Information provided by the grader - thanks! ------------------------------------------------------------------------ I've decided to grade each problem out of 4 points, for a total of 24 points per assignment. HW1. In general a number of people wrote statements as if they were obvious when they weren't. It's important to make clear why and how you are doing something. A good measure for how well-written an argument is if anyone else in the class can read what you wrote and understand it. Specifics: In Exercise 21 of 1.1, a number of people knew what the argument was, but didn't explain why the claims they were making were true. For example, given c in C there is a b in B so that g(b)=c. How do you know this is true? Because g is surjective, but you need to say that. It may seem like a minor point, but once you get into the habit of leaving stuff out it makes arguments hard to follow. This problem was particularly bad in Exercise 6 of 1.3, where plenty of people found good sets, and even wrote down a bijective function, but then never explained why the function they wrote was in fact a bijection. HW6. A number of students had trouble with the first problem: 4.1 #10b. It seems like a number of students don't fully understand the definition of limit, or if they do they can't apply it properly. The key thing to keep in mind is that the choice of delta is based on epsilon. Basically, the bound given by epsilon on the function has to be matched by the bound delta for the variable. Look at figure 4.1.1 and the examples in 4.1.7, especially the ones where they need to take an inf for delta; there's a reason they have to take a minimum. HW7. Also, for what it is worth, a lot of students had trouble with problem C1 from HW7.