MTH 355
Homework 3 Notes:
*For the worksheet, some students did not finish the proof by stating how they had proved not even sum => not same parity
*Similarly, with problem 6, some students only proved one way thereby not proving iff.
*The last common problem is that many students in 11 would by algebra pull out (m+n) and then they would divide both sides by this. However, we weren't guaranteed m+n =/= 0 so I docked a point for this. Not certain if students really recognized that.
Homework 4 Notes:
*Probably the most common mistake was students not stating anything regarding assumptions. That is, they would do the anchor case and then just jump straight into n+1 as though it was true. I docked a point to reinforce that until the end of the proof, these being equal is still an assumption reliant on the function being true. In other words, I simply looked for something along the lines of "by assuming true for n, we consider n+1".
*One main reason multiple students lost points was because they only did 1 question in 2(a)-(f).
*Some students also were dropping terms in the series during the anchor step. For example, in part (g) where the student proves 1/0!+1/1!+1/2!+...+1/n! < 3- (stuff), the student would check n=2 but then would only show 1/2! < 3 - (stuff) without doing a sum.
*Some students were just adding (n+1) to both sides rather than actually plugging this in for the value of n.
*The last common mistake was students not looking at the domain of the series. Specifically for 2(g), we are told n>1 but some students still used either n=0 or n=1 for the anchor step.
*Most other points were lost simply due to algebra mistakes.
Homework5 Notes:
*The first is the difference between combination and permutation. In problem 7(b), many students felt the password where letters are not repeated was 26 Choose 6 without realizing that order matters.
*Another reoccurringerror was for the same problem about 5-8 students dropped the ten's place. That is, for part (a) finding the number of different passwords they did 6^6 instead of 26^6. Similarly, for (b) they did 6!/0! instead of 26!/20!. Not really sure what caused this but it was significant enough to mention.
*The most common error (probably affecting about +25% of students) was misunderstanding 8(b) from 4.2. Many students mistakenly thought the answer was 36^6, presumably misunderstanding that this would not dictate 3 letters and 3 numbers.