| Language of Instruction |
French |
| Course Type |
Elective |
| Course Level |
Bachelor Degree |
| Course Instructor(s) |
Meral TOSUN
mtosun@gsu.edu.tr (Email)
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| Assistant |
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| Objective |
The purpose of this course is to learn about Groebner basis which is useful to solve some problems on algebraic varieties, especially for the solution of systems of equations, to understand how to use it in the proof of theorem extension.
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| Content |
Ring theory and fields (summary), Polynomial rings and affine space, Affine varieties, Parametrization, Ideals, One variable polynomials;
Monomial orders, Division algorithm, Monomial ideals and Dickson's lemma, Hilbert bases theorem, Groebner bases, Properties of Groebner bases, Buchbergers algorithm, Applicaitons of Groebner bases;
Elimination and Extension theorems, Resultants and the extension theorem.
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| Course Learning Outcomes |
To know how to calculate a Groebner base for an ideal by using the algorithm of Buchberger
To know how to use the Groebner bases to solve the appearence problem for an ideal
To be able to use the Groebner bases in the theory of elimination to solve the system of equations
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| Teaching and Learning Methods |
Lecture, discussion, problem solving
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| References |
Ideals, Varieties and Algorithms, D. Cox, J. Little, D. O’Shea.
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