关键词: 群论, 可约表示, 不可约表示, 口诀教学

Abstract: Group theory, as a foundational mathematical tool in modern chemistry, is extensively employed in the study of molecular symmetry, molecular orbital theory, and infrared and Raman spectroscopy. Due to its inherently abstract nature, the instruction of group representation theory poses considerable pedagogical challenges. In particular, the principles and computational procedures involved in the reduction of reducible representations are notoriously difficult to grasp, representing a major hurdle in the curriculum. To address this issue, this paper introduces a “Bone-and-Flesh Mnemonic” teaching method, which establishes a connection between abstract mathematical concepts and intuitive physical pictures, elucidates the underlying significance of characters, and transforms complex reduction operations into clear, accessible reasoning processes. This approach encourages students to move beyond rote formula manipulation and develop a deeper understanding of the essence of symmetry. Validation through representative molecular examples demonstrates that this method effectively streamlines the cognitive process, enhances computational accuracy, alleviates students’ apprehension toward learning, and improves overall classroom efficiency. Furthermore, it offers a practical and valuable reference for pedagogical innovation in group theory courses for chemistry majors.

Key words: Group theory, Reducible representation, Irreducible representation, Mnemonic rhyme teaching