Second Last Week Study

Second Last Week Study

      Time gone by, it is already the second last week. As I expected, this course is getting harder and harder. Especially chapter four and five. During this week, I am doing my assignment three questions, and I can feel that this assignment is much harder than the other two assignments which we did before. Based on this assignment, I found some problems that makes me confused.
      First of all, Big-O and another two bounds questions are really hard to prove. In my opinion, tutorial questions helps me to understand how to prove, but it is not enough to practice. During every tutorial, I listend to our TA and she explained how to do each questions really well, but the problem is that I only understand them at tutorial. For assignment, I have no idea that how to think and how to prove. I read my past blogs and try to find my way to solve problems, but it does not helps me that much. That would shows my understanding for this part is very poor. For example in assignment three, question one. My first time to think about it and I cannot figure out how to prove; and there are is an idea cross my mind that there are two ways to prove this problem, one is prove and the other one is disprove. But I know that is wrong, for a problem it cannot be both prove and disprove, but in some way I do think it would work. I may assume this as I did not understand questions and proves really well. And the rest question in this assignment also confused me. 
         Second of all, I can feel that time is limited so far, and material getting harder. That is how to end a semester, and I need to keep working hard. All I want to say is trust myself! I am busy and not really understand some questions, there must be some students who are same as me, so all I need to do is keep working, keep practicing. 
          All in all, read notes and do assignment, and then get ready for the final exam! 

Some Useful Idea for the Big-oh Study

Some Useful Idea for the Big-oh Study

     We are still working on chapter four during this week. Personally, I think this week’s tutorial is the most important thing for me to study the Big-oh problem, because our TA gave me some awesome ideas to study this part.

     The rough work really helps me to think. During our lecture, my way to remember how to do the Big-oh question is by using form “ Pick c =   pick B =    assume   ”. It is nice to start the working but I got stuck some time by stop at some steps. Usually, I would start with left hand side function after “ assume”. But the problem is with processing, I usually stuck at a step that cannot make me to connect to my proving, which is right hand side, and then I need to redo this problem. During this week’s tutorial, my TA showed us a really nice way to solve the Big-oh questions. I will explain this idea based on tutorial question one. “Write a detailed structured proof that 5n⁴ – 3n² + 1 belongs to O(6n⁵ – 4n³ +2n)”. In my early work, I was thinking that to make 5n⁴ – 3n² + 1 to match form 6n⁵ – 4n³ +2n by some ideas from lecture, which is 5n⁴ – 3n² + 1 < 5n⁴ – 3n² and then multiply n and try to get 6n⁵. But it is really hard to match; even I matched 6n⁵ but it still hard to match – 4n³. Thus I was stuck. Our TA gave me this idea to me, think the left hand side smaller or equal to something and from right hand side to match it too. In this question, the thing is n⁵. From left hand side, 5n⁴ – 3n² + 1 <= 5n⁴ + 1 <= 5n⁴ + n⁴ <= 6n⁴ <= n * n⁴ <= n⁵. Then we think right hand side, 6n⁵ – 4n³ +2n >= 6n⁵ – 4n³ >= 6n⁵ – 4n⁵ >= 2n⁵ >= n⁵. The happiness that this rough work gives to me is much more than solves a problem.

     In conclusion, the most important study for me in this week is the solving idea from my lovely TA. The way to solve a problem is understand what are you going to get to help you solve this problem.

How Did My Study Go This Week

How Did My Study Go This Week

      My apology first, due to some personal reason, I post my SLOG late for this week. For this week’s SLOG, I still want to talk about proves in Chapter three. In my opinion, proves is a hard part to learn, because students need to think how to prove something. Some statements are easy to understand and easy to figure out it is true or not. But the difficult part is how to prove.

At the beginning of the last chapter of this course, loop problems are really hard to understand too.

       First, I am still confused about prove by cases. According to lecture notes’ examples and some tutorial problems, we would do proves by cases. As my understanding, we use cases to prove “^” statements or “v” statements. For example, claim 3.4 from lecture notes: 

“ For all n in Z, there exist a k in Z, such that n² +n=2k.”

In this example, we need to consider n is odd or even, thus we need to use case one to prove n is odd and case two to prove n is even. This is not hard to understand. But question 6 in assignment two is confused me. My partner asked her TA, and she told me that we cannot use cases to prove this question and if we do use cases then we may get wrong. And after we handed in assignment two, professor posted full solutions for assignment on-line. Based on the solution, professor does not use cases to prove question number six. This makes me do not understand when should we use cases to prove and when we should not.

