W, an undergraduate math major, was having trouble in the algebra course she was taking. In desperation she asked a professor she knew, Robert Gunning, what she should do. He told her to contact me, because I was an algebraist. Plenty of male grad students were algebraists; I don't think it was a coincidence that Gunning sent her to one of the few female grad students. W was the only female student in the algebra class.
The course was supposed to cover the basics of group theory. I asked W some questions to try to figure out how much she knew. She floundered. So I asked her to give me an example of a group. She struggled, but eventually I guessed she was trying to give an infinite cyclic group. I asked for an example of a finite group. She was stumped. I asked what examples of finite groups had been given in class. W claimed there had been none. I found her claim to be highly implausible.
W had another implausible claim. She said that the course skipped over the basics and instead taught more advanced material, since the other students had already learned algebra through various programs such as summer math camps.
I found a copy of Herstein's "Topics in Algebra", and I gave her a list of problems to solve before we would meet again the next week.
At tea a few days later I ran into Professor B, who taught the algebra course. I casually enquired about the course. One question I asked was "What examples of groups did you give?" He replied "None. The students should be smart enough to come up with examples on their own." He volunteered that since almost all the students knew the material already from summer math camps and the like, he didn't see a point in teaching them things they already knew, so he assumed the basics and started with more challenging material. He wasn't concerned about the one or two students who hadn't seen the basics.
It was very late in the semester. While it might have been theoretically possible for W to learn the material on her own and catch up to her classmates, it would have been a Herculean task. She did try.
Sensibly, she changed her major to statistics.