Math 361, Spring 2019, Assignment 7
From cartan.math.umb.edu
Read:
- Section 23.
Carefully define the following terms, then give one example and one non-example of each:
- f%g (the remainder when f is divided by g).
- Root (of a polynomial).
- Ideal.
- ⟨a⟩ (the principal ideal generated by a).
Carefully state the following theorems (you need not prove them):
- Theorem concerning polynomial long division.
- Factor theorem.
- Theorem concerning factorization of quadratic and cubic polynomials.
- Eisenstein's criterion.
- Criterion for a principal ideal to be contained in an arbitrary ideal.
- Criterion for a principal ideal to be contained in another principal ideal.
- Criterion for two principal ideals to be equal.
Carefully describe the following algorithms:
- Sieve of Eratosthenes.
Solve the following problems:
- Section 23, problems 1, 3, 9, 11, 12, 13, 14, 18, 19, 20, 21, and 29.