       Second, the loop problems makes me lost and do not know how to count. According to week 8’s lecture. We talked maximum problem. Under each while loops, I can understand that why some lines can be counted. But why the while loop under another while loop should be counted too? For example,

“while i < len(L):       (let us make it as line1, and named while loop1)

    j = i + 1

    while j <= len(L): “  (line3, while loop2)

As my understanding, line1 and line2 should be count as while loop1 then we start to count line3. But from lecture notes, line3 not only counts as while loop2 but also counts as LG for while loop1. I think that would be over counted. But it seems reasonable for count because while loop2 is under while loop1, which means while loop1 belongs to while loop2. I am always stuck here, on one hand, I cannot understand, but one the other hand, I can explain to myself by read lecture notes.

       It is true that we need to solve at least one question for our SLOG, but with studies going on, I think it is more important to ask questions. Solving a problem may not be hard, but from a question students could ask another question then it would be hard. And if those questions can be solved, then students are really understand materials from lectures and notes.

Problems in this week's Assignment and Tutorial Questions

     Problems in This Week's Assignment and Tutorial Questions

     We learned Big-oh problem in this week. It is a really hard topic to understand. I am still confusing about tutorial questions and some examples in class. For SLOG, we supposed to find questions and solve them, unfortunately, I think I found problems but cannot solve them.

     First of all, there are some proves in assignment 2, which my partner and me cannot solve them. I may use word ‘ explain’, instead of using word ‘ solve’. For example, question 2 in assignment two. We need to prove if for all nature number m and n, m < n, then there exist a nature number z, such that m < z < n. If we choose m = 1 < 2 = n, then the answer is obvious: there is no nature number between 1 and 2. The most important problem is how to prove there is no nature number. We came up with some ideas, but they do not work. We went to office hour, but we only asked question 6 in the assignment, because this the most confusing questions for us at that time and we thought that we can figure that out. Therefore, problems still there, and this makes me know that for later work, we need to ask early.

     Second, tutorial questions are hard for me to solve. Professor sent us this tutorial problems by email instead of post on website, that makes me find it and do it later than before. The problem is how to count while loop. After our TA explained to us, I was still confused. For while loop, we need to count “ i < len(L)” and “ j > 0 and L[1] < L[j - 1]”. But the solution that our TA gave us is using ‘ i’ to count. If using i then how about j? So counting loop is really hard for me to understand and deal with. Thus, I think that I need to do more questions and read course notes in order to learn how to solve this problem.

     In conclusion, questions are always there, if there is a question that I cannot solve then I need go to office hours and ask, then I could do well in final exam; if there is a question that I can solve by thinking deeply, then I need to remember that and learn how to solve. The only way to deal with problems is hard work.

My Way to Study Proves

My Way to Study Proves 

    This is the first week after reading week that we start the second half of this semester, and we had been done chapter 3 in this week. Proof is a hard part for me to study CSC165. We had already learned prove universally quantified and existential quantified, also we learned few ways to solve those questions. Based on those solving-ways, I am going to talk about my understanding about proof by practice and google search.

    First of all, practice how to prove statements by do some exercises and read course notes is really helpful for students to learn the way to solve same kind of statements. There is a great example, “ For all natural numbers n, if there is a natural number k such that n = 3k + 1, then there is a natural number j such that n² = 3j + 1”(the first question in Tutorial #5). During our lecture, professor had been given us a same kind of problems, which has different numbers. In other words, proof a statement by form “ if n = a number * k + a number then n² = a number * j + a number”, we did this kind of proof in class, in tutorial questions and in this week’s quiz. Therefore, I had been done this question four times. That makes me REALLY understand how to prove statement by this form. This is how does practice works. I may cannot solve some proves but after I do some similar proves then I know. Do more questions as practice is really helpful for proves.

    Second, google search is helpful for understand a kind of questions when there is nobody can help me. Living out side of campus makes me talk less with other students. Sometimes I spend a lot of time and I cannot figure out how to solve a proof, for example the assignment #2 question 5. Then I did some google search, and there are some similar questions that some people asked before and others answered them. This gives me idea how to solve one kind of problem. The most important point for solve proves is understand the way to solve one kind of proves. It is true that we can get wrong answers from google, but the aim is looking for the solving-way.

    In conclusion, do questions and google some proves are my way to study and they helped me a lot. I will keep this for the rest semester, hard work, good mark.