Math 380, Spring 2018, Assignment 12

"When I think of Euclid even now, I have to wipe my sweaty brow."

- C. M. Bellman

Read:

1. Section 3.2.
2. Section 3.3.

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

1. Extension (of a partial solution to a total solution).

Carefully state the following theorems (you do not need to prove them):

1. Extension theorem (algebraic version).
2. Extension theorem (geometric version).
3. Closure theorem.
4. Rational parametrization theorem.

Note: In all of the above theorems, check the book carefully for the correct hypotheses. In class I may have forgotten to require that $\mathsf{k}$ be algebraically closed. This hypothesis is definitely needed, as you will see in one of the problems below.

Solve the following problems:

1. Section 3.2, problem 4.
2. Section 3.3, problems 6 and 9.

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