I completed my assignment last Friday  with a few hours to spare. I don't think I will do as well on this one as I did on the first one, because there were a couple of points I felt uncertain about. I don't want to look at the sample solution quite yet, just out of nervousness (I'll have to look at it before the test, though), but I'm wondering now whether I did the upper/lower bound section correctly. I followed the general format of what we did in lecture, but I'm still worried about it.

Consistently, the number one issue I have with proofs is manipulating algebra, particularly in cases where there is a very simple mathematical rule that leads to a clean solution, that I am not aware of. This popped up again in the assignment when we were adding together the two instances of the closed form for the Fibonacci, one to the power of n and the other to the power of (n - 1). I destroyed...many pages in my notebook trying to fiddle around with powers and dividing and multiplying and expanding and factoring in different ways and I just could not figure out how to get to the final step in the algebra. I knew that there must be a simple solution, the proof couldn't possibly be so long, so I felt pretty ridiculous. I went to office hours and asked about it and another student pointed out that ϕ to the power of 2 is just (ϕ - 1). I had no idea (I should have read the textbook more carefully, hah). Within three or four steps, the algebra resolved itself neatly and I had completed my proof. 

Similar things have happened to me in the past, especially while manipulating logs. I didn't take Calculus or Advanced Functions when I was in Grade 12 because I was not anticipating taking any  hard science courses in university - until I had a change of heart in third year and decided to switch from humanities to computer science.  By then, I hadn't taken any math courses in six years, and I had to take those Grade 12 credits in night school. I was out of practice with these things for many years, and I still haven't taken first-year Calculus, so these skills are still pretty rusty for me. This is probably why I have trouble with chains of inequalities, too. There is usually some kind of elegant solution that completely evades me.