Difficult: For me, the hardest part of this section was finding the congruence classes. Just like with polynomials, finding congruence classes is very difficult. I have a hard time deciding how many congruence classes there are, and what they even are! I think however, that this section is more difficult than polynomials to determine the congruence classes. I don't quite understand the notation well enough to be able to find what the congruence classes are. Also, I don't really get when a (left) coset is either. How is this different than a congruence class, or is it the same?
Connections: I like that congruence is similar to the congruence that we have been dealing with in the polynomials, or in the integers. I like consistency in definitions, and so I like that this definition is very familiar. It is easier for me to remember when it follows the same pattern as the other kinds of congruence. I also like that theorems 6.4 and 6.5 are similar to the theorems in the other sections about how congruence is reflexive, symmetric, and transitive and that addition and multiplication can follow in congruence. These definitions are definitely something I have seem before, so its nice to have something familiar attached to the new ideas of ideals.
No comments:
Post a Comment