On Monday, January 7, 2013 4:46:37 AM UTC, Dan Christensen wrote: > I am working on some introductory notes for group theory. What difficulties are typically encountered by math or science undergrads in an introductory course on abstract algebra? > Difficulties with the basic concepts of abstraction and applying axioms, insisting on thinking merely with intuition. For example, some wrongly deny that for a group G, the subgroup generated by the empty set is the trivial subgroup. They argue (falsely) "Obviously, the empty set can't generate a group." Common questions like "Is the identity element in any group always equal to 1?" indicate a difficulty with thinking at the right level of abstraction. Many texts help with the necessary types of abstract thinking.