Math 480, Spring 2014, Assignment 5

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

1. Complete symmetric polynomial.
2. Power sum.
3. Homogeneous polynomial.
4. Finite matrix group.
5. Invariant polynomial (for a given finite matrix group.)
6. Reynolds operator.

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

1. Noether's degree bound.

Solve the following problems:

1. Section 7.2, problems 3 and 14(a-c).
2. Section 7.3, problems 3 and 7.

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