Intelligent software has been very useful in education, especially those support studying knowledge. The knowledge of Discrete Mathematics and Graph Theory are essential in STEM education. There have been many computer programs that support students to study in the above knowledge domains such as Wolfram Alpha, Maple, etc. However, they do not satisfy students' requirements. This article will present knowledge representation methods, reasoning and querying techniques to design and to implement an intelligent software for effectively studying Discrete Mathematics and Graph Theory. The system consists of two subsystems for knowledge retrieval, visualization of methods or algorithms, and for solving problems. It can be easily used for studying the knowledge as well as for solving problems.
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