Section 7.1, second part

Difficult: At first, it was hard for me to accept that any movement of a square would result in one of the eight permutations. Then, I realized that the authors were quite specific when describing what the result of the movement had to be. I now understand that the square has to be in one of eight positions after doing a permutation on it. Similarly, other examples in the text were difficult to grasp at first, but after thinking about them further, I was able to understand how they qualified to be groups.

Reflective: I think that the concept of a group is interesting! We can even classify groups in terms of symmetries of shapes. I can see how these ideas are applied outside of "pure mathematics." I wonder, though--how can knowing about groups help us prove things in the future? I just want to know how group theory fits into the big mathematical picture.