3rd Midterm Exam Preparation

Important Topics and Theorems:
I think that the most important theorems, definitions and examples of the sections that we have covered are 1. the definition of a group, 2. the order of an element/group, 3. Theorem 7.8, 4. Theorem 7.10, 5. definition and characteristics of cyclic groups, 6. Theorem 7.18, 7. Theorem 7.19, 8. Theorem 7.25, 9. Lagrange's Theorem, 10. the definition of a normal subgroup, 11. Theorem 7.34, 12. Theorem 7.36, 13. Theorem 7.37, and 14. Theorems 7.42, 7.43, and 7.44. These theorems cover the main concepts of the chapter.

Better Understanding:
I think that I need help especially with the latter part of this chapter. I need help understanding what congruence actually means in groups. I find myself confused often and always have to go back and review the definition because I can't picture it in my head. I also think it would be helpful to go over quotient groups and what they actually represent. It would be nice to do homework problems that we didn't already do in sections 7.5 and 7.8.