Week Seven, Problem Set #4

Meh yea this problem set wasn't really much of a challenge and I think I managed to finish it about 20 minutes before class...and it seemed right so we'll see what I get.

Week Six, Problem Set #3

12/5/2008:Yeaaaa... So I actually did solve this problem set but didn't want to hand it in during the Thursday and also did not want to go to the Friday lecture, so I was -supposed- to give it a friend to hand in for me but ended up not wanting to as i passed by their dorm...so yea...didn't hand it in...but here it is anyways in all its glory minus the actual proof because I can't seem to find that any more (I think I did it by hand on paper somewhere?):

Week 5, Test 1

Yea so test #1 this week, haven't studied for it at all, will see how I end up doing :)

(12/5/2008 Edit: Ended up getting 17/24, not bad at all me thinks. I didn't find the test too difficult over all but I don't really remember enough to give any more of an indepth insight...)

Week 4, Assignment #1

This week we had the first assignment due, which I worked in conjunction with 2 other people. We each focused on one or two questions, and then helped explain the solutions for the others to the rest of the group - this seemed to work out well. 

I mostly focused on the 2nd question which was about the menu problem for the restaurant. The following is my work on the solution using the Polya approach:

1. Understanding the Problem:
   Try to come up with a method to design a menu which suits the constraints given, then prove that it works.
2. Devise a Plan:
   Start with the simpler menu example given and then to 3 items, and onwards, finally generalize to 2^n, and then prove.
3. Carry out the Plan:
   First, I started by creating each of the possible menus using the set of items {L, S} given that any 2 consecutive days must only differ by exactly one meal.
   
   I then extended this to a set of 3 meals, {1, 2, 3} and created a menu cycle where they all differed by only one day. And then once again for 4 meals. At this point my lazyness kicked in and I decided I no longer wanted to write any more meal menus. So I began looking for patterns and realized that the menus, when extended for any n+1 could be represented recursively based on its previous element n. That is,
   
   n+1 = n + [\reverse(n) with the (n+1)th element added to each element in \reverse(n)]After some further testing (I actually ended up doing 5 meals...meh) it seemed to me that this was correct enough, so I wrote out the proof and that's what was handed in.
4. Looking Back:
   Looking back, the solution still seems correct in my mind however I'm not absolutely sure if the format in which I showed my proof is correct. So will have to wait for the assignment to be handed back before I can see the result....
   

1.