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Section 6 Schedule

Subsection 6.1 March 9 – March 15

March 11 🔗: 1.1 Polynomials and Affine Space
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1.2 Affine Varieties
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Subsection 6.2 March 16 – March 22

March 16 🔗: 1.3 Parameterizations of Affine Varieties
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1.4 Ideals
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March 18 🔗: 1.5 Polynomials of One Variable
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2.1 Introduction to Gröbner bases
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Subsection 6.3 March 23 – March 29

March 23 🔗: 2.2 Orderings on the Monomials in \(k[x_1, \ldots, x_n]\)
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2.3 A division Algorithm in \(k[x_1, \ldots, x_n]\)
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March 25 🔗: 2.4 Monomial Ideals and Dickson’s Lemma
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Subsection 6.4 March 30 – April 5

March 30 🔗: 2.5 The Hilbert Basis Theorem and Gröbner Bases
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April 01 🔗: 2.6 Properties of Gröbner Bases
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2.7 Buchberger’s Algorithm
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Subsection 6.5 April 6 – April 12

April 08 🔗: 2.8 First Applications of Gröbner Bases
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Subsection 6.6 April 13 – April 19

April 13 🔗: 2.9 Refinements of the Buchberger Criterion
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2.10 Improvements on Buchberger’s Algorithm
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April 15 🔗: Exam 1
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Subsection 6.7 April 20 – April 26

April 20 🔗: 3.1 The Elimination and the Extension Theorem
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April 22 🔗: 3.2 The Geometry of Elimination
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Subsection 6.8 April 27 – May 3

April 27 🔗: 3.3 Implicitization
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April 29 🔗: 3.4 Singular Points and Envelopes
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Subsection 6.9 May 4 – May 10

May 04 🔗: 3.5 Gröbner Bases and the Extension Theorem
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May 06 🔗: 3.6 Resultants and the Extension Theorem
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Subsection 6.10 May 11 – May 17

May 11 🔗: Exam 2
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May 13 🔗: 4.1 Hilbert’s Nullstellensatz
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Subsection 6.11 May 18 – May 24

May 18 🔗: 4.2 Radical Ideals and the Ideal-Variety Correspondence
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May 20 🔗: Final Exam
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Warning 6.1.

The instructor reserves the right to modify the schedule as needed.

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