Math 380, Spring 2018, Assignment 7

Do not imagine that mathematics is hard and crabbed and repulsive to commmon sense. It is merely the etherealization of common sense.

- Lord Kelvin

Carefully define the following terms, then give one example and one non-example of each:

1. Monomial ideal.

Carefully describe the following algorithms:

1. Algorithm to decide whether $f\in\left\langle m_1,\dots,m_s\right\rangle$ when $m_1,\dots,m_s$ are monomials.

Solve the following problems:

1. Section 2.4, problems 3, 4, and 8.

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