For this thesis, I explore one aspect of commutative ring theory through the explication of the Hilbert Basis Theorem. This includes: (1) clear definitions of all essential terms, (2) a comprehensive self-contained proof of the theorem, (3) an overview of the importance of the theorem, and (4) an example of one application of the theorem using the method of Gröbner bases.
There are fundamental concepts and skills that students must learn throughout their K-16 education to eventually understand advanced mathematics, like the Hilbert Basis Theorem. Misconceptions, particularly of advanced algebra and proof, prevent students from understanding advanced mathematics deeply, which need to be carefully identified and addressed in the K-16 mathematic curriculum. I analyze this body of research, explain its importance to our understanding of how to prepare students for advanced work in mathematics, and provide suggestions for future work in this area.
|School:||California State University, Long Beach|
|School Location:||United States -- California|
|Source:||MAI 47/05M, Masters Abstracts International|
|Subjects:||Mathematics education, Mathematics|
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