathematics, Sungkyunkwan University) ;
  • Nam, Yun (Institute of Basic Science, Sungkyunkwan University) ;
  • Lee, Jae Hwa (Research Institute of Basic Sciences, Sungkyunkwan University) ;
  • Kim, Eung-Ki (Department of Mathematics, Sungkyunkwan University)
  • Received : 2023.04.17
  • Accepted : 2023.06.07
  • Published : 2023.06.30
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Abstract

In mathematics, the concept of convolution is widely used. The convolution operation is required for understanding computer vision and deep learning in artificial intelligence. Therefore, it is vital for this concept to be explained in college mathematics education. In this paper, we present our new teaching and learning materials on convolution available for engineering mathematics. We provide the knowledge and applications on convolution with Python-based code, and introduce Convolutional Neural Network (CNN) used for image classification as an example. These materials can be utilized in class for the teaching of convolution and help students have a good understanding of the related knowledge in artificial intelligence.

합성곱(convolution)은 인공지능(artificial intelligence)에서 컴퓨터 비전(computer vision), 심층학습(deep learning) 등의 분야를 이해하고 응용하려면 알아야 하는 중요한 수학적 연산이다. 그러나 현재의 공학수학 교과과정의 합성곱 내용은 독립적인 주제가 아니라 단편적으로 다루어지고 있어서 그 의미를 충분히 전달하지 못하고 있다. 이에 본 논문에서는 공학수학에서 인공지능 교육과 연계할 수 있도록 개발한 합성곱 교수·학습 자료를 제시한다. 먼저 기존 공학과 인공지능 기술의 통합적 관점에서 합성곱에 대한 배경지식과 응용 사례를 정리하고, 코딩을 이용한 교육이 가능하도록 파이썬(Python)/SageMath 코드를 개발하여 제공한다. 또한 합성곱 지식이 인공지능에서 어떻게 활용되는지 보여주는 구체적인 예시로, 이미지 분류에 사용되는 합성곱신경망(Convolutional Neural Network, CNN)을 개발된 코드와 함께 제공한다. 본 교수·학습자료는 합성곱 개념을 쉽고 효과적으로 교육할 수 있도록 공학수학의 보충 자료로 활용가능하며, 학습자는 코딩을 통해 합성곱을 배우고 본인의 전공과 관련된 인공지능 기술을 학습하는 데 이를 이용할 수 있다.

Keywords

Acknowledgement

이 논문은 정부(과학기술정보통신부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구임(No.2021R1F1A1046714).

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