8.1, Due March 18

Difficult: How you can have something modulo a subgroup.

Interesting:  The parallel of congruence with integers and rings to groups.

7.5, Due March 16

Difficult: I don't understand how this idea of cycles connect to what we have been doing.  Like why is it important?

Interesting: Every transposition is it's own inverse.

7.3, Due March 11

Difficult: There is so much notation that was used one way in earlier math classes and I feel like in this class we are using it in a completely different way.

Interesting: If something is a subset of a group then it is a subgroup if that group.

7.2, Due March 9

Difficult: So just to be clear ab doesn't mean multiplication we are just being lazy and not writing the *? So is a^2=aa, would that be multiplication or is that still what ever operation we are performing on the group? Also this is from the previous section but is order the number of element in a group or is it something else?

Interesting: It's interesting that an element can have order.

7.1, Due March 7

Difficult: In the third edition book what is the point of having a 7.1 and a 7.1 A.  They were essentially the same except 7.1 had theorems and 7.1 A went into more depth on the examples.  So some of the examples in 7.1 were hard to understand but looking at 7.1 A cleared things up.

Interesting: It's interesting that if you take the full ring of Z, R, Q, etc that it is not a group under multiplication but is under addition.  It's just interesting that when you change the operation it is no longer a group.

7.1, Due March 4

Difficult: I'm not quite understanding how example 5 is a representation of a group.  Is it just each rotation represents an element of a group? The *, can that be any operation of your choosing or is it always the composition?

Interesting: It is nice that a group is defined by one operation.

Midterm 2, Due March 2

Most important: Ideal, irreducible/reducible polynomials, showing that polynomials are fields, integral domains, or rings, First Isomorphism Theorem for rings.

Questions expected: Definitions, examples, state and prove a theorem.

Need to work on:  I am very unfamiliar with all of the theorems. There is so much to know and it's not easy stuff to just memorize.  I am not good at proving things.  I just don't know where everything comes from.