I have just come back to school after taking over a year off, so things have taken a bit of getting used to again. The routine of studying, lectures, and assignments is still coming back quite steadily though. This is the first time that my course has required me to keep a blog, and this is the first time that I have ever had one too. And honestly this will take a bit of getting used to, but it seems like an interesting idea.
For the first month we have already had 1 assignment and 2 problem sets. The 2 problem sets were all quite interesting. For the first, I actually finished it without any problems. The problems were similar to the ones done in class(3^n and 4^n are basically the same proofwise, just need to consider different cases; and the second question about pairs of numbers was actually just the same as an example given in class about a new element being in every one of the original subsets of an original set.). Problem set 2 was quite simple as well since it was still about stamps just as the example given in class. The only difference being that the larger "base" values of the stamps meant a much higher minimum base case after which every other natural number could be created with the "base" values.
A1 was technically much more difficult than the problem sets, since there were no equivalent examples given in class, and I found the hints posted by professor Heap extremely helpful while still leaving all the prooving to us. The first question was fairly simple: just add pie radians whenever you add a point(can be prooven by showing the new point would "attach" a new triangle outside of the original polygon, thus adding pie radians to the total sum of interior angles). The second problem was also simple(especially with the profs hints), but I might not have given the right "program" for cycling the menues that the original question was looking for. I used randomness to cycle through every combination, instead of actually making a program to cycle through every possibility from C(0, n) meals to C(n, n) meals then back again. I found the third problem about the golden ratio to be a very intuitive way of prooving irrationals. I had some difficulty with part b at first, but after looking up some of the discussions on the bulletin board, I found how simple this problem really was.
On a special note, A1 was submitted as plain text, and I found it a little hard to get all the ideas into sentences without making it an enormous essay (I still had around 120 lines when I finished). Hope I did as well as I felt about it when I submitted it, or rather I hope the TA's will be able to understand my logic in English. This is probably one of the issues that I will have to pay the most attention to in the future(will need to pay closer attention to how professor Heap articulates his logic in class using words).
I know this is quite a long first post, and I will try to submit shorter ones every week in the future!
