Week 8

Things get more complicated from this week. We learned the formal definitions of O(n²), Ω(n²) and θ(n²). The prof made an analogy of which compared O(n²) with the growing size of chicken and turkeys. This time, I get a better understanding of '700n^2 is no larger than 0.5n^2'. However, the challenging part is to calculate the steps that the maximum slice function takes in the worst case. There are so many while loops that I can hardly figure out the steps for each loop. And the proving part is easier after finding out the solutions to the problems. 
Another great challenge is the penny pile problem. After reading through the instruction, I can easily reach the number 48. However, the follow up question was much more difficult to solve. The number of possible ways to transfer the pennies are huge, and a tree diagram might be a good choice to visualize the problem.      

Week 7

   In this week, we finally finished proving stuff. Proving is actually not that hard as long as I understand the statement. The challenging part for me is the structure. I notice that sometimes my prooving steps are not complete. I often forget to introduce the quantifications and conclude in the end.
I also learned more proving techniques and rules. I find that proof by case is extremely helpful which provides a more easier method for proving. Introduction and elimination rules are also essential, which help me to reach my target statement faster and easier.
   A new unit was introduced this week as well--Algorithm Analysis and Asymptotic Notation, which sounds really computer scientific. We got an idea of how bubble sort and merge sort work through the experiment. It was interesting that the larger the input size is, the advantage of merge over bubble becomes bigger. On the other hand, it is quite odd that "0.5n²and 700n² are no different" according to my existing mathematic knowledge. And there might be more challenges to understand the asymptotic notations. I must pay much attention to the lecture in order to get a better understanding :)

Week 6

 The test was back before the lecture. Though my mark was above the class average, I still have to work harder. It was really regrettable that I forgot to indicate the negations for Q1 part(a) so I did not get 100%. But overall, this test encouraged me that the tests in University are not that difficult and I have the ability to do well; it also warned me to pay more attention to every questions and not to miss anything.
 The lecture this week was still about proves, and non-boolean functions were introduced. After this lecture, I feel comfortable about the structure of proving. I found that proving is quite easy when I understand the definition and get a basic idea of the methods of proving. I also learned how to disprove a statement, which was quite similar to proving a statement. I can just negate the statement and prove the negation is true.
 It seems that we will finish proving next week. I am excited about learning new stuff.

Week5

   The term test1 was in this week. Since this was the first test I had in university, I felt quite nervous and studied really hard for it. The test was similar to the past term test practices as I expected, but I still felt not very confident to this test. I spent lots of time figuring out the symbolic meanings of the first questions, and that caused a hurry for the rest of the questions. Time management is an extemely important to do well on a test, so I must practice more and manage my time more sufficiently.
   The lecture this week introduced more techniques for proving. I found that contradictions and contrapositives are very efficient techniques to prove an implication statement while proving from P to Q is difficult. Somehow I feel more confident about provings than those mathematics symbols, since the proving methods are straight forward and it is obvious to know whether I got the right answer.

Week4

In this week, things get more complicated. I feel not quite comfortable translating Bi-implications into combinations of conjunctions and disjunctions. It is even more confusing to use manipulation rules; for example: (¬P∨Q)∧(¬Q∨P) = [(¬P∨Q)∧¬Q]∨[(¬P∨Q)∧P] = [(¬P∧¬Q)∨(Q∧¬Q)]∨[(¬P∧P)∨(Q∧P)], it is not quite easy to follow this method, though they are similar to mathematical calculating rules. But I believe as I practice more, I will be more familiar with these laws and will feel comfortable using them. Finally, I finished all the mathematical expressions and symbols and started to learn the proof in this week. The proof in this course is quite different to the prooves in math. The format of proof is interesting that I can prove from the 2 different side. It is more sufficient to prove from the 'conclusion'; and such method makes the proof more creative. During the lecture, the 'folding' problem was a little challenging for me and my group members. At first we folded 4 times， it was difficult to figure out the pattern; then we compared this pattern with folding 3 times, twice, and once, we can see that the crease of folding once is always in the middle. Similar to that, we found the left side and right side were somehow related to each other. After the professor's explanation, we finally figured out the pattern. Such activities were really fun and engaging, and I am looking forward to have more activities during lectures.