“正难则反”策略在高等代数中的应用

Application of the “If the Direct Approach is Difficult, Try the Opposite” Strategy in Advanced Algebra

摘要: 在众多复杂的高等代数习题中，有许多问题往往用通常的思维角度思考难以解决，此时灵活地运用解题策略中的正难则反策略中反向思考的解题方法能够使解题过程较之正面解决更为简便，培养灵活变通的解题和推理能力，发展反向思考的数学思维逻辑。

Abstract: Among the numerous complex exercises in Higher Algebra, many problems are often difficult to solve from a conventional way of thinking. In such cases, flexibly applying the problem-solving method of reverse thinking under the strategy of “turning to the opposite when direct approach is difficult” can make the problem-solving process more straightforward compared with the direct approach. This not only cultivates flexible problem-solving and reasoning abilities but also develops the mathematical thinking logic of reverse thinking.