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This paper presents a new mathematics elective for an undergraduate Computational Science program. Algebraic Geometry is a theoretical area of mathematics with a long history, often highlighted by extreme abstraction and difficulty. This changed in the 1960s when Bruno Buchberger created an algorithm that allowed Algebraic Geometers to compute examples for many of their theoretical results and gave birth to a subfield called Computational Algebraic Geometry (CAG). Moreover, it introduced many rich applications to biology, chemistry, economics, robotics, recreational mathematics, etc. Computational Algebraic Geometry is usually taught at the graduate or advanced undergraduate level. However, with a bit of work, it can be an extremely valuable course to anyone with decent algebra skills. This manuscript describes Math 380: Computational Algebraic Geometry and shows the usefulness of the class as an elective to a Computational Science program. In addition, a module that gives students a high-level introduction to this valuable computational method was constructed for our Introductory Computational Science course.
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