4th week journal

The materials are getting harder and harder. This week, we learnt mixed quantifiers, bi-implication, transitivity and the basic proofs. From mixed quantifiers, I knew that the domain of a set is really important. The order of the quantifiers matter a lot, when there are a combination of universal quantifiers and existential quantifiers. For transitivity, this is important for proofs. Same as math, if a>b and b>c, then a>c. For proofs, we learnt the format for writing the proofs, and the starting steps when we first see a proof.

The proofs seem troubles me a lot, because I didn’t understand the example that was given out in the lecture today. I will try to understand it or ask it through piazza. Other than the new materials, we finished our first assignment. This assignment is harder than I thought it would be. Because I studied the materials before doing the assignment and I thought I understood everything. However, when I was doing the assignment with my group, I found that I didn’t know the materials that well. Especially when it comes to venn diagram and the existential statement. I will focus more on these materials while I am studying for my term test.  After doing this assignment, I found myself have a better picture of how everything we learnt links to each other. Doing the assignment in a group is better than doing it individually, since everyone will give out their own opinions and discuss. This is more interactive and I learnt a lot from my group mates. 

We also did a problem solving problem in class this week. It is called folding. We first need to understand the problem. So the purpose for this problem is to predict the sequence of ups and downs for any number of times that we carry out the folding operation. The ups and downs were accounting the creases point vertex up or down. Second, we devised a plan. We decided that one of people would do the folding and the other two would do the recording, so that we could compare our records and avoid mistakes. From our knowledge, we know that the paper can be only folded 5 times. Then we started doing the folding after all the planning. The first 4 could be easily read, but when we folded the paper the 5th time, the ups and downs are hard to distinguish and we checked it over and over again. After we got all the data, we started finding the pattern, since we could not fold the paper again. First, we counted the total number of each fold. The total numbers of ups and downs are 1, 3, 7, 15, 31 accordingly. And we found that the total number of each fold was different by 2 to the n powers. Then we were stuck when finding the patterns of ups and downs. Danny then told us to flip over the paper to look at the hints. After looking at the hint 1, asking that ' is one pattern somehow 'contained' in the other, we suddenly realized that the 2nd fold actually contained the sequence of 1st fold, and the 3rd fold contained the sequence of 2nd fold as its last portion of sequence, and so on. After looking at the second hint, suggesting that we could organize the fold patterns symmetrically. We looked back and carefully rewrite the patterns symmetrically. We finally found the pattern! This was actually a fun problem and following the problem solving steps made the thinking process more organized and clear.