Math 361, Spring 2013, Assignment 5
From cartan.math.umb.edu
The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.
- - Saint Augustine
Carefully define the following terms, then give one example and one non-example of each:[edit]
- Vector space (over a field \(F\)).
- Span (of a set of vectors in some vector space over \(F\)).
- Linearly independent (over \(F\)).
- Basis.
- Dimension.
- Finite extension.
- Degree (of a field extension).
- Algebraically closed field.
Carefully state the following theorems:[edit]
- Dimension formula (Theorem 31.4 in the text).
- Fundamental theorem of algebra.
Do the following problems:[edit]
- Section 30, problems 5, 7, and 9.
- Section 31, problems 1, 3, 5, 7, 9, and 19.
