Computerized proof techniques for undergraduates |
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Authors: | Christopher J Smith Aklilu Zeleke |
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Institution: | 1. Department of Mathematics , Grand Valley State University , Allendale , MI 49401 , USA;2. Department of Statistics and Probability , Lyman Briggs College, Michigan State University , East Lansing , MI 48824 , USA |
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Abstract: | The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf–Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete mathematics. We demonstrate by examples how one can use these computerized proof techniques to raise students' interests in the discovery and proof of mathematical identities and enhance their problem-solving skills. |
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Keywords: | Gosper's algorithm Zeilberger's algorithm combinatorial identities recurrence equations Wilf–Zeilberger |
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